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  • 1.
    Magnusson, Måns
    et al.
    Linköpings universitet, Institutionen för datavetenskap, Statistik och maskininlärning. Linköpings universitet, Filosofiska fakulteten. Aalto University, Espoo, Finland.
    Jonsson, Leif
    Ericsson AB, Stockholm, Sweden.
    Villani, Mattias
    Linköpings universitet, Institutionen för datavetenskap, Statistik och maskininlärning. Linköpings universitet, Filosofiska fakulteten. Stockholm University, Stockholm, Sweden.
    DOLDA: a regularized supervised topic model for high-dimensional multi-class regression2019Ingår i: Computational statistics (Zeitschrift), ISSN 0943-4062, E-ISSN 1613-9658Artikel i tidskrift (Refereegranskat)
    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.

  • 2.
    Dang, Khue-Dung
    et al.
    Univ New South Wales, Australia; ARC Ctr Excellence Math and Stat Frontiers ACEMS, Australia.
    Quiroz, Matias
    ARC Ctr Excellence Math and Stat Frontiers ACEMS, Australia; Univ Technol Sydney, Australia.
    Kohn, Robert
    Univ New South Wales, Australia; ARC Ctr Excellence Math and Stat Frontiers ACEMS, Australia.
    Minh-Ngoc, Tran
    ARC Ctr Excellence Math and Stat Frontiers ACEMS, Australia; Univ Sydney, Australia.
    Villani, Mattias
    Linköpings universitet, Institutionen för datavetenskap, Statistik och maskininlärning. Linköpings universitet, Filosofiska fakulteten. ARC Ctr Excellence Math and Stat Frontiers ACEMS, Australia; Stockholm Univ, Sweden.
    Hamiltonian Monte Carlo with Energy Conserving Subsampling2019Ingår i: Journal of machine learning research, ISSN 1532-4435, E-ISSN 1533-7928, Vol. 20, artikel-id 1Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Hamiltonian Monte Carlo (HMC) samples efficiently from high-dimensional posterior distributions with proposed parameter draws obtained by iterating on a discretized version of the Hamiltonian dynamics. The iterations make HMC computationally costly, especially in problems with large data sets, since it is necessary to compute posterior densities and their derivatives with respect to the parameters. Naively computing the Hamiltonian dynamics on a subset of the data causes HMC to lose its key ability to generate distant parameter proposals with high acceptance probability. The key insight in our article is that efficient subsampling HMC for the parameters is possible if both the dynamics and the acceptance probability are computed from the same data subsample in each complete HMC iteration. We show that this is possible to do in a principled way in a HMC-within-Gibbs framework where the subsample is updated using a pseudo marginal MH step and the parameters are then updated using an HMC step, based on the current subsample. We show that our subsampling methods are fast and compare favorably to two popular sampling algorithms that use gradient estimates from data subsampling. We also explore the current limitations of subsampling HMC algorithms by varying the quality of the variance reducing control variates used in the estimators of the posterior density and its gradients.

  • 3.
    Andersson, Olov
    et al.
    Linköpings universitet, Institutionen för datavetenskap, Artificiell intelligens och integrerade datorsystem. Linköpings universitet, Tekniska fakulteten.
    Sidén, Per
    Linköpings universitet, Institutionen för datavetenskap, Statistik och maskininlärning. Linköpings universitet, Filosofiska fakulteten.
    Dahlin, Johan
    Kotte Consulting AB.
    Doherty, Patrick
    Linköpings universitet, Institutionen för datavetenskap, Artificiell intelligens och integrerade datorsystem. Linköpings universitet, Tekniska fakulteten.
    Villani, Mattias
    Linköpings universitet, Institutionen för datavetenskap, Statistik och maskininlärning. Linköpings universitet, Filosofiska fakulteten. Stockholm University, Stockholm, Sweden.
    Real-Time Robotic Search using Structural Spatial Point Processes2019Konferensbidrag (Refereegranskat)
  • 4.
    Quiroz, Matias
    et al.
    Univ New South Wales, Australia.
    Kohn, Robert
    Univ New South Wales, Australia.
    Villani, Mattias
    Linköpings universitet, Institutionen för datavetenskap, Statistik och maskininlärning. Linköpings universitet, Filosofiska fakulteten.
    Tran, Minh-Ngoc
    Univ Sydney, Australia.
    Speeding Up MCMC by Efficient Data Subsampling2019Ingår i: Journal of the American Statistical Association, ISSN 0162-1459, E-ISSN 1537-274X, Vol. 114, nr 526, s. 831-843Artikel i tidskrift (Refereegranskat)
    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.

  • 5.
    Sidén, Per
    et al.
    Linköpings universitet, Institutionen för datavetenskap, Statistik och maskininlärning. Linköpings universitet, Filosofiska fakulteten.
    Lindgren, Finn
    Univ Edinburgh, Scotland.
    Bolin, David
    Chalmers and Univ Gothenburg, Sweden.
    Villani, Mattias
    Linköpings universitet, Institutionen för datavetenskap, Statistik och maskininlärning. Linköpings universitet, Filosofiska fakulteten.
    Efficient Covariance Approximations for Large Sparse Precision Matrices2018Ingår i: Journal of Computational And Graphical Statistics, ISSN 1061-8600, E-ISSN 1537-2715, Vol. 27, nr 4, s. 898-909Artikel i tidskrift (Refereegranskat)
    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.

  • 6.
    Sidén, Per
    et al.
    Linköpings universitet, Institutionen för datavetenskap, Statistik och maskininlärning. Linköpings universitet, Filosofiska fakulteten.
    Villani, Mattias
    Linköpings universitet, Institutionen för datavetenskap, Statistik och maskininlärning. Linköpings universitet, Filosofiska fakulteten. Stockholm Univ, Sweden.
    Invited Discussion2018Ingår i: Bayesian Analysis, ISSN 1936-0975, E-ISSN 1931-6690, Vol. 13, nr 4, s. 1291-1297Artikel i tidskrift (Övrigt vetenskapligt)
    Abstract [en]

    n/a

  • 7.
    Magnusson, Måns
    et al.
    Linköpings universitet, Institutionen för datavetenskap, Statistik och maskininlärning. Linköpings universitet, Tekniska fakulteten.
    Jonsson, Leif
    Linköpings universitet, Institutionen för datavetenskap. Linköpings universitet, Tekniska fakulteten.
    Villani, Mattias
    Linköpings universitet, Institutionen för datavetenskap, Statistik och maskininlärning. Linköpings universitet, Tekniska fakulteten.
    Broman, David
    School of Information and Communication Technology, Royal Institute of Technology KTH, Stockholm, Sweden.
    Sparse Partially Collapsed MCMC for Parallel Inference in Topic Models2018Ingår i: Journal of Computational And Graphical Statistics, ISSN 1061-8600, E-ISSN 1537-2715, Vol. 27, nr 2, s. 449-463Artikel i tidskrift (Refereegranskat)
    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.

  • 8.
    Quiroz, Matias
    et al.
    Linköpings universitet, Institutionen för datavetenskap, Statistik. Linköpings universitet, Tekniska fakulteten. Research Division, Sveriges Riksbank, Stockholm, Sweden.
    Tran, Minh-Ngoc
    Discipline of Business Analytics, University of Sydney, Camperdown NSW, Australia.
    Villani, Mattias
    Linköpings universitet, Institutionen för datavetenskap, Statistik och maskininlärning. Linköpings universitet, Tekniska fakulteten.
    Kohn, Robert
    Australian School of Business, University of New South Wales, Sydney NSW, Australia.
    Speeding up MCMC by Delayed Acceptance and Data Subsampling2018Ingår i: Journal of Computational And Graphical Statistics, ISSN 1061-8600, E-ISSN 1537-2715, Vol. 27, nr 1, s. 12-22Artikel i tidskrift (Refereegranskat)
    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.

  • 9.
    Quiroz, Matias
    et al.
    Univ New South Wales, Australia.
    Villani, Mattias
    Linköpings universitet, Institutionen för datavetenskap, Statistik och maskininlärning. Linköpings universitet, Filosofiska fakulteten. 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 Statistician2018Ingår i: SANKHYA-SERIES A-MATHEMATICAL STATISTICS AND PROBABILITY, ISSN 0976-836X, Vol. 80, s. 33-69Artikel i tidskrift (Övrigt vetenskapligt)
    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.

  • 10.
    Nalenz, Malte
    et al.
    Linköpings universitet, Institutionen för datavetenskap. Linköpings universitet, Filosofiska fakulteten.
    Villani, Mattias
    Linköpings universitet, Institutionen för datavetenskap, Statistik och maskininlärning. Linköpings universitet, Filosofiska fakulteten.
    TREE ENSEMBLES WITH RULE STRUCTURED HORSESHOE REGULARIZATION2018Ingår i: Annals of Applied Statistics, ISSN 1932-6157, E-ISSN 1941-7330, Vol. 12, nr 4, s. 2379-2408Artikel i tidskrift (Refereegranskat)
    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.

  • 11.
    Eklund, Anders
    et al.
    Linköpings universitet, Institutionen för datavetenskap, Statistik. Linköpings universitet, Institutionen för medicinsk teknik, Avdelningen för medicinsk teknik. Linköpings universitet, Centrum för medicinsk bildvetenskap och visualisering, CMIV. Linköpings universitet, Tekniska fakulteten. Linköpings universitet, Filosofiska fakulteten.
    Lindqvist, Martin A
    Department of Biostatistics, Johns Hopkins University, Baltimore, USA.
    Villani, Mattias
    Linköpings universitet, Institutionen för datavetenskap, Statistik. Linköpings universitet, Filosofiska fakulteten.
    A Bayesian Heteroscedastic GLM with Application to fMRI Data with Motion Spikes2017Ingår i: NeuroImage, ISSN 1053-8119, E-ISSN 1095-9572, Vol. 155, s. 354-369Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We propose a voxel-wise general linear model with autoregressive noise and heteroscedastic noise innovations (GLMH) for analyzing functional magnetic resonance imaging (fMRI) data. The model is analyzed from a Bayesian perspective and has the benefit of automatically down-weighting time points close to motion spikes in a data-driven manner. We develop a highly efficient Markov Chain Monte Carlo (MCMC) algorithm that allows for Bayesian variable selection among the regressors to model both the mean (i.e., the design matrix) and variance. This makes it possible to include a broad range of explanatory variables in both the mean and variance (e.g., time trends, activation stimuli, head motion parameters and their temporal derivatives), and to compute the posterior probability of inclusion from the MCMC output. Variable selection is also applied to the lags in the autoregressive noise process, making it possible to infer the lag order from the data simultaneously with all other model parameters. We use both simulated data and real fMRI data from OpenfMRI to illustrate the importance of proper modeling of heteroscedasticity in fMRI data analysis. Our results show that the GLMH tends to detect more brain activity, compared to its homoscedastic counterpart, by allowing the variance to change over time depending on the degree of head motion.

  • 12.
    Gu, Xuan
    et al.
    Linköpings universitet, Institutionen för medicinsk teknik, Avdelningen för medicinsk teknik. Linköpings universitet, Tekniska fakulteten. Linköpings universitet, Centrum för medicinsk bildvetenskap och visualisering, CMIV.
    Sidén, Per
    Linköpings universitet, Institutionen för datavetenskap, Statistik och maskininlärning. Linköpings universitet, Tekniska fakulteten.
    Wegmann, Bertil
    Linköpings universitet, Institutionen för datavetenskap, Statistik och maskininlärning. Linköpings universitet, Tekniska fakulteten.
    Eklund, Anders
    Linköpings universitet, Institutionen för medicinsk teknik, Avdelningen för medicinsk teknik. Linköpings universitet, Institutionen för datavetenskap, Statistik och maskininlärning. Linköpings universitet, Tekniska fakulteten. Linköpings universitet, Centrum för medicinsk bildvetenskap och visualisering, CMIV.
    Villani, Mattias
    Linköpings universitet, Institutionen för datavetenskap, Statistik och maskininlärning. Linköpings universitet, Tekniska fakulteten.
    Knutsson, Hans
    Linköpings universitet, Institutionen för medicinsk teknik, Avdelningen för medicinsk teknik. Linköpings universitet, Tekniska fakulteten. Linköpings universitet, Centrum för medicinsk bildvetenskap och visualisering, CMIV.
    Bayesian Diffusion Tensor Estimation with Spatial Priors2017Ingår i: CAIP 2017: Computer Analysis of Images and Patterns, 2017, Vol. 10424, s. 372-383Konferensbidrag (Refereegranskat)
    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.

  • 13.
    Wegmann, Bertil
    et al.
    Linköpings universitet, Institutionen för datavetenskap, Statistik och maskininlärning. Linköpings universitet, Tekniska fakulteten.
    Eklund, Anders
    Linköpings universitet, Institutionen för medicinsk teknik, Avdelningen för medicinsk teknik. Linköpings universitet, Tekniska fakulteten. Linköpings universitet, Centrum för medicinsk bildvetenskap och visualisering, CMIV.
    Villani, Mattias
    Linköpings universitet, Institutionen för datavetenskap, Statistik och maskininlärning. Linköpings universitet, Filosofiska fakulteten.
    Bayesian Heteroscedastic Regression for Diffusion Tensor Imaging2017Ingår i: Modeling, Analysis, and Visualization of Anisotropy / [ed] Thomas Schultz; Evren Özarslan; Ingrid Hotz, Springer Publishing Company, 2017, 1, s. 257-282Konferensbidrag (Refereegranskat)
    Abstract [en]

    We propose a single-diffusion tensor model with heteroscedastic noise and a Bayesian approach via a highly efficient Markov Chain Monte Carlo (MCMC) algorithm for inference. The model is very flexible since both the noise-free signal and the noise variance are functions of diffusion covariates, and the relevant covariates in the noise are automatically selected by Bayesian variable selection. We compare the estimated diffusion tensors from our model to a homoscedastic counterpart with no covariates in the noise, and to commonly used linear and nonlinear least squares methods. The estimated single-diffusion tensors within each voxel are compared with respect to fractional anisotropy (FA) and mean diffusivity (MD). Using data from the Human Connectome Project, our results show that the noise is clearly heteroscedastic, especially the posterior variance for MD is substantially underestimated by the homoscedastic model, and inferences from the homoscedastic model are on average spuriously precise. Inferences from commonly used ordinary and weighted least squares methods (OLS and WLS) show that it is not adequate to estimate the single-diffusion tensor from logarithmic measurements.

  • 14.
    Wegmann, Bertil
    et al.
    Linköpings universitet, Institutionen för datavetenskap, Statistik och maskininlärning. Linköpings universitet, Filosofiska fakulteten.
    Eklund, Anders
    Linköpings universitet, Institutionen för medicinsk teknik, Avdelningen för medicinsk teknik. Linköpings universitet, Institutionen för datavetenskap, Statistik och maskininlärning. Linköpings universitet, Tekniska fakulteten. Linköpings universitet, Filosofiska fakulteten. Linköpings universitet, Centrum för medicinsk bildvetenskap och visualisering, CMIV.
    Villani, Mattias
    Linköpings universitet, Institutionen för datavetenskap, Statistik och maskininlärning. Linköpings universitet, Filosofiska fakulteten.
    Bayesian Rician Regression for Neuroimaging2017Ingår i: Frontiers in Neuroscience, ISSN 1662-4548, E-ISSN 1662-453X, Vol. 11, artikel-id 586Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    It is well-known that data from diffusion weighted imaging (DWI) follow the Rician distribution. The Rician distribution is also relevant for functional magnetic resonance imaging (fMRI) data obtained at high temporal or spatial resolution. We propose a general regression model for non-central chi (NC-chi) distributed data, with the heteroscedastic Rician regression model as a prominent special case. The model allows both parameters in the Rician distribution to be linked to explanatory variables, with the relevant variables chosen by Bayesian variable selection. A highly efficient Markov chain Monte Carlo (MCMC) algorithm is proposed to capture full model uncertainty by simulating from the joint posterior distribution of all model parameters and the binary variable selection indicators. Simulated regression data is used to demonstrate that the Rician model is able to detect the signal much more accurately than the traditionally used Gaussian model at low signal-to-noise ratios. Using a diffusion dataset from the Human Connectome Project, it is also shown that the commonly used approximate Gaussian noise model underestimates the mean diffusivity (MD) and the fractional anisotropy (FA) in the single-diffusion tensor model compared to the Rician model.

  • 15.
    Sidén, Per
    et al.
    Linköpings universitet, Institutionen för datavetenskap, Statistik. Linköpings universitet, Filosofiska fakulteten.
    Eklund, Anders
    Linköpings universitet, Institutionen för datavetenskap, Statistik. Linköpings universitet, Institutionen för medicinsk teknik, Medicinsk informatik. Linköpings universitet, Centrum för medicinsk bildvetenskap och visualisering, CMIV. Linköpings universitet, Tekniska fakulteten. Linköpings universitet, Filosofiska fakulteten.
    Bolin, David
    Division of Mathematical Statistics, Department of Mathematical Sciences, Chalmers and University of Gothenburg, Göteborg, Sweden.
    Villani, Mattias
    Linköpings universitet, Institutionen för datavetenskap, Statistik. Linköpings universitet, Filosofiska fakulteten.
    Fast Bayesian whole-brain fMRI analysis with spatial 3D priors2017Ingår i: NeuroImage, ISSN 1053-8119, E-ISSN 1095-9572, Vol. 146, s. 211-225Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Spatial whole-brain Bayesian modeling of task-related functional magnetic resonance imaging (fMRI) is a great computational challenge. Most of the currently proposed methods therefore do inference in subregions of the brain separately or do approximate inference without comparison to the true posterior distribution. A popular such method, which is now the standard method for Bayesian single subject analysis in the SPM software, is introduced in Penny et al. (2005b). The method processes the data slice-by-slice and uses an approximate variational Bayes (VB) estimation algorithm that enforces posterior independence between activity coefficients in different voxels. We introduce a fast and practical Markov chain Monte Carlo (MCMC) scheme for exact inference in the same model, both slice-wise and for the whole brain using a 3D prior on activity coefficients. The algorithm exploits sparsity and uses modern techniques for efficient sampling from high-dimensional Gaussian distributions, leading to speed-ups without which MCMC would not be a practical option. Using MCMC, we are for the first time able to evaluate the approximate VB posterior against the exact MCMC posterior, and show that VB can lead to spurious activation. In addition, we develop an improved VB method that drops the assumption of independent voxels a posteriori. This algorithm is shown to be much faster than both MCMC and the original VB for large datasets, with negligible error compared to the MCMC posterior.

  • 16.
    Rodriguez-Deniz, Hector
    et al.
    KTH Royal Inst Technol, Sweden.
    Jenelius, Erik
    KTH Royal Inst Technol, Sweden.
    Villani, Mattias
    Linköpings universitet, Institutionen för datavetenskap, Statistik och maskininlärning. Linköpings universitet, Filosofiska fakulteten.
    Urban Network Travel Time Prediction via Online Multi-Output Gaussian Process Regression2017Ingår i: 2017 IEEE 20TH INTERNATIONAL CONFERENCE ON INTELLIGENT TRANSPORTATION SYSTEMS (ITSC), IEEE , 2017Konferensbidrag (Refereegranskat)
    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.

  • 17.
    Jonsson, Leif
    et al.
    Linköpings universitet, Institutionen för datavetenskap, PELAB - Laboratoriet för programmeringsomgivningar. Ericsson AB, Sweden.
    Broman, David
    KTH Royal Institute Technology, Sweden; University of Calif Berkeley, CA USA.
    Magnusson, Måns
    Linköpings universitet, Institutionen för datavetenskap, Statistik. Linköpings universitet, Tekniska fakulteten.
    Sandahl, Kristian
    Linköpings universitet, Institutionen för datavetenskap, Programvara och system. Linköpings universitet, Tekniska fakulteten.
    Villani, Mattias
    Linköpings universitet, Institutionen för datavetenskap, Statistik. Linköpings universitet, Filosofiska fakulteten.
    Eldh, Sigrid
    Ericsson AB, Sweden.
    Automatic Localization of Bugs to Faulty Components in Large Scale Software Systems using Bayesian Classification2016Ingår i: 2016 IEEE INTERNATIONAL CONFERENCE ON SOFTWARE QUALITY, RELIABILITY AND SECURITY (QRS 2016), IEEE , 2016, s. 425-432Konferensbidrag (Refereegranskat)
    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.

  • 18.
    Mahfouzi, Rouhollah
    et al.
    Linköpings universitet, Institutionen för datavetenskap, Programvara och system. Linköpings universitet, Tekniska fakulteten.
    Aminifar, Amir
    Linköpings universitet, Institutionen för datavetenskap, Programvara och system. Linköpings universitet, Tekniska fakulteten. École Polytechnique Fédérale de Lausanne (EPFL), Switzerland.
    Eles, Petru
    Linköpings universitet, Institutionen för datavetenskap, Programvara och system. Linköpings universitet, Tekniska fakulteten.
    Peng, Zebo
    Linköpings universitet, Institutionen för datavetenskap, Programvara och system. Linköpings universitet, Tekniska fakulteten.
    Villani, Mattias
    Linköpings universitet, Institutionen för datavetenskap, Statistik. Linköpings universitet, Filosofiska fakulteten.
    Intrusion-Damage Assessment and Mitigation in Cyber-Physical Systems for Control Applications2016Ingår i: RTNS '16 Proceedings of the 24th International Conference on Real-Time Networks and Systems, New York: ACM Press, 2016, s. 141-150Konferensbidrag (Refereegranskat)
    Abstract [en]

    With cyber-physical systems opening to the outside world, security can no longer be considered a secondary issue. One of the key aspects in security of cyber-phyiscal systems is to deal with intrusions. In this paper, we highlight the several unique properties of control applications in cyber-physical systems. Using these unique properties, we propose a systematic intrusion-damage assessment and mitigation mechanism for the class of observable and controllable attacks.

    On the one hand, in cyber-physical systems, the plants follow certain laws of physics and this can be utilized to address the intrusion-damage assessment problem. That is, the states of the controlled plant should follow those expected according to the physics of the system and any major discrepancy is potentially an indication of intrusion. Here, we use a machine learning algorithm to capture the normal behavior of the system according to its dynamics. On the other hand, the control performance strongly depends on the amount of allocated resources and this can be used to address the intrusion-damage mitigation problem. That is, the intrusion-damage mitigation is based on the idea of allocating more resources to the control application under attack. This is done using a feedback-based approach including a convex optimization.

  • 19.
    Maghazeh, Arian
    et al.
    Linköpings universitet, Institutionen för datavetenskap, Programvara och system. Linköpings universitet, Tekniska fakulteten.
    Bordoloi, Unmesh D.
    Linköpings universitet, Institutionen för datavetenskap, Programvara och system. Linköpings universitet, Tekniska fakulteten.
    Villani, Mattias
    Linköpings universitet, Institutionen för datavetenskap, Statistik. Linköpings universitet, Tekniska fakulteten.
    Eles, Petru
    Linköpings universitet, Institutionen för datavetenskap, Programvara och system. Linköpings universitet, Tekniska fakulteten.
    Peng, Zebo
    Linköpings universitet, Institutionen för datavetenskap, Programvara och system. Linköpings universitet, Tekniska fakulteten.
    Perception-aware power management for mobile games via dynamic resolution scaling2015Ingår i: 2015 IEEE/ACM INTERNATIONAL CONFERENCE ON COMPUTER-AIDED DESIGN (ICCAD), IEEE , 2015, s. 613-620Konferensbidrag (Refereegranskat)
    Abstract [en]

    Modern mobile devices provide ultra-high resolutions in their display panels. This imposes ever increasing workload on the GPU leading to high power consumption and shortened battery life. In this paper, we first show that resolution scaling leads to significant power savings. Second, we propose a perception-aware adaptive scheme that sets the resolution during game play. We exploit the fact that game players are often willing to trade quality for longer battery life. Our scheme uses decision theory, where the predicted user perception is combined with a novel asymmetric loss function that encodes users' alterations in their willingness to save power.

  • 20.
    Dahlin, Johan
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Schön, Thomas Bo
    Department of Information Technology, Uppsala University.
    Villani, Mattias
    Linköpings universitet, Institutionen för datavetenskap, Statistik. Linköpings universitet, Filosofiska fakulteten.
    Approximate inference in state space models with intractable likelihoods using Gaussian process optimisation2014Rapport (Övrigt vetenskapligt)
    Abstract [en]

    We propose a novel method for MAP parameter inference in nonlinear state space models with intractable likelihoods. The method is based on a combination of Gaussian process optimisation (GPO), sequential Monte Carlo (SMC) and approximate Bayesian computations (ABC). SMC and ABC are used to approximate the intractable likelihood by using the similarity between simulated realisations from the model and the data obtained from the system. The GPO algorithm is used for the MAP parameter estimation given noisy estimates of the log-likelihood. The proposed parameter inference method is evaluated in three problems using both synthetic and real-world data. The results are promising, indicating that the proposed algorithm converges fast and with reasonable accuracy compared with existing methods.

  • 21.
    Eklund, Anders
    et al.
    Virginia Tech Carilion Research Institute, Virginia Tech, Roanoke, VA, USA.
    Dufort, Paul
    Department of Medical Imaging, University of Toronto, Toronto, ON, Canada.
    Villani, Mattias
    Linköpings universitet, Institutionen för datavetenskap, Statistik. Linköpings universitet, Filosofiska fakulteten.
    LaConte, Stephen
    Virginia Tech Carilion Research Institute, Virginia Tech, Roanoke, VA, USA/School of Biomedical Engineering and Sciences, Virginia Tech-Wake Forest University, Blacksburg, VA, USA.
    BROCCOLI: Software for fast fMRI analysis on many-core CPUs and GPUs2014Ingår i: Frontiers in Neuroinformatics, ISSN 1662-5196, E-ISSN 1662-5196, Vol. 8, nr 24Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Analysis of functional magnetic resonance imaging (fMRI) data is becoming ever more computationally demanding as temporal and spatial resolutions improve, and large, publicly available data sets proliferate. Moreover, methodological improvements in the neuroimaging pipeline, such as non-linear spatial normalization, non-parametric permutation tests and Bayesian Markov Chain Monte Carlo approaches, can dramatically increase the computational burden. Despite these challenges, there do not yet exist any fMRI software packages which leverage inexpensive and powerful graphics processing units (GPUs) to perform these analyses. Here, we therefore present BROCCOLI, a free software package written in OpenCL (Open Computing Language) that can be used for parallel analysis of fMRI data on a large variety of hardware configurations. BROCCOLI has, for example, been tested with an Intel CPU, an Nvidia GPU, and an AMD GPU. These tests show that parallel processing of fMRI data can lead to significantly faster analysis pipelines. This speedup can be achieved on relatively standard hardware, but further, dramatic speed improvements require only a modest investment in GPU hardware. BROCCOLI (running on a GPU) can perform non-linear spatial normalization to a 1 mm3 brain template in 4–6 s, and run a second level permutation test with 10,000 permutations in about a minute. These non-parametric tests are generally more robust than their parametric counterparts, and can also enable more sophisticated analyses by estimating complicated null distributions. Additionally, BROCCOLI includes support for Bayesian first-level fMRI analysis using a Gibbs sampler. The new software is freely available under GNU GPL3 and can be downloaded from github (https://github.com/wanderine/BROCCOLI/).

  • 22.
    Ukhov, Ivan
    et al.
    Linköpings universitet, Institutionen för datavetenskap, ESLAB - Laboratoriet för inbyggda system. Linköpings universitet, Institutionen för datavetenskap, Programvara och system. Linköpings universitet, Tekniska högskolan.
    Villani, Mattias
    Linköpings universitet, Institutionen för datavetenskap, Statistik. Linköpings universitet, Filosofiska fakulteten.
    Eles, Petru
    Linköpings universitet, Institutionen för datavetenskap, ESLAB - Laboratoriet för inbyggda system. Linköpings universitet, Institutionen för datavetenskap, Programvara och system. Linköpings universitet, Tekniska högskolan.
    Peng, Zebo
    Linköpings universitet, Institutionen för datavetenskap, ESLAB - Laboratoriet för inbyggda system. Linköpings universitet, Institutionen för datavetenskap, Programvara och system. Linköpings universitet, Tekniska högskolan.
    Statistical Analysis of Process Variation Based on Indirect Measurements for Electronic System Design2014Ingår i: 2014 19TH ASIA AND SOUTH PACIFIC DESIGN AUTOMATION CONFERENCE (ASP-DAC), New York: IEEE conference proceedings, 2014, s. 436-442Konferensbidrag (Refereegranskat)
    Abstract [en]

    We present a framework for the analysis of process variation across semiconductor wafers. The framework is capable of quantifying the primary parameters affected by process variation, e.g., the effective channel length, which is in contrast with the former techniques wherein only secondary parameters were considered, e.g., the leakage current. Instead of taking direct measurements of the quantity of interest, we employ Bayesian inference to draw conclusions based on indirect observations, e.g., on temperature. The proposed approach has low costs since no deployment of expensive test structures might be needed or only a small subset of the test equipments already deployed for other purposes might need to be activated. The experimental results present an assessment of our framework for a wide range of configurations.

  • 23.
    Giordani, Paolo
    et al.
    Sveriges Riksbank, Sweden.
    Jacobson, Tor
    Sveriges Riksbank, Sweden.
    von Schedvin, Erik
    Sveriges Riksbank, Sweden.
    Villani, Mattias
    Linköpings universitet, Institutionen för datavetenskap, Statistik. Linköpings universitet, Filosofiska fakulteten.
    Taking the Twists into Account: Predicting Firm Bankruptcy Risk with Splines of Financial Ratios2014Ingår i: Journal of financial and quantitative analysis, ISSN 0022-1090, E-ISSN 1756-6916, Vol. 49, nr 4, s. 1071-1099Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We demonstrate improvements in predictive power when introducing spline functions to take account of highly nonlinear relationships between firm failure and leverage, earnings, and liquidity in a logistic bankruptcy model. Our results show that modeling excessive nonlinearities yields substantially improved bankruptcy predictions, on the order of 70%-90%, compared with a standard logistic model. The spline model provides several important and surprising insights into nonmonotonic bankruptcy relationships. We find that low-leveraged as well as highly profitable firms are riskier than those given by a standard model, possibly a manifestation of credit rationing and excess cash-flow volatility.

  • 24.
    Li, Feng
    et al.
    Stockholm University, Sweden .
    Villani, Mattias
    Linköpings universitet, Institutionen för datavetenskap, Statistik. Linköpings universitet, Filosofiska fakulteten.
    Efficient Bayesian Multivariate Surface Regression2013Ingår i: Scandinavian Journal of Statistics, ISSN 0303-6898, E-ISSN 1467-9469, Vol. 40, nr 4, s. 706-723Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Methods for choosing a fixed set of knot locations in additive spline models are fairly well established in the statistical literature. The curse of dimensionality makes it nontrivial to extend these methods to nonadditive surface models, especially when there are more than a couple of covariates. We propose a multivariate Gaussian surface regression model that combines both additive splines and interactive splines, and a highly efficient Markov chain Monte Carlo algorithm that updates all the knot locations jointly. We use shrinkage prior to avoid overfitting with different estimated shrinkage factors for the additive and surface part of the model, and also different shrinkage parameters for the different response variables. Simulated data and an application to firm leverage data show that the approach is computationally efficient, and that allowing for freely estimated knot locations can offer a substantial improvement in out-of-sample predictive performance.

  • 25.
    Eklund, Anders
    et al.
    Virginia Tech Carilion Research Institute, Virginia Tech, Roanoke, USA.
    Villani, Mattias
    Linköpings universitet, Institutionen för datavetenskap, Statistik. Linköpings universitet, Filosofiska fakulteten.
    LaConte, Stephen
    Virginia Tech Carilion Research Institute, Virginia Tech, Roanoke, USA; School of Biomedical Engineering & Sciences, Virginia Tech-Wake Forest University, Blacksburg, USA.
    Harnessing graphics processing units for improved neuroimaging statistics2013Ingår i: Cognitive, Affective, & Behavioral Neuroscience, ISSN 1530-7026, E-ISSN 1531-135X, Vol. 13, nr 3, s. 587-597Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Simple models and algorithms based on restrictive assumptions are often used in the field of neuroimaging for studies involving functional magnetic resonance imaging, voxel based morphometry, and diffusion tensor imaging. Nonparametric statistical methods or flexible Bayesian models can be applied rather easily to yield more trustworthy results. The spatial normalization step required for multisubject studies can also be improved by taking advantage of more robust algorithms for image registration. A common drawback of algorithms based on weaker assumptions, however, is the increase in computational complexity. In this short overview, we will therefore present some examples of how inexpensive PC graphics hardware, normally used for demanding computer games, can be used to enable practical use of more realistic models and accurate algorithms, such that the outcome of neuroimaging studies really can be trusted.

  • 26.
    Villani, Mattias
    et al.
    Linköpings universitet, Institutionen för datavetenskap, Statistik. Linköpings universitet, Tekniska högskolan.
    Kohn, Robert
    University of New South Wales, Sydney, Australia.
    Nott, David J.
    National University of Singapore.
    Generalized Smooth Finite Mixtures2012Ingår i: Journal of Econometrics, ISSN 0304-4076, E-ISSN 1872-6895, Vol. 171, nr 2, s. 121-133Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We propose a general class of models and a unified Bayesian inference methodology for flexibly estimating the density of a response variable conditional on a possibly high-dimensional set of covariates. Our model is a finite mixture of component models with covariate-dependent mixing weights. The component densities can belong to any parametric family, with each model parameter being a deterministic function of covariates through a link function. Our MCMC methodology allows for Bayesian variable selection among the covariates in the mixture components and in the mixing weights. The model's parameterization and variable selection prior are chosen to prevent overtting. We use simulated and real datasets to illustrate the methodology

  • 27.
    Nott, David J.
    et al.
    National University of Singapore.
    Tan, Siew Li
    National University of Singapore.
    Villani, Mattias
    Linköpings universitet, Institutionen för datavetenskap, Statistik. Linköpings universitet, Tekniska högskolan.
    Kohn, Robert
    University of New South Wales, Sydney, Australia.
    Regression density estimation with variational methods and stochastic approximation2012Ingår i: Journal of Computational And Graphical Statistics, ISSN 1061-8600, E-ISSN 1537-2715, Vol. 21, nr 3, s. 797-820Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Regression density estimation is the problem of flexibly estimating a response distribution as a function of covariates. An important approach to regression density estimation uses finite mixture models and our article considers flexible mixtures of heteroscedastic regression (MHR) models where the response distribution is a normal mixture, with the component means, variances and mixture weights all varying as a function of covariates. Our article develops fast variational approximation methods for inference. Our motivation is that alternative computationally intensive MCMC methods for fitting mixture models are difficult to apply when it is desired to fit models repeatedly in exploratory analysis and model choice. Our article makes three contributions. First, a variational approximation for MHR models is described where the variational lower bound is in closed form. Second, the basic approximation can be improved by using stochastic approximation methods to perturb the initial solution to attain higher accuracy. Third, the advantages of our approach for model choice and evaluation compared to MCMC based approaches are illustrated. These advantages are particularly compelling for time series data where repeated refitting for one step ahead prediction in model choice and diagnostics and in rolling window computations is very common. Supplemental materials for the article are available online.

  • 28.
    Villani, Mattias
    Linköpings universitet, Institutionen för datavetenskap, Statistik. Linköpings universitet, Tekniska högskolan. Linköpings universitet, Filosofiska fakulteten. Linköpings universitet, Tekniska fakulteten.
    Fractional Bayesian lag length inference in multivariate autoregressive processes2001Ingår i: Journal of Time Series Analysis, ISSN 0143-9782, E-ISSN 1467-9892, Vol. 22, nr 1, s. 67-86Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The posterior distribution of the number of lags in a multivariate autoregression is derived under an improper prior for the model parameters. The fractional Bayes approach is used to handle the indeterminacy in the model selection caused by the improper prior. An asymptotic equivalence between the fractional approach and the Schwarz Bayesian Criterion (SBC) is proved. Several priors and three loss functions are entertained in a simulation study which focuses on the choice of lag length. The fractional Bayes approach performs very well compared to the three most widely used information criteria, and it seems to be reasonably robust to changes in the prior distribution for the lag length, especially under the zero-one loss.

1 - 28 av 28
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