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Sparse models for high-dimensional linear regression and machine learning have received substantial attention over the past two decades. Model selection, or determining which features or covariates are the best explanatory variables, is…

Graph neural networks (GNNs) model nonlinear representations in graph data with applications in distributed agent coordination, control, and planning among others. Current GNN architectures assume ideal scenarios and ignore link…

In genome-wide prediction, independence of marker allele substitution effects is typically assumed; however, since early stages of this technology it has been known that nature points to correlated effects. In statistics, graphical models…

Interacting systems are prevalent in nature. It is challenging to accurately predict the dynamics of the system if its constituent components are analyzed independently. We develop a graph-based model that unveils the systemic interactions…

Statistical network models are useful for understanding the underlying formation mechanism and characteristics of complex networks. However, statistical models for \textit{signed networks} have been largely unexplored. In signed networks,…

We generalize the technique of smoothed analysis to distributed algorithms in dynamic network models. Whereas standard smoothed analysis studies the impact of small random perturbations of input values on algorithm performance metrics,…

Graph is a flexible and effective tool to represent complex structures in practice and graph neural networks (GNNs) have been shown to be effective on various graph tasks with randomly separated training and testing data. In real…

Multivariate time series forecasting is a challenging task because the data involves a mixture of long- and short-term patterns, with dynamic spatio-temporal dependencies among variables. Existing graph neural networks (GNN) typically model…

We consider the problem of learning a conditional Gaussian graphical model in the presence of latent variables. Building on recent advances in this field, we suggest a method that decomposes the parameters of a conditional Markov random…

Structural Causal Models (SCMs) offer a principled framework to reason about interventions and support out-of-distribution generalization, which are key goals in scientific discovery. However, the task of learning SCMs from observed data…

To date, the instability of prognostic predictors in a sparse high dimensional model, which hinders their clinical adoption, has received little attention. Stable prediction is often overlooked in favour of performance. Yet, stability…

In the context of multilevel longitudinal data, where sample units are collected in clusters, an important aspect that should be accounted for is the unobserved heterogeneity between sample units and between clusters. For this aim we…

We consider a binary response which is potentially affected by a set of continuous variables. Of special interest is the causal effect on the response due to an intervention on a specific variable. The latter can be meaningfully determined…

Linear non-Gaussian causal models postulate that each random variable is a linear function of parent variables and non-Gaussian exogenous error terms. We study identification of the linear coefficients when such models contain latent…

How to model distribution of sequential data, including but not limited to speech and human motions, is an important ongoing research problem. It has been demonstrated that model capacity can be significantly enhanced by introducing…

We present several new results on the feasibility of inferring the hidden states in strongly-connected trackable weak models. Here, a weak model is a directed graph in which each node is assigned a set of colors which may be emitted when…

This work is devoted to the almost sure stabilization of adaptive control systems that involve an unknown Markov chain. The control system displays continuous dynamics represented by differential equations and discrete events given by a…

Stability of recurrent models is closely linked with trainability, generalizability and in some applications, safety. Methods that train stable recurrent neural networks, however, do so at a significant cost to expressibility. We propose an…

Directed acyclic graphs (DAGs) are a popular framework to express multivariate probability distributions. Acyclic directed mixed graphs (ADMGs) are generalizations of DAGs that can succinctly capture much richer sets of conditional…

We consider the problem of learning causal directed acyclic graphs from an observational joint distribution. One can use these graphs to predict the outcome of interventional experiments, from which data are often not available. We show…