Related papers: From bilinear regression to inductive matrix compl…
Matrix completion aims to reconstruct a data matrix based on observations of a small number of its entries. Usually in matrix completion a single matrix is considered, which can be, for example, a rating matrix in recommendation system.…
Matrix completion is the study of recovering an underlying matrix from a sparse subset of noisy observations. Traditionally, it is assumed that the entries of the matrix are "missing completely at random" (MCAR), i.e., each entry is…
We develop Bayesian models for density regression with emphasis on discrete outcomes. The problem of density regression is approached by considering methods for multivariate density estimation of mixed scale variables, and obtaining…
Leveraging the wealth of unlabeled data produced in recent years provides great potential for improving supervised models. When the cost of acquiring labels is high, probabilistic active learning methods can be used to greedily select the…
The recent development of compressed sensing has led to spectacular advances in the understanding of sparse linear estimation problems as well as in algorithms to solve them. It has also triggered a new wave of developments in the related…
We develop a semiparametric Bayesian approach for estimating the mean response in a missing data model with binary outcomes and a nonparametrically modelled propensity score. Equivalently we estimate the causal effect of a treatment,…
This paper introduces a quasi-Bayesian method that integrates frequentist nonparametric estimation with Bayesian inference in a two-stage process. Applied to an endogenous discrete choice model, the approach first uses kernel or sieve…
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…
The matrix completion problem consists of finding or approximating a low-rank matrix based on a few samples of this matrix. We propose a new algorithm for matrix completion that minimizes the least-square distance on the sampling set over…
The goal of tensor completion is to fill in missing entries of a partially known tensor under a low-rank constraint. In this paper, we mainly study low rank third-order tensor completion problems by using Riemannian optimization methods on…
We develop a computationally efficient framework for quasi-Bayesian inference based on linear moment conditions. The approach employs a delayed acceptance Markov chain Monte Carlo (DA-MCMC) algorithm that uses a surrogate target kernel and…
Commonly used methods to analyze incomplete longitudinal clinical trial data include complete case analysis (CC) and last observation carried forward (LOCF). However, such methods rest on strong assumptions, including missing completely at…
Using the simple case of Blasius similarity solution, we illustrate a recently developed general method that reduces a strongly nonlinear problem into a weakly nonlinear analysis. The basic idea is to find a quasi-solution $F_0$ that…
This paper tackles the problem of robust covariance matrix estimation when the data is incomplete. Classical statistical estimation methodologies are usually built upon the Gaussian assumption, whereas existing robust estimation ones assume…
A fully Bayesian approach is proposed for ultrahigh-dimensional nonparametric additive models in which the number of additive components may be larger than the sample size, though ideally the true model is believed to include only a small…
Matrix completion focuses on recovering missing or incomplete information in matrices. This problem arises in various applications, including image processing and network analysis. Previous research proposed Poisson matrix completion for…
We propose a new statistical approach to obtain differential gene expression of non-detects in quantitative real-time PCR (qPCR) experiments through Bayesian hierarchical modeling. We propose to treat non-detects as non-random missing data,…
We address the problem of filling missing entries in a kernel Gram matrix, given a related full Gram matrix. We attack this problem from the viewpoint of regression, assuming that the two kernel matrices can be considered as explanatory…
The quasi likelihood analysis is generalized to the partial quasi likelihood analysis. Limit theorems for the quasi likelihood estimators, especially the quasi Bayesian estimator, are derived in the situation where existence of a slow…
Generalized linear models (GLMs) are routinely used for modeling relationships between a response variable and a set of covariates. The simple form of a GLM comes with easy interpretability, but also leads to concerns about model…