Related papers: Multiple Output Regression with Latent Noise

Frequency estimation from measurements corrupted by noise is a fundamental challenge across numerous engineering and scientific fields. Among the pivotal factors shaping the resolution capacity of any frequency estimation technique are…

High-dimensional inference refers to problems of statistical estimation in which the ambient dimension of the data may be comparable to or possibly even larger than the sample size. We study an instance of high-dimensional inference in…

Stochastic resonance describes the utility of noise in improving the detectability of weak signals in certain types of systems. It has been observed widely in natural and engineered settings, but its utility in image classification with…

We propose robust sparse reduced rank regression for analyzing large and complex high-dimensional data with heavy-tailed random noise. The proposed method is based on a convex relaxation of a rank- and sparsity-constrained non-convex…

The multivariate linear regression model with shuffled data and additive Gaussian noise arises in various correspondence estimation and matching problems. Focusing on the denoising aspect of this problem, we provide a characterization the…

We consider the problem of training a model under the presence of label noise. Current approaches identify samples with potentially incorrect labels and reduce their influence on the learning process by either assigning lower weights to…

In this study, we explore the effects of including noise predictors and noise observations when fitting linear regression models. We present empirical and theoretical results that show that double descent occurs in both cases, albeit with…

We consider the problem of extracting a low-dimensional, linear latent variable structure from high-dimensional random variables. Specifically, we show that under mild conditions and when this structure manifests itself as a linear space…

Deep learning with noisy labels presents significant challenges. In this work, we theoretically characterize the role of label noise from a feature learning perspective. Specifically, we consider a signal-noise data distribution, where each…

In high dimension, it is customary to consider Lasso-type estimators to enforce sparsity. For standard Lasso theory to hold, the regularization parameter should be proportional to the noise level, yet the latter is generally unknown in…

Among the most popular variable selection procedures in high-dimensional regression, Lasso provides a solution path to rank the variables and determines a cut-off position on the path to select variables and estimate coefficients. In this…

In supervised classification tasks, models are trained to predict a label for each data point. In real-world datasets, these labels are often noisy due to annotation errors. While the impact of label noise on the performance of deep…

Motivated by applications in high-dimensional data analysis where strong signals often stand out easily and weak ones may be indistinguishable from the noise, we develop a statistical framework to provide a novel categorization of the data…

Reliability analysis aims at estimating the failure probability of an engineering system. It often requires multiple runs of a limit-state function, which usually relies on computationally intensive simulations. Traditionally, these…

We consider the dynamic linear regression problem, where the predictor vector may vary with time. This problem can be modeled as a linear dynamical system, with non-constant observation operator, where the parameters that need to be learned…

Emulating high-accuracy computationally expensive models is crucial for tasks requiring numerous model evaluations, such as uncertainty quantification and optimization. When lower-fidelity models are available, they can be used to improve…

Robust and sparse estimation of linear regression coefficients is investigated. The situation addressed by the present paper is that covariates and noises are sampled from heavy-tailed distributions, and the covariates and noises are…

Some systems cannot be predicted by classical theories and it is required the development of combined deterministic and stochastic theories that make used of noise for dynamical prediction. Noise is not always an interfering signal which…

Speech representation and modelling in high-dimensional spaces of acoustic waveforms, or a linear transformation thereof, is investigated with the aim of improving the robustness of automatic speech recognition to additive noise. The…

Distant and weak supervision allow to obtain large amounts of labeled training data quickly and cheaply, but these automatic annotations tend to contain a high amount of errors. A popular technique to overcome the negative effects of these…