Related papers: Matching Criterion for Identifiability in Sparse F…
Despite the popularity of factor models with sparse loading matrices, little attention has been given to formally address identifiability of these models beyond standard rotation-based identification such as the positive lower triangular…
Sparse matrix factorization is the problem of approximating a matrix $\mathbf{Z}$ by a product of $J$ sparse factors $\mathbf{X}^{(J)} \mathbf{X}^{(J-1)} \ldots \mathbf{X}^{(1)}$. This paper focuses on identifiability issues that appear in…
We consider the estimation of a sparse factor model where the factor loading matrix is assumed sparse. The estimation problem is reformulated as a penalized M-estimation criterion, while the restrictions for identifying the factor loading…
Factor analysis is a statistical technique that explains correlations among observed random variables with the help of a smaller number of unobserved factors. In traditional full factor analysis, each observed variable is influenced by…
The model implied by factor score predictors does not reproduce the non-diagonal elements of the observed covariance matrix as well as the factor loadings. It is therefore investigated whether it is possible to estimate factor loadings for…
Bayesian sparse factor models have proven useful for characterizing dependence in multivariate data, but scaling computation to large numbers of samples and dimensions is problematic. We propose expandable factor analysis for scalable…
Generalized latent factor analysis not only provides a useful latent embedding approach in statistics and machine learning, but also serves as a widely used tool across various scientific fields, such as psychometrics, econometrics, and…
A variety of machine learning tasks---e.g., matrix factorization, topic modelling, and feature allocation---can be viewed as learning the parameters of a probability distribution over bipartite graphs. Recently, a new class of models for…
Factor analysis is a widely used technique for dimension reduction in high-dimensional data. However, a key challenge in factor models lies in the interpretability of the latent factors. One intuitive way to interpret these factors is…
Factor Analysis is a popular method for modeling dependence in multivariate data. However, determining the number of factors and obtaining a sparse orientation of the loadings are still major challenges. In this paper, we propose a…
Despite the popularity of factor models with sparse loading matrices, little attention has been given to formally address identifiability of these models beyond standard rotation-based identification such as the positive lower triangular…
There has been increased research interest in the subfield of sparse Bayesian factor analysis with shrinkage priors, which achieve additional sparsity beyond the natural parsimonity of factor models. In this spirit, we estimate the number…
This paper addresses the fundamental task of estimating covariance matrix functions for high-dimensional functional data/functional time series. We consider two functional factor structures encompassing either functional factors with scalar…
In this paper, we consider the nonstationary matrix-valued time series with common stochastic trends. Unlike the traditional factor analysis which flattens matrix observations into vectors, we adopt a matrix factor model in order to fully…
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 develop a factor analysis for mixed continuous and binary observed variables. To this end, we utilized a recently developed multivariate probability distribution for mixed-type random variables, the Gaussian-Grassmann distribution. In…
The bifactor model and its extensions are multidimensional latent variable models, under which each item measures up to one subdimension on top of the primary dimension(s). Despite their wide applications to educational and psychological…
Lifted probabilistic inference exploits symmetries in probabilistic graphical models to allow for tractable probabilistic inference with respect to domain sizes. To exploit symmetries in, e.g., factor graphs, it is crucial to identify…
Sparse latent multi-factor models have been used in many exploratory and predictive problems with high-dimensional multivariate observations. Because of concerns with identifiability, the latent factors are almost always assumed to be…
This paper studies the covariance matrix estimation for high-dimensional time series within a new framework that combines low-rank factor and latent variable-specific cluster structures. The popular methods based on assuming the sparse…