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In this paper, we explore the algebraic structures of solution spaces for Gaussian latent factor analysis when the population covariance matrix $\Sigma_x$ has an additional latent graphical constraint, namely, a latent star topology. In…
Factor Analysis (FA) is a technique of fundamental importance that is widely used in classical and modern multivariate statistics, psychometrics and econometrics. In this paper, we revisit the classical rank-constrained FA problem, which…
Graphical models and factor analysis are well-established tools in multivariate statistics. While these models can be both linked to structures exhibited by covariance and precision matrices, they are generally not jointly leveraged within…
Addressing selection bias in latent variable causal discovery is important yet underexplored, largely due to a lack of suitable statistical tools: While various tools beyond basic conditional independencies have been developed to handle…
Suppose we observe samples of a subset of a collection of random variables. No additional information is provided about the number of latent variables, nor of the relationship between the latent and observed variables. Is it possible to…
Our concern is selecting the concentration matrix's nonzero coefficients for a sparse Gaussian graphical model in a high-dimensional setting. This corresponds to estimating the graph of conditional dependencies between the variables. We…
We consider the problem of covariance matrix estimation in the presence of latent variables. Under suitable conditions, it is possible to learn the marginal covariance matrix of the observed variables via a tractable convex program, where…
How to obtain a graph from data samples is an important problem in graph signal processing. One way to formulate this graph learning problem is based on Gaussian maximum likelihood estimation, possibly under particular topology constraints.…
Optimization problems with rank constraints arise in many applications, including matrix regression, structured PCA, matrix completion and matrix decomposition problems. An attractive heuristic for solving such problems is to factorize the…
The tetrad constraint is a condition of which the satisfaction signals a rank reduction of a covariance submatrix and is used to design causal discovery algorithms that detects the existence of latent (unmeasured) variables, such as FOFC.…
The (constrained) minimization of a ratio of set functions is a problem frequently occurring in clustering and community detection. As these optimization problems are typically NP-hard, one uses convex or spectral relaxations in practice.…
Dimensionality reduction methods, such as principal component analysis (PCA) and factor analysis, are central to many problems in data science. There are, however, serious and well-understood challenges to finding robust low dimensional…
Latent or unobserved phenomena pose a significant difficulty in data analysis as they induce complicated and confounding dependencies among a collection of observed variables. Factor analysis is a prominent multivariate statistical modeling…
We consider general Gaussian latent tree models in which the observed variables are not restricted to be leaves of the tree. Extending related recent work, we give a full semi-algebraic description of the set of covariance matrices of any…
Despite the widespread application of latent factor analysis, existing methods suffer from the following weaknesses: requiring the number of factors to be known, lack of theoretical guarantees for learning the model structure, and…
We propose a combined model, which integrates the latent factor model and the logistic regression model, for the citation network. It is noticed that neither a latent factor model nor a logistic regression model alone is sufficient to…
We study the problem of learning latent variables in Gaussian graphical models. Existing methods for this problem assume that the precision matrix of the observed variables is the superposition of a sparse and a low-rank component. In this…
This paper addresses the problem of learning an undirected graph from data gathered at each nodes. Within the graph signal processing framework, the topology of such graph can be linked to the support of the conditional correlation matrix…
Recently, convex formulations of low-rank matrix factorization problems have received considerable attention in machine learning. However, such formulations often require solving for a matrix of the size of the data matrix, making it…
We develop Probabilistic Targeted Factor Analysis (PTFA), a likelihood-based framework for constructing latent factors that are explicitly targeted to variables of economic interest. PTFA provides a probabilistic foundation for Partial…