相关论文: Third-Order Moment Varieties of Linear Non-Gaussia…
Characteristic imsets are 0-1 vectors which correspond to Markov equivalence classes of directed acyclic graphs. The study of their convex hull, named the characteristic imset polytope, has led to new and interesting geometric perspectives…
We consider the problem of learning the underlying causal structure among a set of variables, which are assumed to follow a Bayesian network or, more specifically, a linear recursive structural equation model (SEM) with the associated…
In a traditional Gaussian graphical model, data homogeneity is routinely assumed with no extra variables affecting the conditional independence. In modern genomic datasets, there is an abundance of auxiliary information, which often gets…
In directed graphs, a cycle can be seen as a structure that allows its vertices to loop back to themselves, or as a structure that allows pairs of vertices to reach each other through distinct paths. We extend these concepts to temporal…
Graph-based causal discovery methods aim to capture conditional independencies consistent with the observed data and differentiate causal relationships from indirect or induced ones. Successful construction of graphical models of data…
We study the problem of learning a directed acyclic graph from data generated according to an additive, non-linear structural equation model with Gaussian noise. We express each non-linear function through a basis expansion, and derive a…
In this paper, we introduce a novel class of graphical models for representing time lag specific causal relationships and independencies of multivariate time series with unobserved confounders. We completely characterize these graphs and…
In modern experimental science, there is a common problem of estimating the coefficients of a linear regression in a context where the variables of interest cannot be observed simultaneously. When there is a categorical variable that is…
We study the adjacency spectrum of the toroidal three-dimensional queen graph $G_n$ on $(\mathbb{Z}_n)^3$. Since $G_n$ is a Cayley graph on an abelian group, its adjacency matrix is diagonalized by Fourier characters. For each frequency…
We uncover a hidden Gaussian ensemble inside each of the three circular ensembles of random matrices, which provide novel diagrammatic rules for the calculation of moments. The matrices involved are generic complex for $\beta=2$, complex…
Two directed graphs are called covariance equivalent if they induce the same set of covariance matrices, up to a Lebesgue measure zero set, on the random variables of their associated linear structural equation models. For acyclic graphs,…
Acyclic directed mixed graphs (ADMGs) are graphs that contain directed ($\rightarrow$) and bidirected ($\leftrightarrow$) edges, subject to the constraint that there are no cycles of directed edges. Such graphs may be used to represent the…
We consider the problem of inferring the conditional independence graph (CIG) of a high-dimensional stationary multivariate Gaussian time series. In a time series graph, each component of the vector series is represented by distinct node,…
Causal discovery is a fundamental problem with applications spanning various areas in science and engineering. It is well understood that solely using observational data, one can only orient the causal graph up to its Markov equivalence…
We extend the close interplay between continued fractions, orthogonal polynomials, and Gaussian quadrature rules to several variables in a special but natural setting which we characterize in terms of moment sequences. The crucial condition…
Graphical model selection is a seemingly impossible task when many pairs of variables are never jointly observed; this requires inference of conditional dependencies with no observations of corresponding marginal dependencies. This…
The objective of the paper is to identify and investigate all possible types of asymptotic behavior for the maximum likelihood estimators of the unknown parameters in the second-order linear stochastic ordinary differential equation driven…
An important task in data analysis is the discovery of causal relationships between observed variables. For continuous-valued data, linear acyclic causal models are commonly used to model the data-generating process, and the inference of…
We develop a class of nearest-neighbor mixture models that provide direct, computationally efficient, probabilistic modeling for non-Gaussian geospatial data. The class is defined over a directed acyclic graph, which implies conditional…
We study the generic identifiability of causal effects in linear non-Gaussian acyclic models (LiNGAM) with latent variables. We consider the problem in two main settings: When the causal graph is known a priori, and when it is unknown. In…