Related papers: Generalized infinite factorization models
The algebraic theory of third-order tensors under the $t$-product is naturally formulated over the complex field via Fourier block diagonalization. However, many applications require real-valued representations. In this paper, we…
Structural equation modeling (SEM) is a prevalent approach for studying constructs.Traditionally, these constructs are modeled as reflectively measured latent variables - common factors that account for the variance-covariance structure of…
Matrix factorization is a simple and effective solution to the recommendation problem. It has been extensively employed in the industry and has attracted much attention from the academia. However, it is unclear what the low-dimensional…
Estimates of the approximate factor model are increasingly used in empirical work. Their theoretical properties, studied some twenty years ago, also laid the ground work for analysis on large dimensional panel data models with cross-section…
Bottom-Up Hidden Tree Markov Model is a highly expressive model for tree-structured data. Unfortunately, it cannot be used in practice due to the intractable size of its state-transition matrix. We propose a new approximation which lies on…
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…
Humans have the innate capability to answer diverse questions, which is rooted in the natural ability to correlate different concepts based on their semantic relationships and decompose difficult problems into sub-tasks. On the contrary,…
Factorization machine (FM) is a popular machine learning model to capture the second order feature interactions. The optimal learning guarantee of FM and its generalized version is not yet developed. For a rank $k$ generalized FM of $d$…
Large tensor (multi-dimensional array) data are now routinely collected in a wide range of applications, due to modern data collection capabilities. Often such observations are taken over time, forming tensor time series. In this paper we…
Consider a regression or some regression-type model for a certain response variable where the linear predictor includes an ordered factor among the explanatory variables. The inclusion of a factor of this type can take place is a few…
The ability to represent complex high dimensional probability distributions in a compact form is one of the key insights in the field of graphical models. Factored representations are ubiquitous in machine learning and lead to major…
Resonance counting is an intuitive and widely used tool in Random Matrix Theory and Anderson Localization. Its undoubted advantage is its simplicity: in principle, it is easily applicable to any random matrix ensemble. On the downside, the…
Low-rank matrix factorization (MF) is an important technique in data science. The key idea of MF is that there exists latent structures in the data, by uncovering which we could obtain a compressed representation of the data. By factorizing…
Factorization algebras are local-to-global objects living on manifolds, and they arise naturally in mathematics and physics. Their local structure encompasses examples like associative algebras and vertex algebras; in these examples, their…
With the recent success of representation learning methods, which includes deep learning as a special case, there has been considerable interest in developing techniques that incorporate known physical constraints into the learned…
World models for environments with many objects face a combinatorial explosion of states: as the number of objects increases, the number of possible arrangements grows exponentially. In this paper, we learn to generalize over robotic…
This paper develops an approach to inference in a linear regression model when the number of potential explanatory variables is larger than the sample size. The approach treats each regression coefficient in turn as the interest parameter,…
Factor analysis is a flexible technique for assessment of multivariate dependence and codependence. Besides being an exploratory tool used to reduce the dimensionality of multivariate data, it allows estimation of common factors that often…
Factor models are widely used to reduce dimensionality in modeling high-dimensional data. However, there remains a need for models that can be reliably fit in modest sample sizes and are identifiable, interpretable, and flexible. To address…
This paper is divided into two parts. In the first part, we develop a general method for expressing ranks of matrix expressions that involve Moore-Penrose inverses, group inverses, Drazin inverses, as well as weighted Moore-Penrose inverses…