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Villani, Mattias
Alternative names
Publications (10 of 21) Show all publications
Munezero, P., Villani, M. & Kohn, R. (2023). Dynamic Mixture of Experts Models for Online Prediction. Technometrics, 65(2), 257-268
Open this publication in new window or tab >>Dynamic Mixture of Experts Models for Online Prediction
2023 (English)In: Technometrics, ISSN 0040-1706, E-ISSN 1537-2723, Vol. 65, no 2, p. 257-268Article in journal (Refereed) Published
Abstract [en]

A mixture of experts models the conditional density of a response variable using a mixture of regression models with covariate-dependent mixture weights. We extend the finite mixture of experts model by allowing the parameters in both the mixture components and the weights to evolve in time by following random walk processes. Inference for time-varying parameters in richly parameterized mixture of experts models is challenging. We propose a sequential Monte Carlo algorithm for online inference and based on a tailored proposal distribution built on ideas from linear Bayes methods and the EM algorithm. The method gives a unified treatment for mixtures with time-varying parameters, including the special case of static parameters. We assess the properties of the method on simulated data and on industrial data where the aim is to predict software faults in a continuously upgraded large-scale software project.

Place, publisher, year, edition, pages
TAYLOR & FRANCIS INC, 2023
Keywords
Bayesian sequential inference; Linear Bayes; Mixture models; Particle filtering; Sequential Monte Carlo
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:liu:diva-190621 (URN)10.1080/00401706.2022.2146755 (DOI)000893857500001 ()
Available from: 2022-12-19 Created: 2022-12-19 Last updated: 2023-11-09Bibliographically approved
Rodriguez Déniz, H., Villani, M. & Voltes-Dorta, A. (2022). A multilayered block network model to forecast large dynamic transportation graphs: An application to US air transport. Transportation Research Part C: Emerging Technologies, 137, Article ID 103556.
Open this publication in new window or tab >>A multilayered block network model to forecast large dynamic transportation graphs: An application to US air transport
2022 (English)In: Transportation Research Part C: Emerging Technologies, ISSN 0968-090X, E-ISSN 1879-2359, Vol. 137, article id 103556Article in journal (Refereed) Published
Abstract [en]

Dynamic transportation networks have been analyzed for years by means of static graph-based indicators in order to study the temporal evolution of relevant network components, and to reveal complex dependencies that would not be easily detected by a direct inspection of the data. This paper presents a state-of-the-art probabilistic latent network model to forecast multilayer dynamic graphs that are increasingly common in transportation and proposes a community-based extension to reduce the computational burden. Flexible time series analysis is obtained by modeling the probability of edges between vertices through latent Gaussian processes. The models and Bayesian inference are illustrated on a sample of 10-year data from four major airlines within the US air transportation system. Results show how the estimated latent parameters from the models are related to the airlines’ connectivity dynamics, and their ability to project the multilayer graph into the future for out-of-sample full network forecasts, while stochastic blockmodeling allows for the identification of relevant communities. Reliable network predictions would allow policy-makers to better understand the dynamics of the transport system, and help in their planning on e.g. route development, or the deployment of new regulations.

Place, publisher, year, edition, pages
Oxford, United Kingdom: Elsevier, 2022
Keywords
Transportation networks, Multilayer graphs, Air transport, Machine learning
National Category
Transport Systems and Logistics
Identifiers
urn:nbn:se:liu:diva-182829 (URN)10.1016/j.trc.2022.103556 (DOI)000777337100005 ()2-s2.0-85124142579 (Scopus ID)
Note

Funding: Wallenberg AI, Autonomous Systems and Software Program (WASP) - Knut and Alice Wallenberg Foundation, Sweden

Available from: 2022-02-09 Created: 2022-02-09 Last updated: 2023-01-20Bibliographically approved
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
Magnusson, M., Jonsson, L. & Villani, M. (2020). DOLDA: a regularized supervised topic model for high-dimensional multi-class regression. Computational statistics (Zeitschrift), 35(1), 175-201
Open this publication in new window or tab >>DOLDA: a regularized supervised topic model for high-dimensional multi-class regression
2020 (English)In: Computational statistics (Zeitschrift), ISSN 0943-4062, E-ISSN 1613-9658, Vol. 35, no 1, p. 175-201Article in journal (Refereed) Published
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.

Place, publisher, year, edition, pages
Springer, 2020
Keywords
Text classification, Latent Dirichlet Allocation, Horseshoe prior, Diagonal Orthant probit model, Interpretable models
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:liu:diva-159217 (URN)10.1007/s00180-019-00891-1 (DOI)000516561400012 ()2-s2.0-85067414496 (Scopus ID)
Note

Funding agencies: Aalto University

Available from: 2019-08-05 Created: 2019-08-05 Last updated: 2020-03-19Bibliographically approved
Wilzén, J., Eklund, A. & Villani, M. (2020). Physiological Gaussian process priors for the hemodynamics in fMRI analysis. Journal of Neuroscience Methods, 342, Article ID 108778.
Open this publication in new window or tab >>Physiological Gaussian process priors for the hemodynamics in fMRI analysis
2020 (English)In: Journal of Neuroscience Methods, ISSN 0165-0270, E-ISSN 1872-678X, Vol. 342, article id 108778Article in journal (Refereed) Published
Abstract [en]

Background: Inference from fMRI data faces the challenge that the hemodynamic system that relates neural activity to the observed BOLD fMRI signal is unknown.

New method: We propose a new Bayesian model for task fMRI data with the following features: (i) joint estimation of brain activity and the underlying hemodynamics, (ii) the hemodynamics is modeled non-parametrically with a Gaussian process (GP) prior guided by physiological information and (iii) the predicted BOLD is not necessarily generated by a linear time-invariant (LTI) system. We place a GP prior directly on the predicted BOLD response, rather than on the hemodynamic response function as in previous literature. This allows us to incorporate physiological information via the GP prior mean in aflexible way, and simultaneously gives us the nonparametric flexibility of the GP.

Results: Results on simulated data show that the proposed model is able to discriminate between active and non-active voxels also when the GP prior deviates from the true hemodynamics. Our modelfinds time varying dynamics when applied to real fMRI data.

Comparison with existing method(s): The proposed model is better at detecting activity in simulated data than standard models, without inflating the false positive rate. When applied to real fMRI data, our GP model in several cases finds brain activity where previously proposed LTI models does not.

Conclusions: We have proposed a new non-linear model for the hemodynamics in task fMRI, that is able to detect active voxels, and gives the opportunity to ask new kinds of questions related to hemodynamics.

Place, publisher, year, edition, pages
Elsevier, 2020
Keywords
Bayesian inference, MCMC, fMRI, Hemodynamics, Gaussian processes, Misspecification
National Category
Probability Theory and Statistics Medical Image Processing
Identifiers
urn:nbn:se:liu:diva-167230 (URN)10.1016/j.jneumeth.2020.108778 (DOI)000548505700004 ()
Funder
Swedish Research Council, 20135229
Note

Funding agencies: Swedish Research Council (Vetenskapsradet)Swedish Research Council [2013-5229]; Center for Industrial Information Technology (CENIIT) at Linkoping University

Available from: 2020-06-29 Created: 2020-06-29 Last updated: 2021-05-29
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
Magnusson, M., Jonsson, L., Villani, M. & Broman, D. (2018). Sparse Partially Collapsed MCMC for Parallel Inference in Topic Models. Journal of Computational And Graphical Statistics, 27(2), 449-463
Open this publication in new window or tab >>Sparse Partially Collapsed MCMC for Parallel Inference in Topic Models
2018 (English)In: Journal of Computational And Graphical Statistics, ISSN 1061-8600, E-ISSN 1537-2715, Vol. 27, no 2, p. 449-463Article in journal (Refereed) Published
Abstract [en]

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

Place, publisher, year, edition, pages
Taylor & Francis, 2018
Keywords
Bayesian inference, Gibbs sampling, Latent Dirichlet Allocation, Massive Data Sets, Parallel Computing, Computational complexity
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:liu:diva-140872 (URN)10.1080/10618600.2017.1366913 (DOI)000435688200018 ()
Funder
Swedish Foundation for Strategic Research , SSFRIT 15-0097
Available from: 2017-09-13 Created: 2017-09-13 Last updated: 2022-04-11Bibliographically approved
Quiroz, M., Tran, M.-N., Villani, M. & Kohn, R. (2018). Speeding up MCMC by Delayed Acceptance and Data Subsampling. Journal of Computational And Graphical Statistics, 27(1), 12-22
Open this publication in new window or tab >>Speeding up MCMC by Delayed Acceptance and Data Subsampling
2018 (English)In: Journal of Computational And Graphical Statistics, ISSN 1061-8600, E-ISSN 1537-2715, Vol. 27, no 1, p. 12-22Article in journal (Refereed) Published
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.

Place, publisher, year, edition, pages
Taylor & Francis Group, 2018
Keywords
Bayesian inference, Delayed acceptance MCMC, Large data, Markov chain Monte Carlo, Survey sampling
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:liu:diva-140873 (URN)10.1080/10618600.2017.1307117 (DOI)000430484300002 ()2-s2.0-85026419157 (Scopus ID)
Funder
Swedish Foundation for Strategic Research , RIT 15-0097
Note

Funding agencies: VINNOVA grant [2010-02635]; Business School Pilot Research grant; Swedish Foundation for Strategic Research [RIT 15-0097]; Australian Research Council Centre of Excellence grant [CE140100049]

Available from: 2017-09-13 Created: 2017-09-13 Last updated: 2019-12-30Bibliographically 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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