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Without any assumptions about data generation, multiple causal models may explain our observations equally well. To avoid selecting a single arbitrary model that could result in unsafe decisions if it does not match reality, it is therefore…
Random matrix theory has become a cornerstone in modern statistics and data science, providing fundamental tools for understanding high-dimensional covariance structures. Within this framework, the Wishart matrix plays a central role in…
Causal representation learning aims to recover the latent causal variables and their causal relations, typically represented by directed acyclic graphs (DAGs), from low-level observations such as image pixels. A prevailing line of research…
Recent work on causal abstraction, in particular graphical approaches focusing on causal structure between clusters of variables, aims to summarize a high-dimensional causal structure in terms of a low-dimensional one. Existing methods for…
Gaussian graphical models are useful tools for conditional independence structure inference of multivariate random variables. Unfortunately, Bayesian inference of latent graph structures is challenging due to exponential growth of…
Modeling dependence in high dimensional systems has become an increasingly important topic. Most approaches rely on the assumption of a multivariate Gaussian distribution such as statistical models on directed acyclic graphs (DAGs). They…
In this paper, we first consider the parameter estimation of a multivariate random process distribution using multivariate Gaussian mixture law. The labels of the mixture are allowed to have a general probability law which gives the…
We discuss Bayesian inference for a known-mean Gaussian model with a compound symmetric variance-covariance matrix. Since the space of such matrices is a linear subspace of that of positive definite matrices, we utilize the methods of…
Social science theories often postulate causal relationships among a set of variables or events. Although directed acyclic graphs (DAGs) are increasingly used to represent these theories, their full potential has not yet been realized in…
Understanding the causal relationships between data variables can provide crucial insights into the construction of tabular datasets. Most existing causality learning methods typically focus on applying a single identifiable causal model,…
Distribution data refers to a data set where each sample is represented as a probability distribution, a subject area receiving burgeoning interest in the field of statistics. Although several studies have developed…
When inferring parameters from a Gaussian-distributed data set by computing a likelihood, a covariance matrix is needed that describes the data errors and their correlations. If the covariance matrix is not known a priori, it may be…
We propose a Bayesian approximate inference method for learning the dependence structure of a Gaussian graphical model. Using pseudo-likelihood, we derive an analytical expression to approximate the marginal likelihood for an arbitrary…
Graphical Gaussian models with edge and vertex symmetries were introduced by \citet{HojLaur:2008} who also gave an algorithm to compute the maximum likelihood estimate of the precision matrix for such models. In this paper, we take a…
Learning a faithful directed acyclic graph (DAG) from samples of a joint distribution is a challenging combinatorial problem, owing to the intractable search space superexponential in the number of graph nodes. A recent breakthrough…
Rectangular real $N \times (N + \nu)$ matrices $W$ with a Gaussian distribution appear very frequently in data analysis, condensed matter physics and quantum field theory. A central question concerns the correlations encoded in the spectral…
In the context of inferring a Bayesian network structure (directed acyclic graph, DAG for short), we devise a non-reversible continuous time Markov chain, the ``Causal Zig-Zag sampler'', that targets a probability distribution over classes…
Directed acyclic graphs (DAGs) are directed graphs in which there is no path from a vertex to itself. DAGs are an omnipresent data structure in computer science and the problem of counting the DAGs of given number of vertices and to sample…
In this paper, we develop a new approach to learning high-dimensional Poisson directed acyclic graphical (DAG) models from only observational data without strong assumptions such as faithfulness and strong sparsity. A key component of our…
In this paper, we propose a novel inference method for dynamic genetic networks which makes it possible to face with a number of time measurements n much smaller than the number of genes p. The approach is based on the concept of low order…