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In this paper we study the space of second- and third-order moment tensors of random vectors which satisfy a Linear Non-Gaussian Acyclic Model (LiNGAM). In such a causal model each entry $X_i$ of the random vector $X$ corresponds to a…
Directed Gaussian graphical models are statistical models that use a directed acyclic graph (DAG) to represent the conditional independence structures between a set of jointly normal random variables. The DAG specifies the model through…
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…
The paradigm of linear structural equation modeling readily allows one to incorporate causal feedback loops in the model specification. These appear as directed cycles in the common graphical representation of the models. However, the…
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…
Gaussian graphical models are semi-algebraic subsets of the cone of positive definite covariance matrices. They are widely used throughout natural sciences, computational biology and many other fields. Computing the vanishing ideal of the…
We consider graphical models based on a recursive system of linear structural equations. This implies that there is an ordering, $\sigma$, of the variables such that each observed variable $Y_v$ is a linear function of a variable specific…
In this paper we propose a new method to learn the underlying acyclic mixed graph of a linear non-Gaussian structural equation model given observational data. We build on an algorithm proposed by Wang and Drton, and we show that one can…
Inferring cause-effect relationships from observational data has gained significant attention in recent years, but most methods are limited to scalar random variables. In many important domains, including neuroscience, psychology, social…
Temporal graphs are graphs where the presence or properties of their vertices and edges change over time. When time is discrete, a temporal graph can be defined as a sequence of static graphs over a discrete time span, called lifetime, or…
Directed graphical models specify noisy functional relationships among a collection of random variables. In the Gaussian case, each such model corresponds to a semi-algebraic set of positive definite covariance matrices. The set is given…
We consider recovering causal structure from multivariate observational data. We assume the data arise from a linear structural equation model (SEM) in which the idiosyncratic errors are allowed to be dependent in order to capture possible…
Algebraic tools in statistics have recently been receiving special attention and a number of interactions between algebraic geometry and computational statistics have been rapidly developing. This paper presents another such connection,…
Time series graphical models have recently received considerable attention for characterizing (conditional) dependence structures in multivariate time series. In many applications, the multivariate series exhibit variable-partitioned…
Building on the theory of causal discovery from observational data, we study interactions between multiple (sets of) random variables in a linear structural equation model with non-Gaussian error terms. We give a correspondence between…
Structural equation models and Bayesian networks have been widely used to analyze causal relations between continuous variables. In such frameworks, linear acyclic models are typically used to model the datagenerating process of variables.…
Given a rooted tree $T$ on $n$ non-root leaves with colored and zeroed nodes, we construct a linear space $L_T$ of $n\times n$ symmetric matrices with constraints determined by the combinatorics of the tree. When $L_T$ represents the…
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…
A linear structural equation model relates random variables of interest and corresponding Gaussian noise terms via a linear equation system. Each such model can be represented by a mixed graph in which directed edges encode the linear…
We establish finite-sample guarantees for a polynomial-time algorithm for learning a nonlinear, nonparametric directed acyclic graphical (DAG) model from data. The analysis is model-free and does not assume linearity, additivity,…