Related papers: Robust regression for mixed Poisson-Gaussian model
Gaussian graphical regression is a powerful means that regresses the precision matrix of a Gaussian graphical model on covariates, permitting the numbers of the response variables and covariates to far exceed the sample size. Model fitting…
This paper studies low-rank matrix completion in the presence of heavy-tailed and possibly asymmetric noise, where we aim to estimate an underlying low-rank matrix given a set of highly incomplete noisy entries. Though the matrix completion…
Phase retrieval (PR) is a popular research topic in signal processing and machine learning. However, its performance degrades significantly when the measurements are corrupted by noise or outliers. To address this limitation, we propose a…
This paper studies the problem of robustly learning the correlation function for a univariate time series with the presence of noise, outliers and missing entries. The outliers or anomalies considered here are sparse and rare events that…
Robust estimators for generalized linear models (GLMs) are not easy to develop due to the nature of the distributions involved. Recently, there has been growing interest in robust estimation methods, particularly in contexts involving a…
Machine learning and data analysis have been used in many robotics fields, especially for modelling. Data are usually the result of sensor measurements and, as such, they might be subjected to noise and outliers. The presence of outliers…
We study the fundamental problems of Gaussian mean estimation and linear regression with Gaussian covariates in the presence of Huber contamination. Our main contribution is the design of the first sample near-optimal and almost linear-time…
Most existing bounds for signal reconstruction from compressive measurements make the assumption of additive signal-independent noise. However in many compressive imaging systems, the noise statistics are more accurately represented by…
The sparse linear regression problem is difficult to handle with usual sparse optimization models when both predictors and measurements are either quantized or represented in low-precision, due to non-convexity. In this paper, we provide a…
This article proposes numerically robust algorithms for Gaussian state estimation with singular observation noise. Our approach combines a series of basis changes with Bayes' rule, transforming the singular estimation problem into a…
We study the problem of high-dimensional robust linear regression where a learner is given access to $n$ samples from the generative model $Y = \langle X,w^* \rangle + \epsilon$ (with $X \in \mathbb{R}^d$ and $\epsilon$ independent), in…
Multiresolution image fusion is a key problem for real-time satellite imaging and plays a central role in detecting and monitoring natural phenomena such as floods. It aims to solve the trade-off between temporal and spatial resolution in…
Model mis-specification (e.g. the presence of outliers) is commonly encountered in astronomical analyses, often requiring the use of ad hoc algorithms which are sensitive to arbitrary thresholds (e.g. sigma-clipping). For any given dataset,…
We study least-squares trace regression when the parameter is the sum of a $r$-low-rank matrix and a $s$-sparse matrix and a fraction $\epsilon$ of the labels is corrupted. For subgaussian distributions and feature-dependent noise, we…
Mixed noise, composed of white Gaussian noise (WGN) and impulsive noise (IN), appears in numerous communication scenarios and can severely degrade system performance. In this paper, we optimize the transmitted constellation under mixed…
Robustness to outliers is often a desirable property of statistical estimators. Indeed many well known estimators offer very good optimal performance in theory but are unusable in applied contexts because of their sensitivity to outliers.…
Gaussian Processes are widely used for regression tasks. A known limitation in the application of Gaussian Processes to regression tasks is that the computation of the solution requires performing a matrix inversion. The solution also…
Gaussian Graphical Models (GGMs) are popular tools for studying network structures. However, many modern applications such as gene network discovery and social interactions analysis often involve high-dimensional noisy data with outliers or…
Gaussian process regression is a popular Bayesian framework for surrogate modeling of expensive data sources. As part of a broader effort in scientific machine learning, many recent works have incorporated physical constraints or other a…
Despite a variety of available techniques the issue of the proper regularization parameter choice for inverse problems still remains one of the biggest challenges. The main difficulty lies in constructing a rule, allowing to compute the…