Sparsity-Promoting Bayesian Dynamic Linear Models

Sparsity-promoting priors have become increasingly popular over recent years due to an increased number of regression and classification applications involving a large number of predictors. In time series applications where observations are collected over time, it is often unrealistic to assume that the underlying sparsity pattern is fixed. We propose here an original class of flexible Bayesian linear models for dynamic sparsity modelling. The proposed class of models expands upon the existing Bayesian literature on sparse regression using generalized multivariate hyperbolic distributions. The properties of the models are explored through both analytic results and simulation studies. We demonstrate the model on a financial application where it is shown that it accurately represents the patterns seen in the analysis of stock and derivative data, and is able to detect major events by filtering an artificial portfolio of assets

A sparse multinomial probit model for classification

A recent development in penalized probit modelling using a hierarchical Bayesian approach has led to a sparse binomial (two-class) probit classifier that can be trained via an EM algorithm. A key advantage of the formulation is that no tuning of hyperparameters relating to the penalty is needed thus simplifying the model selection process. The resulting model demonstrates excellent classification performance and a high degree of sparsity when used as a kernel machine. It is, however, restricted to the binary classification problem and can only be used in the multinomial situation via a one-against-all or one-against-many strategy. To overcome this, we apply the idea to the multinomial probit model. This leads to a direct multi-classification approach and is shown to give a sparse solution with accuracy and sparsity comparable with the current state-of-the-art. Comparative numerical benchmark examples are used to demonstrate the method

Sparse Linear Identifiable Multivariate Modeling

In this paper we consider sparse and identifiable linear latent variable (factor) and linear Bayesian network models for parsimonious analysis of multivariate data. We propose a computationally efficient method for joint parameter and model inference, and model comparison. It consists of a fully Bayesian hierarchy for sparse models using slab and spike priors (two-component delta-function and continuous mixtures), non-Gaussian latent factors and a stochastic search over the ordering of the variables. The framework, which we call SLIM (Sparse Linear Identifiable Multivariate modeling), is validated and bench-marked on artificial and real biological data sets. SLIM is closest in spirit to LiNGAM (Shimizu et al., 2006), but differs substantially in inference, Bayesian network structure learning and model comparison. Experimentally, SLIM performs equally well or better than LiNGAM with comparable computational complexity. We attribute this mainly to the stochastic search strategy used, and to parsimony (sparsity and identifiability), which is an explicit part of the model. We propose two extensions to the basic i.i.d. linear framework: non-linear dependence on observed variables, called SNIM (Sparse Non-linear Identifiable Multivariate modeling) and allowing for correlations between latent variables, called CSLIM (Correlated SLIM), for the temporal and/or spatial data. The source code and scripts are available from http://cogsys.imm.dtu.dk/slim/.Comment: 45 pages, 17 figure

Regularization and Bayesian Learning in Dynamical Systems: Past, Present and Future

Regularization and Bayesian methods for system identification have been repopularized in the recent years, and proved to be competitive w.r.t. classical parametric approaches. In this paper we shall make an attempt to illustrate how the use of regularization in system identification has evolved over the years, starting from the early contributions both in the Automatic Control as well as Econometrics and Statistics literature. In particular we shall discuss some fundamental issues such as compound estimation problems and exchangeability which play and important role in regularization and Bayesian approaches, as also illustrated in early publications in Statistics. The historical and foundational issues will be given more emphasis (and space), at the expense of the more recent developments which are only briefly discussed. The main reason for such a choice is that, while the recent literature is readily available, and surveys have already been published on the subject, in the author's opinion a clear link with past work had not been completely clarified.Comment: Plenary Presentation at the IFAC SYSID 2015. Submitted to Annual Reviews in Contro

Interpretable Subgroup Discovery in Treatment Effect Estimation with Application to Opioid Prescribing Guidelines

The dearth of prescribing guidelines for physicians is one key driver of the current opioid epidemic in the United States. In this work, we analyze medical and pharmaceutical claims data to draw insights on characteristics of patients who are more prone to adverse outcomes after an initial synthetic opioid prescription. Toward this end, we propose a generative model that allows discovery from observational data of subgroups that demonstrate an enhanced or diminished causal effect due to treatment. Our approach models these sub-populations as a mixture distribution, using sparsity to enhance interpretability, while jointly learning nonlinear predictors of the potential outcomes to better adjust for confounding. The approach leads to human-interpretable insights on discovered subgroups, improving the practical utility for decision suppor