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We introduce Causal Computational Asymmetry (CCA), a principle for causal direction identification based on optimization dynamics in which one neural network is trained to predict $Y$ from $X$ and another to predict $X$ from $Y$, and the…

We consider the problem of recovering a signal observed in Gaussian noise. If the set of signals is convex and compact, and can be specified beforehand, one can use classical linear estimators that achieve a risk within a constant factor of…

Numerical simulation is powerful to study nonlinear solid mechanics problems. However, mesh-based or particle-based numerical methods suffer from the common shortcoming of being time-consuming, particularly for complex problems with…

Developing suitable approximate models for analyzing and simulating complex nonlinear systems is practically important. This paper aims at exploring the skill of a rich class of nonlinear stochastic models, known as the conditional Gaussian…

Causal discovery methods are intrinsically constrained by the set of assumptions needed to ensure structure identifiability. Moreover additional restrictions are often imposed in order to simplify the inference task: this is the case for…

We introduce priors and algorithms to perform Bayesian inference in Gaussian models defined by acyclic directed mixed graphs. Such a class of graphs, composed of directed and bi-directed edges, is a representation of conditional…

We study the problem of high-dimensional covariance estimation under the constraint that the partial correlations are nonnegative. The sign constraints dramatically simplify estimation: the Gaussian maximum likelihood estimator is well…

We propose a penalized pseudo-likelihood criterion to estimate the graph of conditional dependencies in a discrete Markov random field that can be partially observed. We prove the convergence of the estimator in the case of a finite or…

Existing approaches to differentiable structure learning of directed acyclic graphs (DAGs) rely on strong identifiability assumptions in order to guarantee that global minimizers of the acyclicity-constrained optimization problem identifies…

In this study, we present a multi-class graphical Bayesian predictive classifier that incorporates the uncertainty in the model selection into the standard Bayesian formalism. For each class, the dependence structure underlying the observed…

A class of distributed systems with a cyclic interconnection structure is considered. These systems arise in several biochemical applications and they can undergo diffusion driven instability which leads to a formation of spatially…

The graphical structure of Probabilistic Graphical Models (PGMs) represents the conditional independence (CI) relations that hold in the modeled distribution. Every separator in the graph represents a conditional independence relation in…

This chapter presents specific aspects of Gaussian process modeling in the presence of complex noise. Starting from the standard homoscedastic model, various generalizations from the literature are presented: input varying noise variance,…

Causal discovery based on Independent Component Analysis (ICA) has achieved remarkable success through the LiNGAM framework, which exploits non-Gaussianity and independence of noise variables to identify causal order. However, classical…

We propose a novel graphical model selection (GMS) scheme for high-dimensional stationary time series or discrete time process. The method is based on a natural generalization of the graphical LASSO (gLASSO), introduced originally for GMS…

This paper considers the problem of robust adaptive efficient estimating of a periodic function in a continuous time regression model with the dependent noises given by a general square integrable semimartingale with a conditionally…

The complex Gaussian distribution has been widely used as a fundamental spectral and noise model in signal processing and communication. However, its Gaussian structure often limits its ability to represent the diverse amplitude…

We propose a joint order-based scoring framework for causal structure learning of directed acyclic graph (DAG) models under heterogeneous data settings. We show that leveraging heterogeneity improves the accuracy of causal ordering…

Statistical identification of possibly non-fundamental SVARMA models requires structural errors: (i) to be an i.i.d process, (ii) to be mutually independent across components, and (iii) each of them must be non-Gaussian distributed. Hence,…

We consider the problem of learning causal models from observational data generated by linear non-Gaussian acyclic causal models with latent variables. Without considering the effect of latent variables, one usually infers wrong causal…