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A regime-switching multivariate time series model which is closed under margins is built. The model imposes a restriction on all lower-dimensional sub-processes to follow a regime-switching process sharing the same latent regime sequence…

Latent variable models are powerful statistical tools that can uncover relevant variation between patients or cells, by inferring unobserved hidden states from observable high-dimensional data. A major shortcoming of current methods,…

We present a compartmentalized approach to finding the maximum a-posteriori (MAP) estimate of a latent time series that obeys a dynamic stochastic model and is observed through noisy measurements. We specifically consider modern signal…

Multivariate regression model is a natural generalization of the classical univari- ate regression model for fitting multiple responses. In this paper, we propose a high- dimensional multivariate conditional regression model for…

A Markov network characterizes the conditional independence structure, or Markov property, among a set of random variables. Existing work focuses on specific families of distributions (e.g., exponential families) and/or certain structures…

In an era of unprecedented deluge of (mostly unstructured) data, graphs are proving more and more useful, across the sciences, as a flexible abstraction to capture complex relationships between complex objects. One of the main challenges…

We introduce a novel class of graphical models, termed profile graphical models, that represent, within a single graph, how an external factor influences the dependence structure of a multivariate set of variables. This class is quite…

This work targets the identification of a class of models for hybrid dynamical systems characterized by nonlinear autoregressive exogenous (NARX) components, with finite-dimensional polynomial expansions, and by a Markovian switching…

Recursive max-linear vectors model causal dependence between node variables by a structural equation model, expressing each node variable as a max-linear function of its parental nodes in a directed acyclic graph (DAG) and some exogenous…

With a sequence of regressions, one may generate joint probability distributions. One starts with a joint, marginal distribution of context variables having possibly a concentration graph structure and continues with an ordered sequence of…

Directed acyclic graphs (DAGs) with hidden variables are often used to characterize causal relations between variables in a system. When some variables are unobserved, DAGs imply a notoriously complicated set of constraints on the…

Sparse model selection is ubiquitous from linear regression to graphical models where regularization paths, as a family of estimators upon the regularization parameter varying, are computed when the regularization parameter is unknown or…

The perceived advantage of machine learning (ML) models is that they are flexible and can incorporate a large number of features. However, many of these are typically correlated or dependent, and incorporating all of them can hinder model…

The power of sparse signal modeling with learned over-complete dictionaries has been demonstrated in a variety of applications and fields, from signal processing to statistical inference and machine learning. However, the statistical…

In this thesis we discuss machine learning methods performing automated variable selection for learning sparse predictive models. There are multiple reasons for promoting sparsity in the predictive models. By relying on a limited set of…

We study a class of conditional independence models for discrete data with the property that one or more log-linear interactions are defined within two different marginal distributions and then constrained to 0; all the conditional…

We consider deep multivariate models for heterogeneous collections of random variables. In the context of computer vision, such collections may e.g. consist of images, segmentations, image attributes, and latent variables. When developing…

We consider supervised learning problems where the features are embedded in a graph, such as gene expressions in a gene network. In this context, it is of much interest to automatically select a subgraph with few connected components; by…

State-space models (SSMs) are a powerful statistical tool for modelling time-varying systems via a latent state. In these models, the latent state is never directly observed. Instead, a sequence of data points related to the state are…

A semi-parametric, non-linear regression model in the presence of latent variables is introduced. These latent variables can correspond to unmodeled phenomena or unmeasured agents in a complex networked system. This new formulation allows…