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  • 51.
    Gu, Xuan
    et al.
    Linköping University, Department of Biomedical Engineering, Division of Biomedical Engineering. Linköping University, Faculty of Science & Engineering. Linköping University, Center for Medical Image Science and Visualization (CMIV).
    Sidén, Per
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Science & Engineering.
    Wegmann, Bertil
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Science & Engineering.
    Eklund, Anders
    Linköping University, Department of Biomedical Engineering, Division of Biomedical Engineering. Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Science & Engineering. Linköping University, Center for Medical Image Science and Visualization (CMIV).
    Villani, Mattias
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Science & Engineering.
    Knutsson, Hans
    Linköping University, Department of Biomedical Engineering, Division of Biomedical Engineering. Linköping University, Faculty of Science & Engineering. Linköping University, Center for Medical Image Science and Visualization (CMIV).
    Bayesian Diffusion Tensor Estimation with Spatial Priors2017In: CAIP 2017: Computer Analysis of Images and Patterns, 2017, Vol. 10424, p. 372-383Conference paper (Refereed)
    Abstract [en]

    Spatial regularization is a technique that exploits the dependence between nearby regions to locally pool data, with the effect of reducing noise and implicitly smoothing the data. Most of the currently proposed methods are focused on minimizing a cost function, during which the regularization parameter must be tuned in order to find the optimal solution. We propose a fast Markov chain Monte Carlo (MCMC) method for diffusion tensor estimation, for both 2D and 3D priors data. The regularization parameter is jointly with the tensor using MCMC. We compare FA (fractional anisotropy) maps for various b-values using three diffusion tensor estimation methods: least-squares and MCMC with and without spatial priors. Coefficient of variation (CV) is calculated to measure the uncertainty of the FA maps calculated from the MCMC samples, and our results show that the MCMC algorithm with spatial priors provides a denoising effect and reduces the uncertainty of the MCMC samples.

  • 52.
    Hammi, Malik
    et al.
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning.
    Akdeve, Ahmet Hakan
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning.
    Poweranalys: bestämmelse av urvalsstorlek genom linjära mixade modeller och ANOVA2018Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    In research where experiments on humans and animals is performed, it is in advance important to determine how many observations that is needed in a study to detect any effects in groups and to save time and costs. This could be examined by power analysis, in order to determine a sample size which is enough to detect any effects in a study, a so called “power”. Power is the probability to reject the null hypothesis when the null hypothesis is false.

    Mälardalen University and the Caroline Institute have in cooperation, formed a study (The Climate Friendly and Ecological Food on Microbiota) based on individual’s dietary intake. Every single individual have been assigned to a specific diet during 8 weeks, with the purpose to examine whether emissions of carbon dioxide, CO2, differs reliant to the specific diet each individuals follows. There are two groups, one treatment and one control group. Individuals assigned to the treatment group are supposed to follow a climatarian diet while the individuals in the control group follows a conventional diet. Each individual have been followed up during 8 weeks in total, with three different measurements occasions, 4 weeks apart. The different measurements are Baseline assessment, Midline assessment and End assessment.

    In the CLEAR-study there are a total of 18 individuals, with 9 individuals in each group. The amount of individuals are not enough to reach any statistical significance in a test and therefore the sample size shall be examined through power analysis. In terms of, data, every individual have three different measurements occasions that needs to be modeled through mixed-design ANOVA and linear mixed models. These two methods takes into account, each individual’s different measurements. The models which describes data are applied in the computations of sample sizes and power. All the analysis are done in the programming language R with means and standard deviations from the study and the models as a base.

    Sample sizes and power have been computed for two different linear mixed models and one ANOVA model. The linear mixed models required less individuals than ANOVA in terms of a desired power of 80 percent. 24 individuals in total were required by the linear mixed model that had the factors group, time, id and the covariate sex. 42 individuals were required by ANOVA that includes the variables id, group and time.

  • 53.
    Hedman, Anna
    et al.
    Karolinska Inst, Sweden.
    Breithaupt, Lauren
    Karolinska Inst, Sweden; George Mason Univ, VA 22030 USA.
    Hubel, Christopher
    Karolinska Inst, Sweden; Kings Coll London, England.
    Thornton, Laura M.
    Univ N Carolina, NC 27599 USA.
    Tillander, Annika
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Arts and Sciences. Karolinska Inst, Sweden.
    Norring, Claes
    Karolinska Inst, Sweden; Stockholm Cty Council, Sweden.
    Birgegard, Andreas
    Karolinska Inst, Sweden; Stockholm Cty Council, Sweden.
    Larsson, Henrik
    Karolinska Inst, Sweden; Orebro Univ, Sweden.
    Ludvigsson, Jonas F.
    Karolinska Inst, Sweden; Orebro Univ Hosp, Sweden.
    Savendahl, Lars
    Karolinska Inst, Sweden.
    Almqvist, Catarina
    Karolinska Inst, Sweden; Karolinska Univ Hosp, Sweden.
    Bulik, Cynthia M.
    Karolinska Inst, Sweden; Univ N Carolina, NC 27599 USA; Univ N Carolina, NC 27515 USA.
    Bidirectional relationship between eating disorders and autoimmune diseases2019In: Journal of Child Psychology and Psychiatry and Allied Disciplines, ISSN 0021-9630, E-ISSN 1469-7610, Vol. 60, no 7, p. 803-812Article in journal (Refereed)
    Abstract [en]

    Background Immune system dysfunction may be associated with eating disorders (ED) and could have implications for detection, risk assessment, and treatment of both autoimmune diseases and EDs. However, questions regarding the nature of the relationship between these two disease entities remain. We evaluated the strength of associations for the bidirectional relationships between EDs and autoimmune diseases. Methods In this nationwide population-based study, Swedish registers were linked to establish a cohort of more than 2.5 million individuals born in Sweden between January 1, 1979 and December 31, 2005 and followed up until December 2013. Cox proportional hazard regression models were used to investigate: (a) subsequent risk of EDs in individuals with autoimmune diseases; and (b) subsequent risk of autoimmune diseases in individuals with EDs. Results We observed a strong, bidirectional relationship between the two illness classes indicating that diagnosis in one illness class increased the risk of the other. In women, the diagnoses of autoimmune disease increased subsequent hazards of anorexia nervosa (AN), bulimia nervosa (BN), and other eating disorders (OED). Similarly, AN, BN, and OED increased subsequent hazards of autoimmune diseases.Gastrointestinal-related autoimmune diseases such as, celiac disease and Crohns disease showed a bidirectional relationship with AN and OED. Psoriasis showed a bidirectional relationship with OED. The previous occurence of type 1 diabetes increased the risk for AN, BN, and OED. In men, we did not observe a bidirectional pattern, but prior autoimmune arthritis increased the risk for OED. Conclusions The interactions between EDs and autoimmune diseases support the previously reported associations. The bidirectional risk pattern observed in women suggests either a shared mechanism or a third mediating variable contributing to the association of these illnesses.

  • 54.
    Herwin, Eric
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning.
    Optimizing process parameters to increase the quality of the output in a separator: An application of Deep Kernel Learning in combination with the Basin-hopping optimizer2019Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    Achieving optimal efficiency of production in the industrial sector is a process that is continuously under development. In several industrial installations separators, produced by Alfa Laval, may be found, and therefore it is of interest to make these separators operate more efficiently. The separator that is investigated separates impurities and water from crude oil. The separation performance is partially affected by the settings of process parameters. In this thesis it is investigated whether optimal or near optimal process parametersettings, which minimize the water content in the output, can be obtained.Furthermore, it is also investigated if these settings of a session can be testedto conclude about their suitability for the separator. The data that is usedin this investigation originates from sensors of a factory-installed separator.It consists of five variables which are related to the water content in theoutput. Two additional variables, related to time, are created to enforce thisrelationship. Using this data, optimal or near optimal process parameter settings may be found with an optimization technique. For this procedure, a Gaussian Process with the Deep Kernel Learning extension (GP-DKL) is used to model the relationship between the water content and the sensor data. Three models with different kernel functions are evaluated and the GP-DKL with a Spectral Mixture kernel is demonstrated to be the most suitable option. This combination is used as the objective function in a Basin-hopping optimizer, resulting in settings which correspond to a lower water content.Thus, it is concluded that optimal or near optimal settings can be obtained. Furthermore, the process parameter settings of a session can be tested by utilizing the Bayesian properties of the GP-DKL model. However, due to large posterior variance of the model, it can not be determined if the process parameter settings are suitable for the separator.

  • 55.
    Holm, Rasmus
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning.
    Prediction of Inter-Frequency Measurements in a LTE Network with Deep Learning2018Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    The telecommunications industry faces difficult challenges as more and more devices communicate over the internet. A telecommunications network is a complex system with many parts and some are candidates for further automation. We have focused on interfrequency measurements that are used during inter-frequency handovers, among other procedures. A handover is the procedure when for instance a phone changes the base station it communicates with and the inter-frequency measurements are rather expensive to perform.

    More specifically, we have investigated the possibility of using deep learning—an ever expanding field in machine learning—for predicting inter-frequency measurements in a Long Term Evolution (LTE) network. We have focused on the multi-layer perceptron and extended it with (variational) autoencoders or modified it through dropout such that it approximate the predictive distribution of a Gaussian process.

    The telecommunications network consist of many cells and each cell gather its own data. One of the strengths of deep learning models is that they usually increase their performance as more and more data is used. We have investigated whether we do see an increase in performance if we combine data from multiple cells and the results show that this is not necessarily the case. The performances are comparable between models trained on combined data from multiple cells and models trained on data from individual cells. We can expect the multi-layer perceptron to perform better than a linear regression model.

    The best performing multi-layer perceptron architectures have been rather shallow, 1-2 hidden layers, and the extensions/modifications we have used/done have not shown any significant improvements to warrant their presence.

    For the particular LTE network we have worked with we would recommend to use shallow multi-layer perceptron architectures as far as deep learning models are concerned.

  • 56.
    Hosini, Rebin
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning.
    Detection of high-risk shops in e- commerce2018Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
  • 57.
    Hudson, Joshua
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning.
    A Partially Observable Markov Decision Process for Breast Cancer Screening2019Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    In the US, breast cancer is one of the most common forms of cancer and the most lethal. There are many decisions that must be made by the doctor and/or the patient when dealing with a potential breast cancer. Many of these decisions are made under uncertainty, whether it is the uncertainty related to the progression of the patient's health, or that related to the accuracy of the doctor's tests. Each possible action under consideration can have positive effects, such as a surgery successfully removing a tumour, and negative effects: a post-surgery infection for example. The human mind simply cannot take into account all the variables involved and possible outcomes when making these decisions. In this report, a detailed Partially Observable Markov Decision Process (POMDP) for breast cancer screening decisions is presented. It includes 151 states, covering 144 different cancer states, and 2 competing screening methods. The necessary parameters were first set up using relevant medical literature and a patient history simulator. Then the POMDP was solved optimally for an infinite horizon, using the Perseus algorithm. The resulting policy provided several recommendations for breast cancer screening. The results indicated that clinical breast examinations are important for screening younger women. Regarding the decision to operate on a woman with breast cancer, the policy showed that invasive cancers with either a tumour size above 1.5 cm or which are in metastasis, should be surgically removed as soon as possible. However, the policy also recommended that patients who are certain to be healthy should have a breast biopsy. The cause of this error was explored further and the conclusion was reached that a finite horizon may be more appropriate for this application.

  • 58.
    Izquierdo, Milagros
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Johansson, KarinLinköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Science & Engineering.
    Meeting of the Catalan, Spanish, Swedish Math Societies (CAT‐SP‐SW‐MATH)2017Conference proceedings (editor) (Other academic)
    Abstract [en]

    A joint Meeting of the Catalan, Spanish, Swedish Math Societies (CAT-SP-SW-MATH) will be held in Umeå (Sweden) from 12th to 15th June 2017.

    The meeting is a symposium devoted to mathematics at large.

    The conference is thought as a meeting point between the different areas of mathematics and its applications.

    The programme will consist of several plenary lectures, covering a wide range of areas of mathematics, and special sessions devoted to a single topic or area of mathematics.

    The venue of the conference will be the Department of Mathematics and Mathematical Statistics of Umeå University.

    Welcome!

    Milagros Izquierdo (Svenska matematikersamfundet)

    Xavier Jarque (Societat Catalana de Matemàtiques)

    Francisco José Marcellán (Real Sociedad Matemática Española)

  • 59.
    Jacob, Pierre E.
    et al.
    Harvard Univ, MA 02138 USA.
    Lindsten, Fredrik
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Science & Engineering.
    Schön, Thomas B.
    Uppsala Univ, Sweden.
    Smoothing With Couplings of Conditional Particle Filters2019In: Journal of the American Statistical Association, ISSN 0162-1459, E-ISSN 1537-274XArticle in journal (Refereed)
    Abstract [en]

    In state-space models, smoothing refers to the task of estimating a latent stochastic process given noisy measurements related to the process. We propose an unbiased estimator of smoothing expectations. The lack-of-bias property has methodological benefits: independent estimators can be generated in parallel, and CI can be constructed from the central limit theorem to quantify the approximation error. To design unbiased estimators, we combine a generic debiasing technique for Markov chains, with a Markov chain Monte Carlo algorithm for smoothing. The resulting procedure is widely applicable and we show in numerical experiments that the removal of the bias comes at a manageable increase in variance. We establish the validity of the proposed estimators under mild assumptions. Numerical experiments are provided on toy models, including a setting of highly informative observations, and for a realistic Lotka-Volterra model with an intractable transition density. Supplementary materials for this article are available online.

    The full text will be freely available from 2020-04-30 15:48
  • 60.
    Jesperson, Sara
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning.
    Defining and predicting fast-selling clothing options2019Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    This thesis aims to find a definition of fast-selling clothing options and to find a way to predict them using only a few weeks of sale data as input. The data used for this project contain daily sales and intake quantity for seasonal options, with sale start 2016-2018, provided by the department store chain Åhléns.

    A definition is found to describe fast-selling clothing options as those having sold a certain percentage of their intake after a fixed number of days. An alternative definition based on cluster affiliation is proven less effective.

    Two predictive models are tested, the first one being a probabilistic classifier and the second one being a k-nearest neighbor classifier, using the Euclidean distance. The probabilistic model is divided into three steps: transformation, clustering, and classification. The time series are transformed with B-splines to reduce dimensionality, where each time series is represented by a vector with its length and B-spline coefficients. As a tool to improve the quality of the predictions, the B-spline vectors are clustered with a Gaussian mixture model where every cluster is assigned one of the two labels fast-selling or ordinary, thus dividing the clusters into disjoint sets: one containing fast-selling clusters and the other containing ordinary clusters. Lastly, the time series to be predicted are assumed to be Laplace distributed around a B-spline and using the probability distributions provided by the clustering, the posterior probability for each class is used to classify the new observations.

    In the transformation step, the number of knots for the B-splines are evaluated with cross-validation and the Gaussian mixture models, from the clustering step, are evaluated with the Bayesian information criterion, BIC. The predictive performance of both classifiers is evaluated with accuracy, precision, and recall. The probabilistic model outperforms the k-nearest neighbor model with considerably higher values of accuracy, precision, and recall. The performance of each model is improved by using more data to make the predictions, most prominently with the probabilistic model.

  • 61.
    Jesperson, Sara
    et al.
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning.
    Johansson, Sara
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning.
    Mönster som leder till sjukfrånvaro: Sekvensanalys på longitudinella data2017Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    Absence due to sickness results in a cost to both employers and employees. For an unnamed wholesaler this is a problem at one of their warehouses, where the rate of sick leave is high. The aim of this thesis is to identify interesting patterns over time that lead to sick leave by analyzing data from the company's payroll system and their attendance system.

    The data is longitudinal and to detect the patterns that lead to sick leave, sequence analysis is used. To generate the sequential patterns the algorithm cSPADE is used since it allows time constraints to be specified for the sequences. The relevance of the generated sequences is evaluated with three interest measures: support, confidence and lift.

    Three separate analyses are performed where different variables are used, depending on whether they change over time or have a constant value, and for these analyses the data is aggregated weekly. The most common events that lead to sick leave for the employees are different duration of employment, gender and birth year. A few days sick leave during a week, namely between 8 and 40 hours, is more common among the employees compared to shorter and longer sick leave. It can be noted that the pattern of previous sick leave usually leads to continued sick leave.

    The thesis also highlights the problems that arise in sequence analysis, for example that the constant variables overshadow the non-constant variables in the resulting sequences. This happens when variables that change over time are used in combination with variables that have a constant value, which may occur in longitudinal data.

  • 62.
    Jonsson, Fredrik
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning.
    On the Construction of an Automatic Traffic Sign Recognition System2017Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    This thesis proposes an automatic road sign recognition system, including all steps from the initial detection of road signs from a digital image to the final recognition step that determines the class of the sign.

    We develop a Bayesian approach for image segmentation in the detection step using colour information in the HSV (Hue, Saturation and Value) colour space. The image segmentation uses a probability model which is constructed based on manually extracted data on colours of road signs collected from real images. We show how the colour data is fitted using mixture multivariate normal distributions, where for the case of parameter estimation Gibbs sampling is used. The fitted models are then used to find the (posterior) probability of a pixel colour to belong to a road sign using the Bayesian approach. Following the image segmentation, regions of interest (ROIs) are detected by using the Maximally Stable Extremal Region (MSER) algorithm, followed by classification of the ROIs using a cascade of classifiers.

    Synthetic images are used in training of the classifiers, by applying various random distortions to a set of template images constituting most road signs in Sweden, and we demonstrate that the construction of such synthetic images provides satisfactory recognition rates. We focus on a large set of the signs on the Swedish road network, including almost 200 road signs. We use classification models such as the Support Vector Machine (SVM), and Random Forest (RF), where for features we use Histogram of Oriented Gradients (HOG).

  • 63.
    Karlsson, Henrik
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning.
    Uplift Modeling: Identifying Optimal Treatment Group Allocation and Whom to Contact to Maximize Return on Investment2019Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    This report investigates the possibilities to model the causal effect of treatment within the insurance domain to increase return on investment of sales through telemarketing. In order to capture the causal effect, two or more subgroups are required where one group receives control treatment. Two different uplift models model the causal effect of treatment, Class Transformation Method, and Modeling Uplift Directly with Random Forests. Both methods are evaluated by the Qini curve and the Qini coefficient. To model the causal effect of treatment, the comparison with a control group is a necessity. The report attempts to find the optimal treatment group allocation in order to maximize the precision in the difference between the treatment group and the control group. Further, the report provides a rule of thumb that ensure that the control group is of sufficient size to be able to model the causal effect. If has provided the data material used to model uplift and it consists of approximately 630000 customer interactions and 60 features. The total uplift in the data set, the difference in purchase rate between the treatment group and control group, is approximately 3%. Uplift by random forest with a Euclidean distance splitting criterion that tries to maximize the distributional divergence between treatment group and control group performs best, which captures 15% of the theoretical best model. The same model manages to capture 77% of the total amount of purchases in the treatment group by only giving treatment to half of the treatment group. With the purchase rates in the data set, the optimal treatment group allocation is approximately 58%-70%, but the study could be performed with as much as approximately 97%treatment group allocation.

  • 64.
    Klasson Svensson, Emil
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning.
    Automatic Identification of Duplicates in Literature in Multiple Languages2018Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    As the the amount of books available online the sizes of each these collections are at the same pace growing larger and more commonly in multiple languages. Many of these cor- pora contain duplicates in form of various editions or translations of books. The task of finding these duplicates is usually done manually but with the growing sizes making it time consuming and demanding. The thesis set out to find a method in the field of Text Mining and Natural Language Processing that can automatize the process of manually identifying these duplicates in a corpora mainly consisting of fiction in multiple languages provided by Storytel.

    The problem was approached using three different methods to compute distance measures between books. The first approach was comparing titles of the books using the Levenstein- distance. The second approach used extracting entities from each book using Named En- tity Recognition and represented them using tf-idf and cosine dissimilarity to compute distances. The third approach was using a Polylingual Topic Model to estimate the books distribution of topics and compare them using Jensen Shannon Distance. In order to es- timate the parameters of the Polylingual Topic Model 8000 books were translated from Swedish to English using Apache Joshua a statistical machine translation system. For each method every book written by an author was pairwise tested using a hypothesis test where the null hypothesis was that the two books compared is not an edition or translation of the others. Since there is no known distribution to assume as the null distribution for each book a null distribution was estimated using distance measures of books not written by the author. The methods were evaluated on two different sets of manually labeled data made by the author of the thesis. One randomly sampled using one-stage cluster sampling and one consisting of books from authors that the corpus provider prior to the thesis be considered more difficult to label using automated techniques.

    Of the three methods the Title Matching was the method that performed best in terms of accuracy and precision based of the sampled data. The entity matching approach was the method with the lowest accuracy and precision but with a almost constant recall at around 50 %. It was concluded that there seems to be a set of duplicates that are clearly distin- guished from the estimated null-distributions, with a higher significance level a better pre- cision and accuracy could have been made with a similar recall for the specific method. For topic matching the result was worse than the title matching and when studied the es- timated model was not able to create quality topics the cause of multiple factors. It was concluded that further research is needed for the topic matching approach. None of the three methods were deemed be complete solutions to automatize detection of book duplicates.

  • 65.
    Lindgren, Petter
    et al.
    Department of Biological Agents, Division of CBRN Defence and Security, Swedish Defence Research Agency (FOI), Uemå, Sweden.
    Myrtennäs, Kerstin
    Department of Biological Agents, Division of CBRN Defence and Security, Swedish Defence Research Agency (FOI), Umeå, Sweden..
    Forsman, Mats
    Department of Biological Agents, Division of CBRN Defence and Security, Swedish Defence Research Agency (FOI), Umeå, Sweden.
    Johansson, Anders
    Department of Clinical Microbiology and Molecular Infection Medicine Sweden (MIMS), Umeå University, Sweden.
    Stenberg, Per
    Department of Biological Agents, Division of CBRN Defence and Security, Swedish Defence Research Agency (FOI), Umeå, Sweden and Department of Ecology and Environmental Science (EMG), Umeå University, Sweden.
    Nordgaard, Anders
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Arts and Sciences. Swedish Police Auhtority, National Forensic Centre (NFC).
    Ahlinder, Jon
    Department of Biological Agents, Division of CBRN Defence and Security, Swedish Defence Research Agency (FOI), Umeå, Sweden.
    A likelihood ratio-based approach for improved source attribution in microbiological forensic investigations2019In: Forensic Science International, ISSN 0379-0738, E-ISSN 1872-6283, Forensic Science International, ISSN 0379-0738, Vol. 302, article id 109869Article in journal (Refereed)
    Abstract [en]

    A common objective in microbial forensic investigations is to identify the origin of a recovered pathogenic bacterium by DNA sequencing. However, there is currently no consensus about how degrees of belief in such origin hypotheses should be quantified, interpreted, and communicated to wider audiences. To fill this gap, we have developed a concept based on calculating probabilistic evidential values for microbial forensic hypotheses. The likelihood-ratio method underpinning this concept is widely used in other forensic fields, such as human DNA matching, where results are readily interpretable and have been successfully communicated in juridical hearings. The concept was applied to two case scenarios of interest in microbial forensics: (1) identifying source cultures among series of very similar cultures generated by parallel serial passage of the Tier 1 pathogen Francisella tularensis, and (2) finding the production facilities of strains isolated in a real disease outbreak caused by the human pathogen Listeria monocytogenes. Evidence values for the studied hypotheses were computed based on signatures derived from whole genome sequencing data, including deep-sequenced low-frequency variants and structural variants such as duplications and deletions acquired during serial passages. In the F. tularensis case study, we were able to correctly assign fictive evidence samples to the correct culture batches of origin on the basis of structural variant data. By setting up relevant hypotheses and using data on cultivated batch sources to define the reference populations under each hypothesis, evidential values could be calculated. The results show that extremely similar strains can be separated on the basis of amplified mutational patterns identified by high-throughput sequencing. In the L. monocytogenes scenario, analyses of whole genome sequence data conclusively assigned the clinical samples to specific sources of origin, and conclusions were formulated to facilitate communication of the findings. Taken together, these findings demonstrate the potential of using bacterial whole genome sequencing data, including data on both low frequency SNP signatures and structural variants, to calculate evidence values that facilitate interpretation and communication of the results. The concept could be applied in diverse scenarios, including both epidemiological and forensic source tracking of bacterial infectious disease outbreaks.

  • 66.
    Maghsadhagh, Sevil
    et al.
    independent researcher, Vienna, Austria.
    Eklund, Anders
    Linköping University, Department of Biomedical Engineering, Division of Biomedical Engineering. Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Science & Engineering. Linköping University, Center for Medical Image Science and Visualization (CMIV).
    Behjat, Hamid
    Department of Biomedical Engineering, Lund University, Lund, Sweden.
    Graph Spectral Characterization of Brain Cortical Morphology2019Conference paper (Refereed)
    Abstract [en]

    The human brain cortical layer has a convoluted morphology that is unique to each individual. Characterization of the cortical morphology is necessary in longitudinal studies of structural brain change, as well as in discriminating individuals in health and disease. A method for encoding the cortical morphology in the form of a graph is presented. The design of graphs that encode the global cerebral hemisphere cortices as well as localized cortical regions is proposed. Spectral metrics derived from these graphs are then studied and proposed as descriptors of cortical morphology. As proof-of-concept of their applicability in characterizing cortical morphology, the metrics are studied in the context of hemispheric asymmetry as well as gender dependent discrimination of cortical morphology.

  • 67.
    Magnusson, Måns
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Arts and Sciences.
    Scalable and Efficient Probabilistic Topic Model Inference for Textual Data2018Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    Probabilistic topic models have proven to be an extremely versatile class of mixed-membership models for discovering the thematic structure of text collections. There are many possible applications, covering a broad range of areas of study: technology, natural science, social science and the humanities.

    In this thesis, a new efficient parallel Markov Chain Monte Carlo inference algorithm is proposed for Bayesian inference in large topic models. The proposed methods scale well with the corpus size and can be used for other probabilistic topic models and other natural language processing applications. The proposed methods are fast, efficient, scalable, and will converge to the true posterior distribution.

    In addition, in this thesis a supervised topic model for high-dimensional text classification is also proposed, with emphasis on interpretable document prediction using the horseshoe shrinkage prior in supervised topic models.

    Finally, we develop a model and inference algorithm that can model agenda and framing of political speeches over time with a priori defined topics. We apply the approach to analyze the evolution of immigration discourse in the Swedish parliament by combining theory from political science and communication science with a probabilistic topic model.

    List of papers
    1. Sparse Partially Collapsed MCMC for Parallel Inference in Topic Models
    Open this publication in new window or tab >>Sparse Partially Collapsed MCMC for Parallel Inference in Topic Models
    2018 (English)In: Journal of Computational And Graphical Statistics, ISSN 1061-8600, E-ISSN 1537-2715, Vol. 27, no 2, p. 449-463Article in journal (Refereed) Published
    Abstract [en]

    Topic models, and more specifically the class of Latent Dirichlet Allocation (LDA), are widely used for probabilistic modeling of text. MCMC sampling from the posterior distribution is typically performed using a collapsed Gibbs sampler. We propose a parallel sparse partially collapsed Gibbs sampler and compare its speed and efficiency to state-of-the-art samplers for topic models on five well-known text corpora of differing sizes and properties. In particular, we propose and compare two different strategies for sampling the parameter block with latent topic indicators. The experiments show that the increase in statistical inefficiency from only partial collapsing is smaller than commonly assumed, and can be more than compensated by the speedup from parallelization and sparsity on larger corpora. We also prove that the partially collapsed samplers scale well with the size of the corpus. The proposed algorithm is fast, efficient, exact, and can be used in more modeling situations than the ordinary collapsed sampler.

    Place, publisher, year, edition, pages
    Taylor & Francis, 2018
    Keywords
    Bayesian inference, Gibbs sampling, Latent Dirichlet Allocation, Massive Data Sets, Parallel Computing, Computational complexity
    National Category
    Probability Theory and Statistics
    Identifiers
    urn:nbn:se:liu:diva-140872 (URN)10.1080/10618600.2017.1366913 (DOI)000435688200018 ()
    Funder
    Swedish Foundation for Strategic Research , SSFRIT 15-0097
    Available from: 2017-09-13 Created: 2017-09-13 Last updated: 2018-07-20Bibliographically approved
    2. Automatic Localization of Bugs to Faulty Components in Large Scale Software Systems using Bayesian Classification
    Open this publication in new window or tab >>Automatic Localization of Bugs to Faulty Components in Large Scale Software Systems using Bayesian Classification
    Show others...
    2016 (English)In: 2016 IEEE INTERNATIONAL CONFERENCE ON SOFTWARE QUALITY, RELIABILITY AND SECURITY (QRS 2016), IEEE , 2016, p. 425-432Conference paper, Published paper (Refereed)
    Abstract [en]

    We suggest a Bayesian approach to the problem of reducing bug turnaround time in large software development organizations. Our approach is to use classification to predict where bugs are located in components. This classification is a form of automatic fault localization (AFL) at the component level. The approach only relies on historical bug reports and does not require detailed analysis of source code or detailed test runs. Our approach addresses two problems identified in user studies of AFL tools. The first problem concerns the trust in which the user can put in the results of the tool. The second problem concerns understanding how the results were computed. The proposed model quantifies the uncertainty in its predictions and all estimated model parameters. Additionally, the output of the model explains why a result was suggested. We evaluate the approach on more than 50000 bugs.

    Place, publisher, year, edition, pages
    IEEE, 2016
    Keywords
    Machine Learning; Fault Detection; Fault Location; Software Maintenance; Software Debugging; Software Engineering
    National Category
    Computer Sciences
    Identifiers
    urn:nbn:se:liu:diva-132879 (URN)10.1109/QRS.2016.54 (DOI)000386751700044 ()978-1-5090-4127-5 (ISBN)
    Conference
    IEEE International Conference on Software Quality, Reliability and Security (QRS)
    Available from: 2016-12-06 Created: 2016-11-30 Last updated: 2018-05-17
    3. Pulling Out the Stops: Rethinking Stopword Removal for Topic Models
    Open this publication in new window or tab >>Pulling Out the Stops: Rethinking Stopword Removal for Topic Models
    2017 (English)In: 15th Conference of the European Chapter of the Association for Computational Linguistics: Proceedings of Conference, volume 2: Short Papers, Stroudsburg: Association for Computational Linguistics (ACL) , 2017, Vol. 2, p. 432-436Conference paper, Published paper (Other academic)
    Abstract [en]

    It is often assumed that topic models benefit from the use of a manually curated stopword list. Constructing this list is time-consuming and often subject to user judgments about what kinds of words are important to the model and the application. Although stopword removal clearly affects which word types appear as most probable terms in topics, we argue that this improvement is superficial, and that topic inference benefits little from the practice of removing stopwords beyond very frequent terms. Removing corpus-specific stopwords after model inference is more transparent and produces similar results to removing those words prior to inference.

    Place, publisher, year, edition, pages
    Stroudsburg: Association for Computational Linguistics (ACL), 2017
    National Category
    Probability Theory and Statistics General Language Studies and Linguistics Specific Languages
    Identifiers
    urn:nbn:se:liu:diva-147612 (URN)9781945626357 (ISBN)
    Conference
    15th Conference of the European Chapter of the Association for Computational Linguistics Proceedings of Conference, volume 2: Short Papers April 3-7, 2017, Valencia, Spain
    Available from: 2018-04-27 Created: 2018-04-27 Last updated: 2018-04-27Bibliographically approved
  • 68.
    Magnusson, Måns
    et al.
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Arts and Sciences. Aalto University, Espoo, Finland.
    Jonsson, Leif
    Ericsson AB, Stockholm, Sweden.
    Villani, Mattias
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Arts and Sciences. Stockholm University, Stockholm, Sweden.
    DOLDA: a regularized supervised topic model for high-dimensional multi-class regression2019In: Computational statistics (Zeitschrift), ISSN 0943-4062, E-ISSN 1613-9658Article in journal (Refereed)
    Abstract [en]

    Generating user interpretable multi-class predictions in data-rich environments with many classes and explanatory covariates is a daunting task. We introduce Diagonal Orthant Latent Dirichlet Allocation (DOLDA), a supervised topic model for multi-class classification that can handle many classes as well as many covariates. To handle many classes we use the recently proposed Diagonal Orthant probit model (Johndrow et al., in: Proceedings of the sixteenth international conference on artificial intelligence and statistics, 2013) together with an efficient Horseshoe prior for variable selection/shrinkage (Carvalho et al. in Biometrika 97:465–480, 2010). We propose a computationally efficient parallel Gibbs sampler for the new model. An important advantage of DOLDA is that learned topics are directly connected to individual classes without the need for a reference class. We evaluate the model’s predictive accuracy and scalability, and demonstrate DOLDA’s advantage in interpreting the generated predictions.

  • 69.
    Magnusson, Måns
    et al.
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Science & Engineering.
    Jonsson, Leif
    Linköping University, Department of Computer and Information Science. Linköping University, Faculty of Science & Engineering.
    Villani, Mattias
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Science & Engineering.
    Broman, David
    School of Information and Communication Technology, Royal Institute of Technology KTH, Stockholm, Sweden.
    Sparse Partially Collapsed MCMC for Parallel Inference in Topic Models2018In: Journal of Computational And Graphical Statistics, ISSN 1061-8600, E-ISSN 1537-2715, Vol. 27, no 2, p. 449-463Article in journal (Refereed)
    Abstract [en]

    Topic models, and more specifically the class of Latent Dirichlet Allocation (LDA), are widely used for probabilistic modeling of text. MCMC sampling from the posterior distribution is typically performed using a collapsed Gibbs sampler. We propose a parallel sparse partially collapsed Gibbs sampler and compare its speed and efficiency to state-of-the-art samplers for topic models on five well-known text corpora of differing sizes and properties. In particular, we propose and compare two different strategies for sampling the parameter block with latent topic indicators. The experiments show that the increase in statistical inefficiency from only partial collapsing is smaller than commonly assumed, and can be more than compensated by the speedup from parallelization and sparsity on larger corpora. We also prove that the partially collapsed samplers scale well with the size of the corpus. The proposed algorithm is fast, efficient, exact, and can be used in more modeling situations than the ordinary collapsed sampler.

  • 70.
    Min, Liu
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning.
    Extended Summer 2018 vs. Extended Summers 1961 - 2017 in Sweden: Pattern Recognition and Anomaly Detection2019Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    Sweden experienced an extraordinarily hot summer that started earlier in May in 2018. Our study focuses on identifying if monthly mean of the daily maximum temperature patterns of the extended summer in 2018 (consists of May, June, July and August) are anomalous in comparison to the patterns detected from the same month periods from 1961 to 2017. Principal components analysis (PCA) is used to extract important features and reduce dimensionality of our data provided by the Swedish Meteorological and Hydrological Institute (SMHI) reanalysis study. The projected data on the new subspace spanning along the two principal axes is then analysed by Density-based Spatial Clustering of Application with Noise (DBSCAN) to identify if the projected data points in the extended summer 2018 follow similar patterns extracted from the previous months. Two Bayesian models with unique intercept are applied to the regional data subsets to have a further study on temperature patterns within the month classes (May, June, July and August, four month classes). By combining the two models with Akaike weights, we obtain the predicted intervals of temperatures with 90.9\% probability for the four months in 2018 across the regions.

    PCA projected months observations, PCA-based clustering and Bayesian analysis all identify that the temperatures in May and July 2018 are anomalously high, while the monthly temperature in August follows the similar pattern as the previous months during the years from 1961 to 2017. The southern Sweden experienced much higher temperature than the past in June 2018. Also, we identify that an anomalous change of temperatures existed in the extended summer 2018. The change among the months in 2018 shows a different amplitude and direction due to anomalously higher temperatures in both May and July.

  • 71.
    Mitov, Venelin
    et al.
    Swiss Fed Inst Technol, Switzerland; Swiss Inst Bioinformat SIB, Switzerland.
    Bartoszek, Krzysztof
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Arts and Sciences.
    Stadler, Tanja
    Swiss Fed Inst Technol, Switzerland; Swiss Inst Bioinformat SIB, Switzerland.
    Automatic generation of evolutionary hypotheses using mixed Gaussian phylogenetic models2019In: Proceedings of the National Academy of Sciences of the United States of America, ISSN 0027-8424, E-ISSN 1091-6490, Vol. 116, no 34, p. 16921-16926Article in journal (Refereed)
    Abstract [en]

    Phylogenetic comparative methods are widely used to understand and quantify the evolution of phenotypic traits, based on phylogenetic trees and trait measurements of extant species. Such analyses depend crucially on the underlying model. Gaussian phylogenetic models like Brownian motion and Ornstein-Uhlenbeck processes are the workhorses of modeling continuous-trait evolution. However, these models fit poorly to big trees, because they neglect the heterogeneity of the evolutionary process in different lineages of the tree. Previous works have addressed this issue by introducing shifts in the evolutionary model occurring at inferred points in the tree. However, for computational reasons, in all current implementations, these shifts are "intramodel," meaning that they allow jumps in 1 or 2 model parameters, keeping all other parameters "global" for the entire tree. There is no biological reason to restrict a shift to a single model parameter or, even, to a single type of model. Mixed Gaussian phylogenetic models (MGPMs) incorporate the idea of jointly inferring different types of Gaussian models associated with different parts of the tree. Here, we propose an approximate maximum-likelihood method for fitting MGPMs to comparative data comprising possibly incomplete measurements for several traits from extant and extinct phylogenetically linked species. We applied the method to the largest published tree of mammal species with body-and brain-mass measurements, showing strong statistical support for an MGPM with 12 distinct evolutionary regimes. Based on this result, we state a hypothesis for the evolution of the brain-body-mass allometry over the past 160 million y.

  • 72.
    Nalenz, Malte
    et al.
    Linköping University, Department of Computer and Information Science. Linköping University, Faculty of Arts and Sciences.
    Villani, Mattias
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Arts and Sciences.
    TREE ENSEMBLES WITH RULE STRUCTURED HORSESHOE REGULARIZATION2018In: Annals of Applied Statistics, ISSN 1932-6157, E-ISSN 1941-7330, Vol. 12, no 4, p. 2379-2408Article in journal (Refereed)
    Abstract [en]

    We propose a new Bayesian model for flexible nonlinear regression and classification using tree ensembles. The model is based on the RuleFit approach in Friedman and Popescu [Ann. Appl. Stat. 2 (2008) 916-954] where rules from decision trees and linear terms are used in a Ll -regularized regression. We modify RuleFit by replacing the L1-regularization by a horseshoe prior, which is well known to give aggressive shrinkage of noise predictors while leaving the important signal essentially untouched. This is especially important when a large number of rules are used as predictors as many of them only contribute noise. Our horseshoe prior has an additional hierarchical layer that applies more shrinkage a priori to rules with a large number of splits, and to rules that are only satisfied by a few observations. The aggressive noise shrinkage of our prior also makes it possible to complement the rules from boosting in RuleFit with an additional set of trees from Random Forest, which brings a desirable diversity to the ensemble. We sample from the posterior distribution using a very efficient and easily implemented Gibbs sampler. The new model is shown to outperform state-of-the-art methods like RuleFit, BART and Random Forest on 16 datasets. The model and its interpretation is demonstrated on the well known Boston housing data, and on gene expression data for cancer classification. The posterior sampling, prediction and graphical tools for interpreting the model results are implemented in a publicly available R package.

  • 73.
    Neville, Kevin
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning.
    Channel attribution modelling using clickstream data from an online store2017Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    In marketing, behaviour of users is analysed in order to discover which channels (for instance TV, Social media etc.) are important for increasing the user’s intention to buy a product. The search for better channel attribution models than the common last-click model is of major concern for the industry of marketing. In this thesis, a probabilistic model for channel attribution has been developed, and this model is demonstrated to be more data-driven than the conventional last- click model. The modelling includes an attempt to include the time aspect in the modelling which have not been done in previous research. Our model is based on studying different sequence length and computing conditional probabilities of conversion by using logistic regression models. A clickstream dataset from an online store was analysed using the proposed model. This thesis has revealed proof of that the last-click model is not optimal for conducting these kinds of analyses. 

  • 74.
    Nordgaard, Anders
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Arts and Sciences. Swedish Police Auhtority, National Forensic Centre (NFC).
    Classification of percentages in seizures of narcotic material2017Conference paper (Other academic)
    Abstract [en]

    The percentage of the narcotic substance in a drug seizure may vary a lot depending on when and from whom the seizure was taken. Seizures from a typical consumer would in general show low percentages, while seizures from the early stages of a drug dealing chain would show higher percentages (these will be diluted). Legal fact finders must have an up-to-date picture of what is an expected level of the percentage and what levels are to be treated as unusually low or unusually high. This is important for the determination of the sentences to be given in a drug case.

    In this work we treat the probability distribution of the percentage of a narcotic substance in a seizure from year to year as a time series of beta density functions, which are successively updated with the use of point mass posteriors for the shape parameters. The predictive distribution for a new year is a weighted sum of beta distributions for the previous years where the weights are found from forward validation. We show that this method of prediction is more accurate than one that uses a predictive distribution built on a likelihood based on all previous years.

  • 75.
    Nordgaard, Anders
    et al.
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Arts and Sciences. Swedish Police Auhtority, National Forensic Centre (NFC).
    Aitken, Colin
    School of Mathematics, University of Edinburgh, Edinburgh, United Kingdom.
    Prediction of the distribution of thepercentages of narcotic substances in drug seizures2016Conference paper (Other academic)
    Abstract [en]

    The percentage of the narcotic substance in a drug seizure may vary a lot depending on when and from whom the seizure was taken. Seizures from a typical consumer would in general show low percentages, while seizures from the early stages of a drug dealing chain would show higher percentages (these will be diluted). Historical records from the determination of the percentage of narcotic substance in seized drugs reveal that the mean percentage but also the variation of the percentage can differ between years. Some drugs show close to monotonic trends while others are more irregular in the temporal variation.

    Legal fact finders must have an up-to-date picture of what is an expected level of the percentage and what levels are to be treated as unusually low or unusually high. This is important for the determination of the sentences to be given in a drug case.

    In this work we treat the probability distribution of the percentage of a narcotic substance in a seizure from year to year as a time series of functions. The functions are probability density functions of beta distributions, which are successively updated with the use of point mass posteriors for the shape parameters. The predictive distribution for a new year is a weighted sum of beta distributions for the previous years where the weights are found from forward validation. We show that this method of prediction is more accurate than one that uses a predictive distribution built on a likelihood based on all previous years.

  • 76.
    Nordgaard, Anders
    et al.
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Arts and Sciences. Swedish Police Auhtority, National Forensic Centre (NFC).
    Correll, Raymond
    Rho Environmetrics, Adelaide, Australia.
    Sampling strategies2018In: Integrated Analytical Approaches for Pesticide Management / [ed] Britt Maestroni and Andrew Cannavan, Elsevier, 2018, 1, p. 31-46Chapter in book (Other academic)
  • 77.
    Nordgaard, Anders
    et al.
    Linköping University, Faculty of Arts and Sciences. Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning.
    Grimvall, Anders
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Arts and Sciences.
    A resampling technique for estimating the power of non-parametric trend tests2006In: Environmetrics, ISSN 1180-4009, E-ISSN 1099-095X, Vol. 17, p. 257-267Article in journal (Refereed)
    Abstract [en]

    The power of Mann–Kendall tests and other non-parametric trend tests is normally estimated by performingMonte Carlo simulations in which artificial data are generated according to simple parametric models. Here weintroduce a resampling technique for power assessments that can be fully automated and accommodate almost anyvariation in the collected time series data. A rank regression model is employed to extract error terms representingirregular variation in data that are collected over several seasons and may contain a non-linear trend. Thereafter,an autoregressive moving average (ARMA) bootstrap method is used to generate new time series of error termsfor power simulations. A study of water quality data from two Swedish rivers illustrates how our methodcan provide site- and variable-specific information about the power of the Hirsch and Slack test for monotonictrends. In particular, we show how to clarify the impact of sampling frequency on the power of the trend tests.

  • 78.
    Nordgaard, Anders
    et al.
    Linköping University, Department of Computer and Information Science, Statistics. Linköping University, Faculty of Arts and Sciences. Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Polismyndigheten - Nationellt Forensiskt Centrum.
    Rasmusson, Birgitta
    Polismyndigheten - Nationellt Forensiskt Centrum.
    Professionell värdering av forensiska fynd borgar för rättssäkerhet2017In: Juridisk Tidskrift, ISSN 1100-7761, Vol. 29, no 1, p. 228-232Article in journal (Other (popular science, discussion, etc.))
  • 79.
    Pena, Jose M
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Science & Engineering.
    Representing independence models with elementary triplets2017In: International Journal of Approximate Reasoning, ISSN 0888-613X, E-ISSN 1873-4731, Vol. 88, p. 587-601Article in journal (Refereed)
    Abstract [en]

    In an independence model, the triplets that represent conditional independences between singletons are called elementary. It is known that the elementary triplets represent the independence model unambiguously under some conditions. In this paper, we show how this representation helps performing some operations with independence models, such as finding the dominant triplets or a minimal independence map of an independence model, or computing the union or intersection of a pair of independence models, or performing causal reasoning. For the latter, we rephrase in terms of conditional independences some of Pearls results for computing causal effects. (C) 2016 Elsevier Inc. All rights reserved.

  • 80.
    Pena, Jose M
    et al.
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Science & Engineering.
    Bendtsen, Marcus
    Linköping University, Department of Computer and Information Science, Database and information techniques. Linköping University, Faculty of Science & Engineering.
    Causal effect identification in acyclic directed mixed graphs and gated models2017In: International Journal of Approximate Reasoning, ISSN 0888-613X, E-ISSN 1873-4731, Vol. 90, p. 56-75Article in journal (Refereed)
    Abstract [en]

    We introduce a new family of graphical models that consists of graphs with possibly directed, undirected and bidirected edges but without directed cycles. We show that these models are suitable for representing causal models with additive error terms. We provide a set of sufficient graphical criteria for the identification of arbitrary causal effects when the new models contain directed and undirected edges but no bidirected edge. We also provide a necessary and sufficient graphical criterion for the identification of the causal effect of a single variable on the rest of the variables. Moreover, we develop an exact algorithm for learning the new models from observational and interventional data via answer set programming. Finally, we introduce gated models for causal effect identification, a new family of graphical models that exploits context specific independences to identify additional causal effects. (C) 2017 Elsevier Inc. All rights reserved.

  • 81.
    Pernet, Cyril
    et al.
    Centre for Clinical Brain Sciences, Edinburgh Imaging, University of Edinburgh, UK.
    Marinazzo, Daniele
    Faculty of Psychological and Educational Sciences, Gent University, Belgium.
    Stippich, Christoph
    Department of Neuroradiology, University Hospital Zürich, Switzerland.
    Beisteiner, Roland
    Department of Neurology, High Field MR Center, Medical University of Vienna, Austria.
    Douw, Linda
    VU University Medical Center, University of Amsterdam, Netherlands.
    Eklund, Anders
    Linköping University, Department of Biomedical Engineering, Division of Biomedical Engineering. Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Science & Engineering. Linköping University, Center for Medical Image Science and Visualization (CMIV).
    A new repository to share brain tumour data: European Network for Brain Imaging of Tumours2019Conference paper (Refereed)
  • 82.
    Pettersson, Tove
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning.
    Word2vec2syn: Synonymidentifiering med Word2vec2019Independent thesis Basic level (degree of Bachelor), 12 credits / 18 HE creditsStudent thesis
    Abstract [en]

    One of the main challenges in the field of natural language processing (NLP) is synonym identification. Fodina Language Technology AB is the company behind the tool, Termograph, that aims to collect terms and provide a consistent language within companies. A combination of multiple methods from the field of language technology constitutes the synonym identification and Fodina would like to improve the area of coverage and increase the dynamics of the working process. The focus of this thesis was therefore to evaluate a new method for synonym identification beyond the already used combination. Initially a trained Word2vec model was used and for the synonym identification the built-in-function for cosine similarity was applied in order to create clusters. The model was validated, tested and evaluated relative to the combination. The validation implicated that the model made estimations within a fair human-based range in an average of 60.30% and Spearmans correlation indicated a strong significant correlation. The testing showed that 32% of the processed synonym clusters contained matching synonym suggestions. The evaluation showed that the synonym suggestions from the model was correct in 5.73% of all cases compared to 3.07% for the combination in the cases where the clusters did not match. The interrater reliability indicated a slight agreement, Fleiss’ Kappa = 0.19, CI(0.06, 0.33). Despite uncertainty in the results, opportunities for further use of Word2vec-models within Fodina’s synonym identification are nevertheless demonstrated.

  • 83.
    Peña, Jose M.
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Science & Engineering.
    Causal Effect Identification in Alternative Acyclic Directed Mixed Graphs2017In: Proceedings of the 3rd Workshop on Advanced Methodologies for Bayesian Networks (AMBN 2017) - Proceedings of Machine Learning Research 73, 21-32, 2017Conference paper (Refereed)
  • 84.
    Peña, Jose M.
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Science & Engineering.
    Identification of Strong Edges in AMP Chain Graphs2018In: Proceedings of the 34th Conference on Uncertainty in Artificial Intelligence (UAI 2018), 2018Conference paper (Refereed)
  • 85.
    Peña, Jose M.
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Science & Engineering.
    Learning Causal AMP Chain Graphs2017In: Proceedings of the 3rd Workshop on Advanced Methodologies for Bayesian Networks (AMBN 2017) - Proceedings of Machine Learning Research 73, 33-44., 2017Conference paper (Refereed)
  • 86.
    Peña, Jose M.
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Science & Engineering.
    Reasoning with Alternative Acyclic Directed Mixed Graphs2018In: Behaviormetrika, ISSN 0385-7417, E-ISSN 1349-6964, Vol. 45, no 2, p. 389-422Article in journal (Refereed)
    Abstract [en]

    Acyclic directed mixed graphs (ADMGs) are the graphs used by Pearl (Causality: models, reasoning, and inference. Cambridge University Press, Cambridge, 2009) for causal effect identification. Recently, alternative acyclic directed mixed graphs (aADMGs) have been proposed by Peña (Proceedings of the 32nd conference on uncertainty in artificial intelligence, 577–586, 2016) for causal effect identification in domains with additive noise. Since the ADMG and the aADMG of the domain at hand may encode different model assumptions, it may be that the causal effect of interest is identifiable in one but not in the other. Causal effect identification in ADMGs is well understood. In this paper, we introduce a sound algorithm for identifying arbitrary causal effects from aADMGs. We show that the algorithm follows from a calculus similar to Pearl’s do-calculus. Then, we turn our attention to Andersson–Madigan–Perlman chain graphs, which are a subclass of aADMGs, and propose a factorization for the positive discrete probability distributions that are Markovian with respect to these chain graphs. We also develop an algorithm to perform maximum likelihood estimation of the factors in the factorization.

  • 87.
    Peña, Jose M.
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Science & Engineering.
    Unifying DAGs and UGs2018In: Proceedings of the 9th International Conference on Probabilistic Graphical Models (PGM 2018) - Proceedings of Machine Learning Research 72, 2018Conference paper (Refereed)
  • 88.
    Pham, Tuan
    Linköping University, Department of Biomedical Engineering, Division of Biomedical Engineering. Linköping University, Faculty of Science & Engineering.
    Eklund, Anders
    Linköping University, Department of Biomedical Engineering, Division of Biomedical Engineering. Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Science & Engineering. Linköping University, Center for Medical Image Science and Visualization (CMIV).
    Salerud, Göran
    Linköping University, Department of Biomedical Engineering. Linköping University, Faculty of Science & Engineering.
    Classification of Short Time Series in Early Parkinson’s Disease With Deep Learning of Fuzzy Recurrence Plots2019In: IEEE/CAA Journal of Automatica SinicaArticle in journal (Refereed)
    Abstract [en]

    There are many techniques using sensors and wearable devices for detecting and monitoring patients with Parkinson's disease (PD). A recent development is the utilization of human interaction with computer keyboards for analyzing and identifying motor signs in the early stages of the disease. Current designs for classification of time series of computer-key hold durations recorded from healthy control and PD subjects require the time series of length to be considerably long. With an attempt to avoid discomfort to participants in performing long physical tasks for data recording, this paper introduces the use of fuzzy recurrence plots of very short time series as input data for the machine training and classification with long short-term memory (LSTM) neural networks. Being an original approach that is able to both significantly increase the feature dimensions and provides the property of deterministic dynamical systems of very short time series for information processing carried out by an LSTM layer architecture, fuzzy recurrence plots provide promising results and outperform the direct input of the time series for the classification of healthy control and early PD subjects.

  • 89.
    Prihodko, Nikolajs
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning.
    Machine Learning for Forecasting Signal Strength in Mobile Networks2018Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    In this thesis we forecast the future signal strength of base stations in mobile networks. Better forecasts might improve handover of mobile phones between base stations, thus improving overall user experience. Future values are forecast using a series of past sig- nal strength measurements. We use vector autoregression (VAR), a multilayer perceptron (MLP), and a gated recurrent unit (GRU) network. Hyperparameters, including the set of lags, of these models are optimised using Bayesian optimisation (BO) with Gaussian pro- cess (GP) priors. In addition to BO of the VAR model, we optimise the set of lags in it using a standard bottom-up and top-down heuristic. Both approaches result in similar predictive mean squared error (MSE) for the VAR model, but BO requires fewer model estimations. The GRU model provides the best predictive performance out of the three models. How- ever, none of the models (VAR, MLP, or GRU) achieves the accuracy required for practical applicability of the results. Therefore, we suggest adding more information to the model or reformulating the problem.

  • 90.
    Quiroz, Matias
    et al.
    Univ New South Wales, Australia.
    Kohn, Robert
    Univ New South Wales, Australia.
    Villani, Mattias
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Arts and Sciences.
    Tran, Minh-Ngoc
    Univ Sydney, Australia.
    Speeding Up MCMC by Efficient Data Subsampling2019In: Journal of the American Statistical Association, ISSN 0162-1459, E-ISSN 1537-274X, Vol. 114, no 526, p. 831-843Article in journal (Refereed)
    Abstract [en]

    We propose subsampling Markov chain Monte Carlo (MCMC), an MCMC framework where the likelihood function for n observations is estimated from a random subset of m observations. We introduce a highly efficient unbiased estimator of the log-likelihood based on control variates, such that the computing cost is much smaller than that of the full log-likelihood in standard MCMC. The likelihood estimate is bias-corrected and used in two dependent pseudo-marginal algorithms to sample from a perturbed posterior, for which we derive the asymptotic error with respect to n and m, respectively. We propose a practical estimator of the error and show that the error is negligible even for a very small m in our applications. We demonstrate that subsampling MCMC is substantially more efficient than standard MCMC in terms of sampling efficiency for a given computational budget, and that it outperforms other subsampling methods for MCMC proposed in the literature. Supplementary materials for this article are available online.

  • 91.
    Quiroz, Matias
    et al.
    Linköping University, Department of Computer and Information Science, Statistics. Linköping University, Faculty of Science & Engineering. Research Division, Sveriges Riksbank, Stockholm, Sweden.
    Tran, Minh-Ngoc
    Discipline of Business Analytics, University of Sydney, Camperdown NSW, Australia.
    Villani, Mattias
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Science & Engineering.
    Kohn, Robert
    Australian School of Business, University of New South Wales, Sydney NSW, Australia.
    Speeding up MCMC by Delayed Acceptance and Data Subsampling2018In: Journal of Computational And Graphical Statistics, ISSN 1061-8600, E-ISSN 1537-2715, Vol. 27, no 1, p. 12-22Article in journal (Refereed)
    Abstract [en]

    The complexity of the Metropolis–Hastings (MH) algorithm arises from the requirement of a likelihood evaluation for the full dataset in each iteration. One solution has been proposed to speed up the algorithm by a delayed acceptance approach where the acceptance decision proceeds in two stages. In the first stage, an estimate of the likelihood based on a random subsample determines if it is likely that the draw will be accepted and, if so, the second stage uses the full data likelihood to decide upon final acceptance. Evaluating the full data likelihood is thus avoided for draws that are unlikely to be accepted. We propose a more precise likelihood estimator that incorporates auxiliary information about the full data likelihood while only operating on a sparse set of the data. We prove that the resulting delayed acceptance MH is more efficient. The caveat of this approach is that the full dataset needs to be evaluated in the second stage. We therefore propose to substitute this evaluation by an estimate and construct a state-dependent approximation thereof to use in the first stage. This results in an algorithm that (i) can use a smaller subsample m by leveraging on recent advances in Pseudo-Marginal MH (PMMH) and (ii) is provably within O(m^-2) of the true posterior.

  • 92.
    Quiroz, Matias
    et al.
    Univ New South Wales, Australia.
    Villani, Mattias
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Arts and Sciences. Stockholm Univ, Sweden.
    Kohn, Robert
    Univ New South Wales, Australia.
    Tran, Minh-Ngoc
    Univ Sydney, Australia.
    Dang, Khue-Dung
    Univ New South Wales, Australia.
    Subsampling MCMC - an Introduction for the Survey Statistician2018In: SANKHYA-SERIES A-MATHEMATICAL STATISTICS AND PROBABILITY, ISSN 0976-836X, Vol. 80, p. 33-69Article in journal (Other academic)
    Abstract [en]

    The rapid development of computing power and efficient Markov Chain Monte Carlo (MCMC) simulation algorithms have revolutionized Bayesian statistics, making it a highly practical inference method in applied work. However, MCMC algorithms tend to be computationally demanding, and are particularly slow for large datasets. Data subsampling has recently been suggested as a way to make MCMC methods scalable on massively large data, utilizing efficient sampling schemes and estimators from the survey sampling literature. These developments tend to be unknown by many survey statisticians who traditionally work with non-Bayesian methods, and rarely use MCMC. Our article explains the idea of data subsampling in MCMC by reviewing one strand of work, Subsampling MCMC, a so called Pseudo-Marginal MCMC approach to speeding up MCMC through data subsampling. The review is written for a survey statistician without previous knowledge of MCMC methods since our aim is to motivate survey sampling experts to contribute to the growing Subsampling MCMC literature.

  • 93.
    Raoufi-Danner, Torrin
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning.
    Effects of Missing Values on Neural Network Survival Time Prediction2018Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    Data sets with missing values are a pervasive problem within medical research. Building lifetime prediction models based solely upon complete-case data can bias the results, so imputation is preferred over listwise deletion. In this thesis, artificial neural networks (ANNs) are used as a prediction model on simulated data with which to compare various imputation approaches. The construction and optimization of ANNs is discussed in detail, and some guidelines are presented for activation functions, number of hidden layers and other tunable parameters. For the simulated data, binary lifetime prediction at five years was examined. The ANNs here performed best with tanh activation, binary cross-entropy loss with softmax output and three hidden layers of between 15 and 25 nodes. The imputation methods examined are random, mean, missing forest, multivariate imputation by chained equations (MICE), pooled MICE with imputed target and pooled MICE with non-imputed target. Random and mean imputation performed poorly compared to the others and were used as a baseline comparison case. The other algorithms all performed well up to 50% missingness. There were no statistical differences between these methods below 30% missingness, however missing forest had the best performance above this amount. It is therefore the recommendation of this thesis that the missing forest algorithm is used to impute missing data when constructing ANNs to predict breast cancer patient survival at the five-year mark.

  • 94.
    Risuleo, Riccardo Sven
    et al.
    KTH Royal Inst Technol, Sweden.
    Lindsten, Fredrik
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Science & Engineering.
    Hjalmarsson, Hakan
    KTH Royal Inst Technol, Sweden.
    Bayesian nonparametric identification of Wiener systems2019In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 108, article id UNSP 108480Article in journal (Refereed)
    Abstract [en]

    We propose a nonparametric approach for the identification of Wiener systems. We model the impulse response of the linear block and the static nonlinearity using Gaussian processes. The hyperparameters of the Gaussian processes are estimated using an iterative algorithm based on stochastic approximation expectation-maximization. In the iterations, we use elliptical slice sampling to approximate the posterior distribution of the impulse response and update the hyperparameter estimates. The same sampling is finally used to sample the posterior distribution and to compute point estimates. We compare the proposed approach with a parametric approach and a semi-parametric approach. In particular, we show that the proposed method has an advantage when a parametric model for the system is not readily available. (C) 2019 Elsevier Ltd. All rights reserved.

  • 95.
    Rodriguez-Deniz, Hector
    et al.
    KTH Royal Inst Technol, Sweden.
    Jenelius, Erik
    KTH Royal Inst Technol, Sweden.
    Villani, Mattias
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Arts and Sciences.
    Urban Network Travel Time Prediction via Online Multi-Output Gaussian Process Regression2017In: 2017 IEEE 20TH INTERNATIONAL CONFERENCE ON INTELLIGENT TRANSPORTATION SYSTEMS (ITSC), IEEE , 2017Conference paper (Refereed)
    Abstract [en]

    The paper explores the potential of Multi-Output Gaussian Processes to tackle network-wide travel time prediction in an urban area. Forecasting in this context is challenging due to the complexity of the traffic network, noisy data and unexpected events. We build on recent methods to develop an online model that can be trained in seconds by relying on prior network dependences through a coregionalized covariance. The accuracy of the proposed model outperforms historical means and other simpler methods on a network of 47 streets in Stockholm, by using probe data from GPS-equipped taxis. Results show how traffic speeds are dependent on the historical correlations, and how prediction accuracy can be improved by relying on prior information while using a very limited amount of current-day observations, which allows for the development of models with low estimation times and high responsiveness.

  • 96.
    Sandberg, Martina
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning.
    Credit Risk Evaluation using Machine Learning2017Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
  • 97.
    Sans Fuentes, Carles
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning.
    Markov Decision Processes and ARIMA models to analyze and predict Ice Hockey player’s performance2019Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    In this thesis, player’s performance on ice hockey is modelled to create newmetricsby match and season for players. AD-trees have been used to summarize ice hockey matches using state variables, which combine context and action variables to estimate the impact of each action under that specific state using Markov Decision Processes. With that, an impact measure has been described and four player metrics have been derived by match for regular seasons 2007-2008 and 2008-2009. General analysis has been performed for these metrics and ARIMA models have been used to analyze and predict players performance. The best prediction achieved in the modelling is the mean of the previous matches. The combination of several metrics including the ones created in this thesis could be combined to evaluate player’s performance using salary ranges to indicate whether a player is worth hiring/maintaining/firing

  • 98.
    Schofield, Alexandra
    et al.
    Cornell University Ithaca, NY, USA.
    Magnusson, Måns
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Science & Engineering.
    Mimno, David
    Cornell University Ithaca, NY, USA.
    Pulling Out the Stops: Rethinking Stopword Removal for Topic Models2017In: 15th Conference of the European Chapter of the Association for Computational Linguistics: Proceedings of Conference, volume 2: Short Papers, Stroudsburg: Association for Computational Linguistics (ACL) , 2017, Vol. 2, p. 432-436Conference paper (Other academic)
    Abstract [en]

    It is often assumed that topic models benefit from the use of a manually curated stopword list. Constructing this list is time-consuming and often subject to user judgments about what kinds of words are important to the model and the application. Although stopword removal clearly affects which word types appear as most probable terms in topics, we argue that this improvement is superficial, and that topic inference benefits little from the practice of removing stopwords beyond very frequent terms. Removing corpus-specific stopwords after model inference is more transparent and produces similar results to removing those words prior to inference.

  • 99.
    Shipitsyn, Aleksey
    Linköping University, Faculty of Arts and Sciences. Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning.
    Statistical Learning with Imbalanced Data2017Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    In this thesis several sampling methods for Statistical Learning with imbalanced data have been implemented and evaluated with a new metric, imbalanced accuracy. Several modifications and new algorithms have been proposed for intelligent sampling: Border links, Clean Border Undersampling, One-Sided Undersampling Modified, DBSCAN Undersampling, Class Adjusted Jittering, Hierarchical Cluster Based Oversampling, DBSCAN Oversampling, Fitted Distribution Oversampling, Random Linear Combinations Oversampling, Center Repulsion Oversampling.

    A set of requirements on a satisfactory performance metric for imbalanced learning have been formulated and a new metric for evaluating classification performance has been developed accordingly. The new metric is based on a combination of the worst class accuracy and geometric mean.

    In the testing framework nonparametric Friedman's test and post hoc Nemenyi’s test have been used to assess the performance of classifiers, sampling algorithms, combinations of classifiers and sampling algorithms on several data sets. A new approach of detecting algorithms with dominating and dominated performance has been proposed with a new way of visualizing the results in a network.

    From experiments on simulated and several real data sets we conclude that: i) different classifiers are not equally sensitive to sampling algorithms, ii) sampling algorithms have different performance within specific classifiers, iii) oversampling algorithms perform better than undersampling algorithms, iv) Random Oversampling and Random Undersampling outperform many well-known sampling algorithms, v) our proposed algorithms Hierarchical Cluster Based Oversampling, DBSCAN Oversampling with FDO, and Class Adjusted Jittering perform much better than other algorithms, vi) a few good combinations of a classifier and sampling algorithm may boost classification performance, while a few bad combinations may spoil the performance, but the majority of combinations are not significantly different in performance.

  • 100.
    Sidén, Per
    et al.
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Arts and Sciences.
    Lindgren, Finn
    Univ Edinburgh, Scotland.
    Bolin, David
    Chalmers and Univ Gothenburg, Sweden.
    Villani, Mattias
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Arts and Sciences.
    Efficient Covariance Approximations for Large Sparse Precision Matrices2018In: Journal of Computational And Graphical Statistics, ISSN 1061-8600, E-ISSN 1537-2715, Vol. 27, no 4, p. 898-909Article in journal (Refereed)
    Abstract [en]

    The use of sparse precision (inverse covariance) matrices has become popular because they allow for efficient algorithms for joint inference in high-dimensional models. Many applications require the computation of certain elements of the covariance matrix, such as the marginal variances, which may be nontrivial to obtain when the dimension is large. This article introduces a fast Rao-Blackwellized Monte Carlo sampling-based method for efficiently approximating selected elements of the covariance matrix. The variance and confidence bounds of the approximations can be precisely estimated without additional computational costs. Furthermore, a method that iterates over subdomains is introduced, and is shown to additionally reduce the approximation errors to practically negligible levels in an application on functional magnetic resonance imaging data. Both methods have low memory requirements, which is typically the bottleneck for competing direct methods.

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