Related papers: Dimensions of Higher Order Factor Analysis Models

Clustering and estimating cluster means are core problems in statistics and machine learning, with k-means and Expectation Maximization (EM) being two widely used algorithms. In this work, we provide a theoretical explanation for the…

This paper provides a unified framework for analyzing tensor estimation problems that allow for nonlinear observations, heteroskedastic noise, and covariate information. We study a general class of high-dimensional models where each…

We review Quasi Maximum Likelihood estimation of factor models for high-dimensional panels of time series. We consider two cases: (1) estimation when no dynamic model for the factors is specified (Bai and Li, 2012, 2016); (2) estimation…

Higher-order tensor datasets arise commonly in recommendation systems, neuroimaging, and social networks. Here we develop probable methods for estimating a possibly high rank signal tensor from noisy observations. We consider a generative…

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…

In this paper, we develop new statistical theory for probabilistic principal component analysis models in high dimensions. The focus is the estimation of the noise variance, which is an important and unresolved issue when the number of…

This work considers estimation and forecasting in a multivariate, possibly high-dimensional count time series model constructed from a transformation of a latent Gaussian dynamic factor series. The estimation of the latent model parameters…

This paper introduces a Projected Principal Component Analysis (Projected-PCA), which employs principal component analysis to the projected (smoothed) data matrix onto a given linear space spanned by covariates. When it applies to…

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…

Factor modeling is a powerful statistical technique that permits to capture the common dynamics in a large panel of data with a few latent variables, or factors, thus alleviating the curse of dimensionality. Despite its popularity and…

As is known, factor analysis is a popular method to reduce dimension for high-dimensional data. For matrix data, the dimension reduction can be more effectively achieved through both row and column directions. In this paper, we introduce a…

In a very high-dimensional vector space, two randomly-chosen vectors are almost orthogonal with high probability. Starting from this observation, we develop a statistical factor model, the random factor model, in which factors are chosen at…

We consider tensor factorizations based on sparse measurements of the components of relatively high rank tensors. The measurements are designed in a way that the underlying graph of interactions is a random graph. The setup will be useful…

Participation factors (PFs) quantify the interaction between system modes and state variables, and they play a crucial role in various applications such as modal analysis, model reduction, and control design. With increasing system…

Matrix-variate data of high dimensions are frequently observed in finance and economics, spanning extended time periods, such as the long-term data on international trade flows among numerous countries. To address potential structural…

This paper considers the maximum likelihood estimation of factor models of high dimension, where the number of variables (N) is comparable with or even greater than the number of observations (T). An inferential theory is developed. We…

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…

Motivated by Tucker tensor decomposition, this paper imposes low-rank structures to the column and row spaces of coefficient matrices in a multivariate infinite-order vector autoregression (VAR), which leads to a supervised factor model…

In this paper, we study a new two-way factor model for high-dimensional matrix-variate time series. To estimate the number of factors in this two-way factor model, we decompose the series into two parts: one being a non-weakly correlated…

Tensor models are a generalization of matrix models (their graphs being dual to higher-dimensional triangulations) and, in their colored version, admit a 1/N expansion and a continuum limit. We introduce a new class of colored tensor models…