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  • 1.
    Abramian, David
    et al.
    Linköpings universitet, Centrum för medicinsk bildvetenskap och visualisering, CMIV. Linköpings universitet, Tekniska fakulteten. Linköpings universitet, Institutionen för medicinsk teknik, Avdelningen för medicinsk teknik.
    Sidén, Per
    Linköpings universitet, Institutionen för datavetenskap, Statistik och maskininlärning. Linköpings universitet, Filosofiska fakulteten.
    Knutsson, Hans
    Linköpings universitet, Tekniska fakulteten. Linköpings universitet, Institutionen för medicinsk teknik, Avdelningen för medicinsk teknik. Linköpings universitet, Centrum för medicinsk bildvetenskap och visualisering, CMIV.
    Villani, Mattias
    Linköpings universitet, Institutionen för datavetenskap, Statistik och maskininlärning. Linköpings universitet, Filosofiska fakulteten. Linköpings universitet, Centrum för medicinsk bildvetenskap och visualisering, CMIV. Department of Statistics, Stockholm University.
    Eklund, Anders
    Linköpings universitet, Institutionen för datavetenskap, Statistik och maskininlärning. Linköpings universitet, Tekniska fakulteten. Linköpings universitet, Institutionen för medicinsk teknik, Avdelningen för medicinsk teknik. Linköpings universitet, Centrum för medicinsk bildvetenskap och visualisering, CMIV.
    Anatomically Informed Bayesian Spatial Priors for FMRI Analysis2020Ingår i: ISBI 2020: IEEE International Symposium on Biomedical Imaging / [ed] IEEE, IEEE, 2020Konferensbidrag (Refereegranskat)
    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.
    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 Processes2020Ingår i: 35TH UNCERTAINTY IN ARTIFICIAL INTELLIGENCE CONFERENCE (UAI 2019), Association For Uncertainty in Artificial Intelligence (AUAI) , 2020, Vol. 115, s. 995-1005Konferensbidrag (Refereegranskat)
    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.
    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.

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  • 4.
    Oskarsson, Joel
    et al.
    Linköpings universitet, Institutionen för datavetenskap, Statistik och maskininlärning. Linköpings universitet, Tekniska fakulteten.
    Sidén, Per
    Linköpings universitet, Institutionen för datavetenskap, Statistik och maskininlärning. Linköpings universitet, Tekniska fakulteten. Arriver Software AB, Sweden.
    Lindsten, Fredrik
    Linköpings universitet, Tekniska fakulteten. Linköpings universitet, Institutionen för datavetenskap, Statistik och maskininlärning.
    Scalable Deep Gaussian Markov Random Fields for General Graphs2022Ingår i: Proceedings of the 39th International Conference on Machine Learning / [ed] Kamalika Chaudhuri, Stefanie Jegelka, Le Song, Csaba Szepesvari, Gang Niu, Sivan Sabato, 2022, s. 17117-17137Konferensbidrag (Refereegranskat)
    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. Beställ onlineKöp publikationen >>
    Sidén, Per
    Linköpings universitet, Institutionen för datavetenskap, Statistik och maskininlärning. Linköpings universitet, Filosofiska fakulteten.
    Scalable Bayesian spatial analysis with Gaussian Markov random fields2020Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
    Abstract [sv]

    Tillförlitlig statistisk analys av spatiala data är viktigt inom många tillämpningar. Om inte korrekt hänsyn tas till spatial autokorrelation kan det ofta leda till felaktiga slutsatser. Samtidigt ökar ständigt storleken på de spatiala datamaterialen vilket utgör en stor beräkningsmässig utmaning, eftersom många standardmetoder för spatial analys är begränsade till några tusental datapunkter.

    I denna avhandling utforskar vi hur Gaussiska Markov-fält (eng: Gaussian Markov random fields, GMRF) kan användas för mer skalbara analyser av spatiala data. GMRF-modeller är nära besläktade med de ofta använda Gaussiska processerna, men har gleshetsegenskaper som gör dem beräkningsmässigt effektiva både vad gäller tids- och minnesåtgång. Det Bayesianska synsättet gör det möjligt att använda GMRF som en spatial prior som innefattar antagandet om långsam spatial variation och ger ett principiellt tillvägagångssätt för att skatta parametrar och propagera osäkerhet.

    Vi utvecklar nya algoritmer som gör det möjligt att använda GMRF-priors i 3D för den hjärnaktivitet som indirekt kan observeras i hjärnbilder framtagna med tekniken fMRI, som innehåller milliontals datapunkter. Vi visar att våra metoder är både snabbare och mer korrekta än tidigare forskning. En metod för att approximera utvalda element i den inversa precisionsmatrisen (dvs. kovariansmatrisen) framförs också, vilket är viktigt för att kunna evaluera osäkerheten i posteriorn. Vidare gör vi en koppling mellan GMRF och djupa neurala faltningsnätverk, som har använts framgångsrikt för mängder av bildrelaterade problem inom maskininlärning, vilket mynnar ut i en djup GMRF-modell. Slutligen visar vi hur GMRF kan användas i realtid av autonoma drönare för räddningsinsatser i katastrofområden för att modellera den spatiala fördelningen av skadade personer.

    Delarbeten
    1. Fast Bayesian whole-brain fMRI analysis with spatial 3D priors
    Öppna denna publikation i ny flik eller fönster >>Fast Bayesian whole-brain fMRI analysis with spatial 3D priors
    2017 (Engelska)Ingår i: NeuroImage, ISSN 1053-8119, E-ISSN 1095-9572, Vol. 146, s. 211-225Artikel i tidskrift (Refereegranskat) 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.

    Ort, förlag, år, upplaga, sidor
    Elsevier, 2017
    Nyckelord
    fMRI, Spatial priors, Variational Bayes, Markov chain Monte Carlo, Gaussian Markov random fields, General linear model
    Nationell ämneskategori
    Medicinteknik
    Identifikatorer
    urn:nbn:se:liu:diva-132945 (URN)10.1016/j.neuroimage.2016.11.040 (DOI)000394560700019 ()27876654 (PubMedID)2-s2.0-84999622353 (Scopus ID)
    Anmärkning

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

    Tillgänglig från: 2016-12-05 Skapad: 2016-12-05 Senast uppdaterad: 2020-06-29Bibliografiskt granskad
    2. Efficient Covariance Approximations for Large Sparse Precision Matrices
    Öppna denna publikation i ny flik eller fönster >>Efficient Covariance Approximations for Large Sparse Precision Matrices
    2018 (Engelska)Ingår i: Journal of Computational And Graphical Statistics, ISSN 1061-8600, E-ISSN 1537-2715, Vol. 27, nr 4, s. 898-909Artikel i tidskrift (Refereegranskat) 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.

    Ort, förlag, år, upplaga, sidor
    AMER STATISTICAL ASSOC, 2018
    Nyckelord
    Gaussian Markov random fields; Selected inversion; Sparse precision matrix; Spatial analysis; Stochastic approximation
    Nationell ämneskategori
    Sannolikhetsteori och statistik
    Identifikatorer
    urn:nbn:se:liu:diva-153715 (URN)10.1080/10618600.2018.1473782 (DOI)000453029500018 ()
    Anmärkning

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

    Tillgänglig från: 2019-01-07 Skapad: 2019-01-07 Senast uppdaterad: 2020-06-29
    3. Deep Gaussian Markov Random Fields
    Öppna denna publikation i ny flik eller fönster >>Deep Gaussian Markov Random Fields
    2020 (Engelska)Ingår i: Proceedings of the 37th International Conference on Machine Learning / [ed] Hal Daumé III, Aarti Singh, PMLR , 2020, Vol. 119, s. 8916-8926Konferensbidrag, Publicerat paper (Refereegranskat)
    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.

    Ort, förlag, år, upplaga, sidor
    PMLR, 2020
    Serie
    Proceedings of Machine Learning Research, ISSN 2640-3498 ; 119
    Nationell ämneskategori
    Sannolikhetsteori och statistik
    Identifikatorer
    urn:nbn:se:liu:diva-171582 (URN)
    Konferens
    International Conference on Machine Learning, 13-18 July 2020, Virtual
    Tillgänglig från: 2020-11-24 Skapad: 2020-11-24 Senast uppdaterad: 2020-11-24
    4. Real-Time Robotic Search using Structural Spatial Point Processes
    Öppna denna publikation i ny flik eller fönster >>Real-Time Robotic Search using Structural Spatial Point Processes
    Visa övriga...
    2020 (Engelska)Ingår i: 35TH UNCERTAINTY IN ARTIFICIAL INTELLIGENCE CONFERENCE (UAI 2019), Association For Uncertainty in Artificial Intelligence (AUAI) , 2020, Vol. 115, s. 995-1005Konferensbidrag, Publicerat paper (Refereegranskat)
    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.

    Ort, förlag, år, upplaga, sidor
    Association For Uncertainty in Artificial Intelligence (AUAI), 2020
    Serie
    Proceedings of Machine Learning Research (PMLR), E-ISSN 2640-3498 ; 115
    Nationell ämneskategori
    Data- och informationsvetenskap
    Identifikatorer
    urn:nbn:se:liu:diva-159698 (URN)000722423500092 ()2-s2.0-85084016675 (Scopus ID)
    Konferens
    Proceedings of the 35th Conference on Uncertainty in Artificial Intelligence (UAI 2019), Tel Aviv, Israel, July 22-25, 2019
    Anmärkning

    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

    Tillgänglig från: 2019-08-19 Skapad: 2019-08-19 Senast uppdaterad: 2023-04-05Bibliografiskt granskad
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  • 6.
    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, Göteborg, Sweden; 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.

    Ladda ner fulltext (pdf)
    fulltext
  • 7.
    Sidén, Per
    et al.
    Linköpings universitet, Institutionen för datavetenskap, Statistik och maskininlärning. Linköpings universitet, Tekniska fakulteten.
    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
    Linköpings universitet, Institutionen för medicinsk teknik, Avdelningen för medicinsk teknik. Linköpings universitet, Tekniska fakulteten. Linköpings universitet, Centrum för medicinsk bildvetenskap och visualisering, CMIV. Linköpings universitet, Institutionen för datavetenskap, Statistik och maskininlärning.
    Villani, Mattias
    Linköpings universitet, Institutionen för datavetenskap, Statistik och maskininlärning. Linköpings universitet, Filosofiska fakulteten. Department of Statistics, Stockholm University.
    Spatial 3D Matérn Priors for Fast Whole-Brain fMRI Analysis2021Ingår i: Bayesian Analysis, ISSN 1936-0975, E-ISSN 1931-6690, Vol. 16, nr 4, s. 1251-1278Artikel i tidskrift (Refereegranskat)
    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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  • 8.
    Sidén, Per
    et al.
    Linköpings universitet, Institutionen för datavetenskap, Statistik och maskininlärning. Linköpings universitet, Filosofiska fakulteten.
    Lindgren, Finn
    Univ Edinburgh, Scotland.
    Bolin, David
    Chalmers, Sweden; 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.

    Ladda ner fulltext (pdf)
    fulltext
  • 9.
    Sidén, Per
    et al.
    Linköpings universitet, Institutionen för datavetenskap, Statistik och maskininlärning. Linköpings universitet, Tekniska fakulteten.
    Lindsten, Fredrik
    Linköpings universitet, Institutionen för datavetenskap, Statistik och maskininlärning. Linköpings universitet, Tekniska fakulteten.
    Deep Gaussian Markov Random Fields2020Ingår i: Proceedings of the 37th International Conference on Machine Learning / [ed] Hal Daumé III, Aarti Singh, PMLR , 2020, Vol. 119, s. 8916-8926Konferensbidrag (Refereegranskat)
    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.

  • 10.
    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

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