Related papers: Identifiable and interpretable nonparametric facto…
Nearly all identifiability results in unsupervised representation learning inspired by, e.g., independent component analysis, factor analysis, and causal representation learning, rely on assumptions of additive independent noise or…
An old problem in multivariate statistics is that linear Gaussian models are often unidentifiable, i.e. some parameters cannot be uniquely estimated. In factor (component) analysis, an orthogonal rotation of the factors is unidentifiable,…
In this paper, we introduce a probabilistic model for learning nonnegative matrix factorization (NMF) that is commonly used for predicting missing values and finding hidden patterns in the data, in which the matrix factors are latent…
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…
Latent factor models are widely used to measure unobserved latent traits in social and behavioral sciences, including psychology, education, and marketing. When used in a confirmatory manner, design information is incorporated, yielding…
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…
In this letter, we propose a new identification criterion that guarantees the recovery of the low-rank latent factors in the nonnegative matrix factorization (NMF) model, under mild conditions. Specifically, using the proposed criterion, it…
We introduce a probabilistic model with implicit norm regularization for learning nonnegative matrix factorization (NMF) that is commonly used for predicting missing values and finding hidden patterns in the data, in which the matrix…
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…
Factor structures or interactive effects are convenient devices to incorporate latent variables in panel data models. We consider fixed effect estimation of nonlinear panel single-index models with factor structures in the unobservables,…
Factor analysis models are widely utilized in social and behavioral sciences, such as psychology, education, and marketing, to measure unobservable latent traits. In this article, we introduce a nonlinear structured latent factor analysis…
Latent variable models are popularly used to measure latent factors (e.g., abilities and personalities) from large-scale assessment data. Beyond understanding these latent factors, the covariate effect on responses controlling for latent…
Connectivity estimation is challenging in the context of high-dimensional data. A useful preprocessing step is to group variables into clusters, however, it is not always clear how to do so from the perspective of connectivity estimation.…
Nonnegative matrix factorization (NMF) has become a workhorse for signal and data analytics, triggered by its model parsimony and interpretability. Perhaps a bit surprisingly, the understanding to its model identifiability---the major…
Probabilistic programming provides the means to represent and reason about complex probabilistic models using programming language constructs. Even simple probabilistic programs can produce models with infinitely many variables. Factored…
This paper studies the problems of identifiability and estimation in high-dimensional nonparametric latent structure models. We introduce an identifiability theorem that generalizes existing conditions, establishing a unified framework…
Latent feature models (LFM)s are widely employed for extracting latent structures of data. While offering high, parameter estimation is difficult with LFMs because of the combinational nature of latent features, and non-identifiability is a…
We show how to incorporate information from labeled examples into nonnegative matrix factorization (NMF), a popular unsupervised learning algorithm for dimensionality reduction. In addition to mapping the data into a space of lower…
In recent years, diffusion models, and more generally score-based deep generative models, have achieved remarkable success in various applications, including image and audio generation. In this paper, we view diffusion models as an implicit…
This paper studies optimal estimation of large-dimensional nonlinear factor models. The key challenge is that the observed variables are possibly nonlinear functions of some latent variables where the functional forms are left unspecified.…