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Due to the wide range of timescales that are present in macromolecular systems, hierarchical multiscale strategies are necessary for their computational study. Coarse-graining (CG) allows to establish a link between different system…

The estimator of a causal directed acyclic graph (DAG) with the PC algorithm is known to be consistent based on independent and identically distributed samples. In this paper, we consider the scenario when the multivariate samples are…

This paper considers the problem of learning, from samples, the dependency structure of a system of linear stochastic differential equations, when some of the variables are latent. In particular, we observe the time evolution of some…

Ordered sequences of univariate or multivariate regressions provide statistical models for analysing data from randomized, possibly sequential interventions, from cohort or multi-wave panel studies, but also from cross-sectional or…

Constraint programming (CP) is a powerful technique for solving constraint satisfaction and optimization problems. In CP solvers, the variable ordering strategy used to select which variable to explore first in the solving process has a…

Autoregressive models enable tractable sampling from learned probability distributions, but their performance critically depends on the variable ordering used in the factorization via complexities of the resulting conditional distributions.…

We introduce a new dependence order, termed the conditional convex order, whose minimal and maximal elements characterize independence and perfect dependence. Moreover, it characterizes conditional independence, satisfies information…

Many questions in science center around the fundamental problem of understanding causal relationships. However, most constraint-based causal discovery algorithms, including the well-celebrated PC algorithm, often incur an exponential number…

Graphical models are widely used in diverse application domains to model the conditional dependencies amongst a collection of random variables. In this paper, we consider settings where the graph structure is covariate-dependent, and…

We consider the computation by simulation and neural net regression of conditional expectations, or more general elicitable statistics, of functionals of processes $(X, Y )$. Here an exogenous component $Y$ (Markov by itself) is…

High-dimensional networks play a key role in understanding complex relationships. These relationships are often dynamic in nature and can change with multiple external factors (e.g., time and groups). Methods for estimating graphical models…

Causality is essential for understanding complex systems, such as the economy, the brain, and the climate. Constructing causal graphs often relies on either data-driven or expert-driven approaches, both fraught with challenges. The former…

Constraint-based methods are one of the main approaches for causal structure learning that are particularly valued as they are asymptotically guaranteed to find a structure that is Markov equivalent to the causal graph of the system. On the…

Graph Neural Networks (GNN) have recently gained popularity in the forecasting domain due to their ability to model complex spatial and temporal patterns in tasks such as traffic forecasting and region-based demand forecasting. Most of…

Enhancing node-level Out-Of-Distribution (OOD) generalization on graphs remains a crucial area of research. In this paper, we develop a Structural Causal Model (SCM) to theoretically dissect the performance of two prominent invariant…

Max-linear Bayesian networks (MLBNs) are a relatively recent class of structural equation models which arise when the random variables involved have heavy-tailed distributions. Unlike most directed graphical models, MLBNs are typically not…

We consider the problem of learning the causal MAG of a system from observational data in the presence of latent variables and selection bias. Constraint-based methods are one of the main approaches for solving this problem, but the…

It is a long-standing question to discover causal relations among a set of variables in many empirical sciences. Recently, Reinforcement Learning (RL) has achieved promising results in causal discovery from observational data. However,…

Structure learning of Gaussian graphical models is an extensively studied problem in the classical multivariate setting where the sample size n is larger than the number of random variables p, as well as in the more challenging setting when…

Dynamic Bayesian networks have been well explored in the literature as discrete-time models: however, their continuous-time extensions have seen comparatively little attention. In this paper, we propose the first constraint-based algorithm…