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Sidén, Per
Publications (7 of 7) Show all publications
Oskarsson, J., Sidén, P. & Lindsten, F. (2022). Scalable Deep Gaussian Markov Random Fields for General Graphs. In: Kamalika Chaudhuri, Stefanie Jegelka, Le Song, Csaba Szepesvari, Gang Niu, Sivan Sabato (Ed.), Proceedings of the 39th International Conference on Machine Learning: . Paper presented at The 39th International Conference on Machine Learning, ICML, 17-23 July 2022, Baltimore, Maryland, USA (pp. 17117-17137).
Open this publication in new window or tab >>Scalable Deep Gaussian Markov Random Fields for General Graphs
2022 (English)In: 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, Published 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.

Series
Proceedings of Machine Learning Research, ISSN 2640-3498 ; 162
Keywords
machine learning, graphs, gmrf, deep gmrf, variational inference, gaussian, markov random field
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:liu:diva-187178 (URN)000900064907012 ()
Conference
The 39th International Conference on Machine Learning, ICML, 17-23 July 2022, Baltimore, Maryland, USA
Funder
Wallenberg AI, Autonomous Systems and Software Program (WASP)ELLIIT - The Linköping‐Lund Initiative on IT and Mobile CommunicationsSwedish Research Council, 2020-04122
Available from: 2022-08-10 Created: 2022-08-10 Last updated: 2023-05-10
Sidén, P., Lindgren, F., Bolin, D., Eklund, A. & Villani, M. (2021). Spatial 3D Matérn Priors for Fast Whole-Brain fMRI Analysis. Bayesian Analysis, 16(4), 1251-1278
Open this publication in new window or tab >>Spatial 3D Matérn Priors for Fast Whole-Brain fMRI Analysis
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2021 (English)In: Bayesian Analysis, ISSN 1936-0975, E-ISSN 1931-6690, Vol. 16, no 4, p. 1251-1278Article in journal (Refereed) Published
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.

Place, publisher, year, edition, pages
INT SOC BAYESIAN ANALYSIS, 2021
Keywords
spatial priors, Gaussian Markov random fields, fMRI, spatiotemporal modeling, efficient computation
National Category
Probability Theory and Statistics Radiology, Nuclear Medicine and Medical Imaging
Identifiers
urn:nbn:se:liu:diva-178090 (URN)10.1214/21-BA1283 (DOI)000754390900008 ()
Funder
Swedish Research Council, 2013-5229Swedish Research Council, 2016-04187EU, Horizon 2020, 640171
Note

Funding: Swedish Research Council (Vetenskapsadet)Swedish Research Council [2013-5229, 2016-04187]; European Unions Horizon 2020 Programme for Research and Innovation [640171]; Center for Industrial Information Technology (CENIIT) at Linkoping University

Available from: 2021-07-29 Created: 2021-07-29 Last updated: 2022-03-15
Abramian, D., Sidén, P., Knutsson, H., Villani, M. & Eklund, A. (2020). Anatomically Informed Bayesian Spatial Priors for FMRI Analysis. In: IEEE (Ed.), ISBI 2020: IEEE International Symposium on Biomedical Imaging. Paper presented at IEEE 17th International Symposium on Biomedical Imaging (ISBI), Iowa City, IA, USA, 3-7 April 2020. IEEE
Open this publication in new window or tab >>Anatomically Informed Bayesian Spatial Priors for FMRI Analysis
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2020 (English)In: ISBI 2020: IEEE International Symposium on Biomedical Imaging / [ed] IEEE, IEEE, 2020Conference paper, Published 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.

Place, publisher, year, edition, pages
IEEE, 2020
Series
IEEE International Symposium on Biomedical Imaging, ISSN 1945-7928, E-ISSN 1945-8452
Keywords
Bayesian statistics, functional MRI, activation mapping, adaptive smoothing
National Category
Medical Image Processing
Identifiers
urn:nbn:se:liu:diva-165856 (URN)10.1109/ISBI45749.2020.9098342 (DOI)000578080300208 ()978-1-5386-9330-8 (ISBN)
Conference
IEEE 17th International Symposium on Biomedical Imaging (ISBI), Iowa City, IA, USA, 3-7 April 2020
Funder
Swedish Research Council, 2017- 04889
Note

Funding agencies:  Swedish Research CouncilSwedish Research Council [201704889]; Center for Industrial Information Technology (CENIIT) at Linkoping University

Available from: 2020-05-29 Created: 2020-05-29 Last updated: 2023-03-31Bibliographically approved
Sidén, P. & Lindsten, F. (2020). Deep Gaussian Markov Random Fields. In: Hal Daumé III, Aarti Singh (Ed.), Proceedings of the 37th International Conference on Machine Learning: . Paper presented at International Conference on Machine Learning, 13-18 July 2020, Virtual (pp. 8916-8926). PMLR, 119
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
Andersson, O., Sidén, P., Dahlin, J., Doherty, P. & Villani, M. (2020). Real-Time Robotic Search using Structural Spatial Point Processes. In: 35TH UNCERTAINTY IN ARTIFICIAL INTELLIGENCE CONFERENCE (UAI 2019): . Paper presented at Proceedings of the 35th Conference on Uncertainty in Artificial Intelligence (UAI 2019), Tel Aviv, Israel, July 22-25, 2019 (pp. 995-1005). Association For Uncertainty in Artificial Intelligence (AUAI), 115
Open this publication in new window or tab >>Real-Time Robotic Search using Structural Spatial Point Processes
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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
Sidén, P. (2020). Scalable Bayesian spatial analysis with Gaussian Markov random fields. (Doctoral dissertation). Linköping: Linköping University Electronic Press
Open this publication in new window or tab >>Scalable Bayesian spatial analysis with Gaussian Markov random fields
2020 (English)Doctoral thesis, comprehensive summary (Other academic)
Alternative title[sv]
Skalbar Bayesiansk spatial analys med Gaussiska Markov-fält
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.

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.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2020. p. 53
Series
Linköping Studies in Arts and Sciences, ISSN 0282-9800 ; 790Linköping Studies in Statistics, ISSN 1651-1700 ; 15
Keywords
Spatial statistics, Bayesian statistics, Gaussian Markov random fields, fMRI, Machine learning, Spatial statistik, Bayesiansk statistik, Gaussiska Markov-fält, fMRI, Maskininlärning
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:liu:diva-165872 (URN)10.3384/diss.diva-165872 (DOI)9789179298180 (ISBN)
Public defence
2020-09-18, Ada Lovelace, B Building, Campus Valla, Linköping, 10:15 (English)
Opponent
Supervisors
Available from: 2020-08-17 Created: 2020-06-01 Last updated: 2020-11-24Bibliographically approved
Gu, X., Sidén, P., Wegmann, B., Eklund, A., Villani, M. & Knutsson, H. (2017). Bayesian Diffusion Tensor Estimation with Spatial Priors. In: CAIP 2017: Computer Analysis of Images and Patterns. Paper presented at International Conference on Computer Analysis of Images and Patterns (pp. 372-383). , 10424
Open this publication in new window or tab >>Bayesian Diffusion Tensor Estimation with Spatial Priors
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2017 (English)In: CAIP 2017: Computer Analysis of Images and Patterns, 2017, Vol. 10424, p. 372-383Conference paper, Published 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.

Series
Lecture Notes in Computer Science, ISSN 0302-9743, E-ISSN 1611-3349 ; 10424
Keywords
Spatial regularization, Diffusion tensor, Spatial priors Markov chain, Monte Carlo Fractional anisotropy
National Category
Medical Engineering
Identifiers
urn:nbn:se:liu:diva-139844 (URN)10.1007/978-3-319-64689-3_30 (DOI)000432085900030 ()978-3-319-64689-3 (ISBN)978-3-319-64688-6 (ISBN)
Conference
International Conference on Computer Analysis of Images and Patterns
Note

Funding agencies: Information Technology for European Advancement (ITEA) 3 Project BENEFIT (better effectiveness and efficiency by measuring and modelling of interventional therapy); Swedish Research Council [2015-05356, 2013-5229]; National Institute of Dental and Craniof

Available from: 2017-08-17 Created: 2017-08-17 Last updated: 2019-11-19
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