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  • 1.
    Abramian, David
    et al.
    Linköping University, Center for Medical Image Science and Visualization (CMIV). Linköping University, Faculty of Science & Engineering. Linköping University, Department of Biomedical Engineering, Division of Biomedical Engineering.
    Sidén, Per
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Arts and Sciences.
    Knutsson, Hans
    Linköping University, Faculty of Science & Engineering. Linköping University, Department of Biomedical Engineering, Division of Biomedical 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 Arts and Sciences. Linköping University, Center for Medical Image Science and Visualization (CMIV). Department of Statistics, Stockholm University.
    Eklund, Anders
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Science & Engineering. Linköping University, Department of Biomedical Engineering, Division of Biomedical Engineering. Linköping University, Center for Medical Image Science and Visualization (CMIV).
    Anatomically Informed Bayesian Spatial Priors for FMRI Analysis2020In: ISBI 2020: IEEE International Symposium on Biomedical Imaging / [ed] IEEE, IEEE, 2020Conference paper (Refereed)
    Abstract [en]

    Existing Bayesian spatial priors for functional magnetic resonance imaging (fMRI) data correspond to stationary isotropic smoothing filters that may oversmooth at anatomical boundaries. We propose two anatomically informed Bayesian spatial models for fMRI data with local smoothing in each voxel based on a tensor field estimated from a T1-weighted anatomical image. We show that our anatomically informed Bayesian spatial models results in posterior probability maps that follow the anatomical structure.

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  • 2.
    Andersson, Olov
    et al.
    Linköping University, Department of Computer and Information Science, Artificial Intelligence and Integrated Computer Systems. Linköping University, Faculty of Science & Engineering.
    Sidén, Per
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Arts and Sciences.
    Dahlin, Johan
    Kotte Consulting AB.
    Doherty, Patrick
    Linköping University, Department of Computer and Information Science, Artificial Intelligence and Integrated Computer Systems. 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 Arts and Sciences. Stockholm University, Stockholm, Sweden.
    Real-Time Robotic Search using Structural Spatial Point Processes2020In: 35TH UNCERTAINTY IN ARTIFICIAL INTELLIGENCE CONFERENCE (UAI 2019), Association For Uncertainty in Artificial Intelligence (AUAI) , 2020, Vol. 115, p. 995-1005Conference paper (Refereed)
    Abstract [en]

    Aerial robots hold great potential for aiding Search and Rescue (SAR) efforts over large areas, such as during natural disasters. Traditional approaches typically search an area exhaustively, thereby ignoring that the density of victims varies based on predictable factors, such as the terrain, population density and the type of disaster. We present a probabilistic model to automate SAR planning, with explicit minimization of the expected time to discovery. The proposed model is a spatial point process with three interacting spatial fields for i) the point patterns of persons in the area, ii) the probability of detecting persons and iii) the probability of injury. This structure allows inclusion of informative priors from e.g. geographic or cell phone traffic data, while falling back to latent Gaussian processes when priors are missing or inaccurate. To solve this problem in real-time, we propose a combination of fast approximate inference using Integrated Nested Laplace Approximation (INLA), and a novel Monte Carlo tree search tailored to the problem. Experiments using data simulated from real world Geographic Information System (GIS) maps show that the framework outperforms competing approaches, finding many more injured in the crucial first hours.

  • 3.
    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.

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  • 4.
    Oskarsson, Joel
    et al.
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Science & Engineering.
    Sidén, Per
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Science & Engineering. Arriver Software AB, Sweden.
    Lindsten, Fredrik
    Linköping University, Faculty of Science & Engineering. Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning.
    Scalable Deep Gaussian Markov Random Fields for General Graphs2022In: Proceedings of the 39th International Conference on Machine Learning / [ed] Kamalika Chaudhuri, Stefanie Jegelka, Le Song, Csaba Szepesvari, Gang Niu, Sivan Sabato, 2022, p. 17117-17137Conference paper (Refereed)
    Abstract [en]

    Machine learning methods on graphs have proven useful in many applications due to their ability to handle generally structured data. The framework of Gaussian Markov Random Fields (GMRFs) provides a principled way to define Gaussian models on graphs by utilizing their sparsity structure. We propose a flexible GMRF model for general graphs built on the multi-layer structure of Deep GMRFs, originally proposed for lattice graphs only. By designing a new type of layer we enable the model to scale to large graphs. The layer is constructed to allow for efficient training using variational inference and existing software frameworks for Graph Neural Networks. For a Gaussian likelihood, close to exact Bayesian inference is available for the latent field. This allows for making predictions with accompanying uncertainty estimates. The usefulness of the proposed model is verified by experiments on a number of synthetic and real world datasets, where it compares favorably to other both Bayesian and deep learning methods.

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  • 5. Order onlineBuy this publication >>
    Sidén, Per
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Arts and Sciences.
    Scalable Bayesian spatial analysis with Gaussian Markov random fields2020Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    Accurate statistical analysis of spatial data is important in many applications. Failing to properly account for spatial autocorrelation may often lead to false conclusions. At the same time, the ever-increasing sizes of spatial datasets pose a great computational challenge, as many standard methods for spatial analysis are limited to a few thousand data points.

    In this thesis, we explore how Gaussian Markov random fields (GMRFs) can be used for scalable analysis of spatial data. GMRFs are closely connected to the commonly used Gaussian processes, but have sparsity properties that make them computationally cheap both in time and memory. The Bayesian framework enables a GMRF to be used as a spatial prior, comprising the assumption of smooth variation over space, and gives a principled way to estimate the parameters and propagate uncertainty.

    We develop new algorithms that enable applying GMRF priors in 3D to the brain activity inherent in functional magnetic resonance imaging (fMRI) data, with millions of observations. We show that our methods are both faster and more accurate than previous work. A method for approximating selected elements of the inverse precision matrix (i.e. the covariance matrix) is also proposed, which is important for evaluating the posterior uncertainty. In addition, we establish a link between GMRFs and deep convolutional neural networks, which have been successfully used in countless machine learning tasks for images, resulting in a deep GMRF model. Finally, we show how GMRFs can be used in real-time robotic search and rescue operations, for modeling the spatial distribution of injured persons.

    List of papers
    1. Fast Bayesian whole-brain fMRI analysis with spatial 3D priors
    Open this publication in new window or tab >>Fast Bayesian whole-brain fMRI analysis with spatial 3D priors
    2017 (English)In: NeuroImage, ISSN 1053-8119, E-ISSN 1095-9572, Vol. 146, p. 211-225Article in journal (Refereed) Published
    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.

    Place, publisher, year, edition, pages
    Elsevier, 2017
    Keywords
    fMRI, Spatial priors, Variational Bayes, Markov chain Monte Carlo, Gaussian Markov random fields, General linear model
    National Category
    Medical Engineering
    Identifiers
    urn:nbn:se:liu:diva-132945 (URN)10.1016/j.neuroimage.2016.11.040 (DOI)000394560700019 ()27876654 (PubMedID)2-s2.0-84999622353 (Scopus ID)
    Note

    Funding agencies: Swedish Research Council (Vetenskapsradet) [20135229]; Knut and Alice Wallenberg Foundation [KAW 20012.0067]

    Available from: 2016-12-05 Created: 2016-12-05 Last updated: 2020-06-29Bibliographically approved
    2. Efficient Covariance Approximations for Large Sparse Precision Matrices
    Open this publication in new window or tab >>Efficient Covariance Approximations for Large Sparse Precision Matrices
    2018 (English)In: Journal of Computational And Graphical Statistics, ISSN 1061-8600, E-ISSN 1537-2715, Vol. 27, no 4, p. 898-909Article in journal (Refereed) Published
    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.

    Place, publisher, year, edition, pages
    AMER STATISTICAL ASSOC, 2018
    Keywords
    Gaussian Markov random fields; Selected inversion; Sparse precision matrix; Spatial analysis; Stochastic approximation
    National Category
    Probability Theory and Statistics
    Identifiers
    urn:nbn:se:liu:diva-153715 (URN)10.1080/10618600.2018.1473782 (DOI)000453029500018 ()
    Note

    Funding Agencies|Swedish Research Council (Vetenskapsradet) [2013-5229, 2016-04187]; European Unions Horizon 2020 Programme for Research and Innovation [640171]

    Available from: 2019-01-07 Created: 2019-01-07 Last updated: 2020-06-29
    3. Deep Gaussian Markov Random Fields
    Open this publication in new window or tab >>Deep Gaussian Markov Random Fields
    2020 (English)In: Proceedings of the 37th International Conference on Machine Learning / [ed] Hal Daumé III, Aarti Singh, PMLR , 2020, Vol. 119, p. 8916-8926Conference paper, Published paper (Refereed)
    Abstract [en]

    Gaussian Markov random fields (GMRFs) are probabilistic graphical models widely used in spatial statistics and related fields to model dependencies over spatial structures. We establish a formal connection between GMRFs and convolutional neural networks (CNNs). Common GMRFs are special cases of a generative model where the inverse mapping from data to latent variables is given by a 1-layer linear CNN. This connection allows us to generalize GMRFs to multi-layer CNN architectures, effectively increasing the order of the corresponding GMRF in a way which has favorable computational scaling. We describe how well-established tools, such as autodiff and variational inference, can be used for simple and efficient inference and learning of the deep GMRF. We demonstrate the flexibility of the proposed model and show that it outperforms the state-of-the-art on a dataset of satellite temperatures, in terms of prediction and predictive uncertainty.

    Place, publisher, year, edition, pages
    PMLR, 2020
    Series
    Proceedings of Machine Learning Research, ISSN 2640-3498 ; 119
    National Category
    Probability Theory and Statistics
    Identifiers
    urn:nbn:se:liu:diva-171582 (URN)
    Conference
    International Conference on Machine Learning, 13-18 July 2020, Virtual
    Available from: 2020-11-24 Created: 2020-11-24 Last updated: 2020-11-24
    4. Real-Time Robotic Search using Structural Spatial Point Processes
    Open this publication in new window or tab >>Real-Time Robotic Search using Structural Spatial Point Processes
    Show others...
    2020 (English)In: 35TH UNCERTAINTY IN ARTIFICIAL INTELLIGENCE CONFERENCE (UAI 2019), Association For Uncertainty in Artificial Intelligence (AUAI) , 2020, Vol. 115, p. 995-1005Conference paper, Published paper (Refereed)
    Abstract [en]

    Aerial robots hold great potential for aiding Search and Rescue (SAR) efforts over large areas, such as during natural disasters. Traditional approaches typically search an area exhaustively, thereby ignoring that the density of victims varies based on predictable factors, such as the terrain, population density and the type of disaster. We present a probabilistic model to automate SAR planning, with explicit minimization of the expected time to discovery. The proposed model is a spatial point process with three interacting spatial fields for i) the point patterns of persons in the area, ii) the probability of detecting persons and iii) the probability of injury. This structure allows inclusion of informative priors from e.g. geographic or cell phone traffic data, while falling back to latent Gaussian processes when priors are missing or inaccurate. To solve this problem in real-time, we propose a combination of fast approximate inference using Integrated Nested Laplace Approximation (INLA), and a novel Monte Carlo tree search tailored to the problem. Experiments using data simulated from real world Geographic Information System (GIS) maps show that the framework outperforms competing approaches, finding many more injured in the crucial first hours.

    Place, publisher, year, edition, pages
    Association For Uncertainty in Artificial Intelligence (AUAI), 2020
    Series
    Proceedings of Machine Learning Research (PMLR), E-ISSN 2640-3498 ; 115
    National Category
    Computer and Information Sciences
    Identifiers
    urn:nbn:se:liu:diva-159698 (URN)000722423500092 ()2-s2.0-85084016675 (Scopus ID)
    Conference
    Proceedings of the 35th Conference on Uncertainty in Artificial Intelligence (UAI 2019), Tel Aviv, Israel, July 22-25, 2019
    Note

    Funding: Wallenberg AI, Autonomous Systems and Software Program (WASP); WASP Autonomous Research Arenas - Knut and Alice Wallenberg Foundation; Swedish Foundation for Strategic Research (SSF)Swedish Foundation for Strategic Research; ELLIIT Excellence Center at Link opingLund for Information Technology

    Available from: 2019-08-19 Created: 2019-08-19 Last updated: 2023-04-05Bibliographically approved
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  • 6.
    Sidén, Per
    et al.
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Science & Engineering.
    Lindgren, Finn
    School of Mathematics, The University of Edinburgh, United Kingdom.
    Bolin, David
    CEMSE Division, King Abdullah University of Science and Technology, Saudi Arabia.
    Eklund, Anders
    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). Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning.
    Villani, Mattias
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Arts and Sciences. Department of Statistics, Stockholm University.
    Spatial 3D Matérn Priors for Fast Whole-Brain fMRI Analysis2021In: Bayesian Analysis, ISSN 1936-0975, E-ISSN 1931-6690, Vol. 16, no 4, p. 1251-1278Article in journal (Refereed)
    Abstract [en]

    Bayesian whole-brain functional magnetic resonance imaging (fMRI) analysis with three-dimensional spatial smoothing priors has been shown to produce state-of-the-art activity maps without pre-smoothing the data. The proposed inference algorithms are computationally demanding however, and the spatial priors used have several less appealing properties, such as being improper and having infinite spatial range.We propose a statistical inference framework for whole-brain fMRI analysis based on the class of Mat ern covariance functions. The framework uses the Gaussian Markov random field (GMRF) representation of possibly anisotropic spatial Mat ern fields via the stochastic partial differential equation (SPDE) approach of Lindgren et al. (2011). This allows for more flexible and interpretable spatial priors, while maintaining the sparsity required for fast inference in the high-dimensional whole-brain setting. We develop an accelerated stochastic gradient descent (SGD) optimization algorithm for empirical Bayes (EB) inference of the spatial hyperparameters. Conditionally on the inferred hyperparameters, we make a fully Bayesian treatment of the brain activity. The Mat ern prior is applied to both simulated and experimental task-fMRI data and clearly demonstrates that it is a more reasonable choice than the previously used priors, using comparisons of activity maps, prior simulation and cross-validation.

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  • 7.
    Sidén, Per
    et al.
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Science & Engineering.
    Lindsten, Fredrik
    Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Science & Engineering.
    Deep Gaussian Markov Random Fields2020In: Proceedings of the 37th International Conference on Machine Learning / [ed] Hal Daumé III, Aarti Singh, PMLR , 2020, Vol. 119, p. 8916-8926Conference paper (Refereed)
    Abstract [en]

    Gaussian Markov random fields (GMRFs) are probabilistic graphical models widely used in spatial statistics and related fields to model dependencies over spatial structures. We establish a formal connection between GMRFs and convolutional neural networks (CNNs). Common GMRFs are special cases of a generative model where the inverse mapping from data to latent variables is given by a 1-layer linear CNN. This connection allows us to generalize GMRFs to multi-layer CNN architectures, effectively increasing the order of the corresponding GMRF in a way which has favorable computational scaling. We describe how well-established tools, such as autodiff and variational inference, can be used for simple and efficient inference and learning of the deep GMRF. We demonstrate the flexibility of the proposed model and show that it outperforms the state-of-the-art on a dataset of satellite temperatures, in terms of prediction and predictive uncertainty.

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