相关论文: Robust matrix completion via Novel M-estimator Fun…

We consider the matrix completion problem under a form of row/column weighted entrywise sampling, including the case of uniform entrywise sampling as a special case. We analyze the associated random observation operator, and prove that with…

This paper describes recursive algorithms for state estimation of linear dynamical systems when measurements are noisy with unknown bias and/or outliers. For situations with noisy and biased measurements, algorithms are proposed that…

The task of estimating a matrix given a sample of observed entries is known as the \emph{matrix completion problem}. Most works on matrix completion have focused on recovering an unknown real-valued low-rank matrix from a random sample of…

We consider a conforming finite element approximation of the Reissner-Mindlin system. We propose a new robust a posteriori error estimator based on H(div) conforming finite elements and equilibrated fluxes. It is shown that this estimator…

We develop a mixture-based approach to robust density modeling and outlier detection for experimental multivariate data that includes measurement error information. Our model is designed to infer atypical measurements that are not due to…

There has been a surge of interest in developing robust estimators for models with heavy-tailed and bounded variance data in statistics and machine learning, while few works impose unbounded variance. This paper proposes two type of robust…

This paper proposes a theoretical and computational framework for training and robustness verification of implicit neural networks based upon non-Euclidean contraction theory. The basic idea is to cast the robustness analysis of a neural…

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…

Real-world network applications must cope with failing nodes, malicious attacks, or, somehow, nodes facing corrupted data --- classified as outliers. One enabling application is the geographic localization of the network nodes. However,…

Robust Principal Component Analysis (RPCA) and its associated non-convex relaxation methods constitute a significant component of matrix completion problems, wherein matrix factorization strategies effectively reduce dimensionality and…

The scalar-on-function regression model has become a popular analysis tool to explore the relationship between a scalar response and multiple functional predictors. Most of the existing approaches to estimate this model are based on the…

Real-world network applications must cope with failing nodes, malicious attacks, or nodes facing corrupted data - data classified as outliers. Our work addresses these concerns in the scope of the sensor network localization problem where,…

This paper revisits classical works of Rauch (1963, et al. 1965) and develops a novel method for maximum likelihood (ML) smoothing estimation from incomplete information/data of stochastic state-space systems. Score function and conditional…

This paper presents uniform estimation and inference theory for a large class of nonparametric partitioning-based M-estimators. The main theoretical results include: (i) uniform consistency for convex and non-convex objective functions;…

The task of reconstructing a matrix given a sample of observedentries is known as the matrix completion problem. It arises ina wide range of problems, including recommender systems, collaborativefiltering, dimensionality reduction, image…

Robust density estimation refers to the consistent estimation of the density function even when the data is contaminated by outliers. We find that existing forest density estimation at a certain point is inherently resistant to the outliers…

The goal of compressed sensing is to estimate a high dimensional vector from an underdetermined system of noisy linear equations. In analogy to classical compressed sensing, here we assume a generative model as a prior, that is, we assume…

Matrix completion is a modern missing data problem where both the missing structure and the underlying parameter are high dimensional. Although missing structure is a key component to any missing data problems, existing matrix completion…

This paper studies the matrix completion problem under arbitrary sampling schemes. We propose a new estimator incorporating both max-norm and nuclear-norm regularization, based on which we can conduct efficient low-rank matrix recovery…

We consider the matrix completion problem of recovering a structured low rank matrix with partially observed entries with mixed data types. Vast majority of the solutions have proposed computationally feasible estimators with strong…