Related papers: Rank-Constrained Least-Squares: Prediction and Inf…
If a dynamic system has active constraints on the state vector and they are known, then taking them into account during modeling is often advantageous. Unfortunately, in the constrained discrete-time state-space estimation, the state…
The problem of approximating a matrix by a low-rank one has been extensively studied. This problem assumes, however, that the whole matrix has a low-rank structure. This assumption is often false for real-world matrices. We consider the…
The aim of reduced rank regression is to connect multiple response variables to multiple predictors. This model is very popular, especially in biostatistics where multiple measurements on individuals can be re-used to predict multiple…
In this paper we consider the trace regression model. Assume that we observe a small set of entries or linear combinations of entries of an unknown matrix $A_0$ corrupted by noise. We propose a new rank penalized estimator of $A_0$. For…
We consider the problem of approximately reconstructing a partially-observed, approximately low-rank matrix. This problem has received much attention lately, mostly using the trace-norm as a surrogate to the rank. Here we study low-rank…
This paper introduces a simple principle for robust high-dimensional statistical inference via an appropriate shrinkage on the data. This widens the scope of high-dimensional techniques, reducing the moment conditions from sub-exponential…
This paper investigates the optimality analysis of the recursive least-squares (RLS) algorithm for autoregressive systems with exogenous inputs (ARX systems). A key challenge in analyzing is managing the potential unboundedness of the…
It has been proposed that complex populations, such as those that arise in genomics studies, may exhibit dependencies among observations as well as among variables. This gives rise to the challenging problem of analyzing unreplicated…
Invariance-based randomization tests -- such as permutation tests, rotation tests, or sign changes -- are an important and widely used class of statistical methods. They allow drawing inferences under weak assumptions on the data…
In this paper, we consider signals with a low-rank covariance matrix which reside in a low-dimensional subspace and can be written in terms of a finite (small) number of parameters. Although such signals do not necessarily have a sparse…
In learning to rank area, industry-level applications have been dominated by gradient boosting framework, which fits a tree using least square error principle. While in classification area, another tree fitting principle, weighted least…
Factor analysis, a classical multivariate statistical technique is popularly used as a fundamental tool for dimensionality reduction in statistics, econometrics and data science. Estimation is often carried out via the Maximum Likelihood…
A common problem in genetics is that of testing whether a set of highly dependent gene expressions differ between two populations, typically in a high-dimensional setting where the data dimension is larger than the sample size. Most…
We consider the problem of fitting the parameters of a high-dimensional linear regression model. In the regime where the number of parameters $p$ is comparable to or exceeds the sample size $n$, a successful approach uses an…
Addressing selection bias in latent variable causal discovery is important yet underexplored, largely due to a lack of suitable statistical tools: While various tools beyond basic conditional independencies have been developed to handle…
This paper proposes the capped least squares regression with an adaptive resistance parameter, hence the name, adaptive capped least squares regression. The key observation is, by taking the resistant parameter to be data dependent, the…
This paper studies the inferential theory for estimating low-rank matrices. It also provides an inference method for the average treatment effect as an application. We show that the least square estimation of eigenvectors following the…
The estimation of parameters in a linear model is considered under the hypothesis that the noise, with finite second order statistics, can be represented in a given deterministic basis by random coefficients. An extended underdetermined…
This preliminary note presents a heuristic for determining rank constrained solutions to linear matrix equations (LME). The method proposed here is based on minimizing a non-convex quadratic functional, which will hence-forth be termed as…
This paper considers the estimation and inference of the low-rank components in high-dimensional matrix-variate factor models, where each dimension of the matrix-variates ($p \times q$) is comparable to or greater than the number of…