Related papers: Matrix Factor Analysis: From Least Squares to Iter…
Given a collection of feature maps indexed by a set $\mathcal{T}$, we study the performance of empirical risk minimization (ERM) on regression problems with square loss over the union of the linear classes induced by these feature maps.…
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…
We examine a special case of the multilevel factor model, with covariance given by multilevel low rank (MLR) matrix~\cite{parshakova2023factor}. We develop a novel, fast implementation of the expectation-maximization algorithm, tailored for…
High-dimensional data analysis using traditional models suffers from overparameterization. Two types of techniques are commonly used to reduce the number of parameters - regularization and dimension reduction. In this project, we combine…
Phase retrieval (PR) is a popular research topic in signal processing and machine learning. However, its performance degrades significantly when the measurements are corrupted by noise or outliers. To address this limitation, we propose a…
The bus-factor is a critical risk indicator that quantifies how many key contributors a project can afford to lose before core knowledge or functionality is compromised. Despite its practical importance, accurately computing the bus-factor…
We study semiparametric factor models in high-dimensional panels where the factor loadings consist of a nonparametric component explained by observed covariates and an idiosyncratic component capturing unobserved heterogeneity. A key…
In this paper, we set up the theoretical foundations for a high-dimensional functional factor model approach in the analysis of large cross-sections (panels) of functional time series (FTS). We first establish a representation result…
Heavy-tailed errors impair the accuracy of the least squares estimate, which can be spoiled by a single grossly outlying observation. As argued in the seminal work of Peter Huber in 1973 [{\it Ann. Statist.} {\bf 1} (1973) 799--821], robust…
Least-squares fits are an important tool in many data analysis applications. In this paper, we review theoretical results, which are relevant for their application to data from counting experiments. Using a simple example, we illustrate the…
We study a functional linear regression model that deals with functional responses and allows for both functional covariates and high-dimensional vector covariates. The proposed model is flexible and nests several functional regression…
The Khatri-Rao product is extensively used in array processing, tensor decomposition, and multi-way data analysis. Many applications require a least-squares (LS) Khatri-Rao factorization. In broadband sensor array problems, polynomial…
We study randomized sketching methods for approximately solving least-squares problem with a general convex constraint. The quality of a least-squares approximation can be assessed in different ways: either in terms of the value of the…
Matrix factorization (MF) has been widely used to discover the low-rank structure and to predict the missing entries of data matrix. In many real-world learning systems, the data matrix can be very high-dimensional but sparse. This poses an…
This paper introduces a straightforward sieve-based approach for estimating and conducting inference on regression parameters in panel data models with interactive fixed effects. The method's key assumption is that factor loadings can be…
Solving sparse linear systems from discretized PDEs is challenging. Direct solvers have in many cases quadratic complexity (depending on geometry), while iterative solvers require problem dependent preconditioners to be robust and…
Robust estimation has played an important role in statistical and machine learning. However, its applications to functional linear regression are still under-developed. In this paper, we focus on Huber's loss with a diverging robustness…
A new variant of Newton's method for empirical risk minimization is studied, where at each iteration of the optimization algorithm, the gradient and Hessian of the objective function are replaced by robust estimators taken from existing…
Many results have been proved for various nuclear norm penalized estimators of the uniform sampling matrix completion problem. However, most of these estimators are not robust: in most of the cases the quadratic loss function and its…
Given sparse multi-dimensional data (e.g., (user, movie, time; rating) for movie recommendations), how can we discover latent concepts/relations and predict missing values? Tucker factorization has been widely used to solve such problems…