Related papers: Optimal quasi-Bayesian reduced rank regression wit…
In this paper, we consider the problem of Robust Matrix Completion (RMC) where the goal is to recover a low-rank matrix by observing a small number of its entries out of which a few can be arbitrarily corrupted. We propose a simple…
Ordinal categorical data are routinely encountered in many practical applications. When the primary goal is to construct a regression model for ordinal outcomes, cumulative link models represent one of the most popular choices to link the…
We consider the problem of robust matrix completion, which aims to recover a low rank matrix $L_*$ and a sparse matrix $S_*$ from incomplete observations of their sum $M=L_*+S_*\in\mathbb{R}^{m\times n}$. Algorithmically, the robust matrix…
We present a novel Bayesian nonparametric regression model for covariates X and continuous, real response variable Y. The model is parametrized in terms of marginal distributions for Y and X and a regression function which tunes the…
Recently, fundamental conditions on the sampling patterns have been obtained for finite completability of low-rank matrices or tensors given the corresponding ranks. In this paper, we consider the scenario where the rank is not given and we…
The low-rank matrix completion problem can be succinctly stated as follows: given a subset of the entries of a matrix, find a low-rank matrix consistent with the observations. While several low-complexity algorithms for matrix completion…
We study low-rank matrix regression in settings where matrix-valued predictors and scalar responses are observed across multiple individuals. Rather than assuming a fully homogeneous coefficient matrices across individuals, we accommodate…
The paper addresses the problem of low-rank trace norm minimization. We propose an algorithm that alternates between fixed-rank optimization and rank-one updates. The fixed-rank optimization is characterized by an efficient factorization…
The Bayesian approach provides powerful methods for variable selection. The ability to incorporate sparsity through prior beliefs and account for parameter uncertainty allows Bayesian variable selection to consistently identify which of the…
In this paper, we consider the challenge of reconstructing jointly sparse vectors from linear measurements. Firstly, we show that by utilizing the rank of the output data matrix we can reduce the problem to a full column rank case. This…
We study the problem of matrix completion in this paper. A spectral scaled Student prior is exploited to favour the underlying low-rank structure of the data matrix. We provide a thorough theoretical investigation for our approach through…
Fr\'echet regression has emerged as a promising approach for regression analysis involving non-Euclidean response variables. However, its practical applicability has been hindered by its reliance on ideal scenarios with abundant and…
After the phenomenal success of the PageRank algorithm, many researchers have extended the PageRank approach to ranking graphs with richer structures beside the simple linkage structure. In some scenarios we have to deal with…
We consider supervised learning problems within the positive-definite kernel framework, such as kernel ridge regression, kernel logistic regression or the support vector machine. With kernels leading to infinite-dimensional feature spaces,…
We provide new approximation guarantees for greedy low rank matrix estimation under standard assumptions of restricted strong convexity and smoothness. Our novel analysis also uncovers previously unknown connections between the low rank…
Motivated by the increasing use of and rapid changes in array technologies, we consider the prediction problem of fitting a linear regression relating a continuous outcome $Y$ to a large number of covariates $\mathbf {X}$, for example,…
Linear regression is a fundamental modeling tool in statistics and related fields. In this paper, we study an important variant of linear regression in which the predictor-response pairs are partially mismatched. We use an optimization…
This paper considers theoretical analysis of recovering a low rank matrix given a few expansion coefficients with respect to any basis. The current approach generalizes the existing analysis for the low-rank matrix completion problem with…
Due to challenging applications such as collaborative filtering, the matrix completion problem has been widely studied in the past few years. Different approaches rely on different structure assumptions on the matrix in hand. Here, we focus…
Low-rank approximation of a matrix by means of structured random sampling has been consistently efficient in its extensive empirical studies around the globe, but adequate formal support for this empirical phenomenon has been missing so…