相关论文: Two-Sided Nearest Neighbors: An adaptive and minim…

We consider a variant of matrix completion where entries are revealed in a biased manner. We wish to understand the extent to which such bias can be exploited in improving predictions. Towards that, we propose a natural model where the…

In this technical note, we introduce and analyze AWNN: an adaptively weighted nearest neighbor method for performing matrix completion. Nearest neighbor (NN) methods are widely used in missing data problems across multiple disciplines such…

Synthetic Nearest Neighbors (SNN) provides a principled solution to causal matrix completion under missing-not-at-random (MNAR) by exploiting local low-rank structure through fully observed anchor submatrices. However, its effectiveness…

We introduce and analyze an improved variant of nearest neighbors (NN) for estimation with missing data in latent factor models. We consider a matrix completion problem with missing data, where the $(i, t)$-th entry, when observed, is given…

Biased sampling and missing data complicates statistical problems ranging from causal inference to reinforcement learning. We often correct for biased sampling of summary statistics with matching methods and importance weighting. In this…

Originally developed for imputing missing entries in low rank, or approximately low rank matrices, matrix completion has proven widely effective in many problems where there is no reason to assume low-dimensional linear structure in the…

Nearest neighbor (NN) matching as a tool to align data sampled from different groups is both conceptually natural and practically well-used. In a landmark paper, Abadie and Imbens (2006) provided the first large-sample analysis of NN…

Nearest neighbor (NN) methods have re-emerged as competitive tools for matrix completion, offering strong empirical performance and recent theoretical guarantees, including entry-wise error bounds, confidence intervals, and minimax…

Conventional matrix completion methods approximate the missing values by assuming the matrix to be low-rank, which leads to a linear approximation of missing values. It has been shown that enhanced performance could be attained by using…

We describe several algorithms for matrix completion and matrix approximation when only some of its entries are known. The approximation constraint can be any whose approximated solution is known for the full matrix. For low rank…

The problem of finding the missing values of a matrix given a few of its entries, called matrix completion, has gathered a lot of attention in the recent years. Although the problem under the standard low rank assumption is NP-hard,…

Matrix completion is often applied to data with entries missing not at random (MNAR). For example, consider a recommendation system where users tend to only reveal ratings for items they like. In this case, a matrix completion method that…

Motivated by applications in computer vision and databases, we introduce and study the Simultaneous Nearest Neighbor Search (SNN) problem. Given a set of data points, the goal of SNN is to design a data structure that, given a collection of…

We consider the problem of minimizing the composition of a nonsmooth function with a smooth mapping in the case where the proximity operator of the nonsmooth function can be explicitly computed. We first show that this proximity operator…

We consider the setup of nonparametric {\em blind regression} for estimating the entries of a large $m \times n$ matrix, when provided with a small, random fraction of noisy measurements. We assume that all rows $u \in [m]$ and columns $i…

While the matrix completion problem has attracted considerable attention over the decades, few works address the nonignorable missing issue and all have their limitations. In this article, we propose a nuclear norm regularized row- and…

The $k$-nearest neighbor algorithm ($k$-NN) is a widely used non-parametric method for classification and regression. We study the mean squared error of the $k$-NN estimator when $k$ is chosen by leave-one-out cross-validation (LOOCV).…

In the era of deep learning, understanding over-fitting phenomenon becomes increasingly important. It is observed that carefully designed deep neural networks achieve small testing error even when the training error is close to zero. One…

Submodular function minimization is well studied, and existing algorithms solve it exactly or up to arbitrary accuracy. However, in many applications, such as structured sparse learning or batch Bayesian optimization, the objective function…

Recent work in the matrix completion literature has shown that prior knowledge of a matrix's row and column spaces can be successfully incorporated into reconstruction programs to substantially benefit matrix recovery. This paper proposes a…