Related papers: Low-Rank Approximations of Nonseparable Panel Mode…
Estimating a policy that maps states to actions is a central problem in reinforcement learning. Traditionally, policies are inferred from the so called value functions (VFs), but exact VF computation suffers from the curse of…
Nonnegative matrix factorization (NMF) has an established reputation as a useful data analysis technique in numerous applications. However, its usage in practical situations is undergoing challenges in recent years. The fundamental factor…
Partial least squares regression---or PLS---is a multivariate method in which models are estimated using either the SIMPLS or NIPALS algorithm. PLS regression has been extensively used in applied research because of its effectiveness in…
Optimization problems with rank constraints arise in many applications, including matrix regression, structured PCA, matrix completion and matrix decomposition problems. An attractive heuristic for solving such problems is to factorize the…
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…
It has long been established that, if a panel dataset suffers from attrition, auxiliary (refreshment) sampling restores full identification under additional assumptions that still allow for nontrivial attrition mechanisms. Such…
Principal component analysis continues to be a powerful tool in dimension reduction of high dimensional data. We assume a variance-diverging model and use the high-dimension, low-sample-size asymptotics to show that even though the…
While most of the convergence results in the literature on high dimensional covariance matrix are concerned about the accuracy of estimating the covariance matrix (and precision matrix), relatively less is known about the effect of…
In this work, we discuss low-parametric approaches for approximating SimRank matrices, which estimate the similarity between pairs of nodes in a graph. Although SimRank matrices and their computation require a significant amount of memory,…
In this note, we investigate how well we can reconstruct the best rank-$r$ approximation of a large matrix from a small number of its entries. We show that even if a data matrix is of full rank and cannot be approximated well by a low-rank…
This work studies low-rank approximation of a positive semidefinite matrix from partial entries via nonconvex optimization. We characterized how well local-minimum based low-rank factorization approximates a fixed positive semidefinite…
In light of recent data science trends, new interest has fallen in alternative matrix factorizations. By this, we mean various ways of factorizing particular data matrices so that the factors have special properties and reveal insights into…
We develop an estimation methodology for a factor model for high-dimensional matrix-valued time series, where common stochastic trends and common stationary factors can be present. We study, in particular, the estimation of (row and column)…
Nonignorable missing outcomes are common in real world datasets and often require strong parametric assumptions to achieve identification. These assumptions can be implausible or untestable, and so we may forgo them in favour of partially…
Tensor methods are among the most prominent tools for the numerical solution of high-dimensional problems where functions of multiple variables have to be approximated. These methods exploit the tensor structure of function spaces and apply…
Square matrices appear in many machine learning problems and models. Optimization over a large square matrix is expensive in memory and in time. Therefore an economic approximation is needed. Conventional approximation approaches factorize…
The use of low-rank approximation filters in the field of NMR is increasing due to their flexibility and effectiveness. Despite their ability to reduce the Mean Square Error between the processed signal and the true signal is well known,…
High-dimensional matrix regression has been studied in various aspects, such as statistical properties, computational efficiency and application to specific instances including multivariate regression, system identification and matrix…
Low-rank matrix completion is the task of recovering unknown entries of a matrix by assuming that the true matrix admits a good low-rank approximation. Sometimes additional information about the variables is known, and incorporating this…
Similarity matrix serves as a fundamental tool at the core of numerous downstream machine-learning tasks. However, missing data is inevitable and often results in an inaccurate similarity matrix. To address this issue, Similarity Matrix…