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Previous studies demonstrate DNNs' vulnerability to adversarial examples and adversarial training can establish a defense to adversarial examples. In addition, recent studies show that deep neural networks also exhibit vulnerability to…

Machine Learning · Computer Science 2022-04-15 Zhiyuan Zhang , Ruixuan Luo , Xuancheng Ren , Qi Su , Liangyou Li , Xu Sun

We consider the problem of estimating a signal corrupted by independent interference with the assistance of a cost-constrained helper who knows the interference causally or noncausally. When the interference is known causally, we…

Information Theory · Computer Science 2012-03-21 Yeow-Khiang Chia , Rajiv Soundararajan , Tsachy Weissman

Incorrectly labelled training data are frustratingly ubiquitous in both benchmark and specially curated datasets. Such mislabelling clearly adversely affects the performance and generalizability of models trained through supervised learning…

Machine Learning · Computer Science 2025-11-27 Nicholas Pellegrino , David Szczecina , Paul Fieguth

Missing data theory deals with the statistical methods in the occurrence of missing data. Missing data occurs when some values are not stored or observed for variables of interest. However, most of the statistical theory assumes that data…

We consider the problem of sparsity testing in the high-dimensional linear regression model. The problem is to test whether the number of non-zero components (aka the sparsity) of the regression parameter $\theta^*$ is less than or equal to…

Statistics Theory · Mathematics 2020-04-24 Alexandra Carpentier , Nicolas Verzelen

We study the problem of learning Bayesian networks where an $\epsilon$-fraction of the samples are adversarially corrupted. We focus on the fully-observable case where the underlying graph structure is known. In this work, we present the…

Machine Learning · Computer Science 2021-05-13 Yu Cheng , Honghao Lin

Seemingly unrelated linear regression models are introduced in which the distribution of the errors is a finite mixture of Gaussian components. Identifiability conditions are provided. The score vector and the Hessian matrix are derived.…

Methodology · Statistics 2014-03-18 Giuliano Galimberti , Elena Scardovi , Gabriele Soffritti

The shuffled linear regression problem aims to recover linear relationships in datasets where the correspondence between input and output is unknown. This problem arises in a wide range of applications including survey data, in which one…

Computation · Statistics 2022-10-03 Efe Onaran , Soledad Villar

(Partial) ranking loss is a commonly used evaluation measure for multi-label classification, which is usually optimized with convex surrogates for computational efficiency. Prior theoretical work on multi-label ranking mainly focuses on…

Machine Learning · Computer Science 2021-05-12 Guoqiang Wu , Chongxuan Li , Kun Xu , Jun Zhu

Inferring causal relationships or related associations from observational data can be invalidated by the existence of hidden confounding. We focus on a high-dimensional linear regression setting, where the measured covariates are affected…

Methodology · Statistics 2021-07-22 Zijian Guo , Domagoj Ćevid , Peter Bühlmann

We consider regression models with parametric (linear or nonlinear) regression function and allow responses to be ``missing at random.'' We assume that the errors have mean zero and are independent of the covariates. In order to estimate…

Statistics Theory · Mathematics 2009-08-24 Ursula U. Müller

Over the last few years, the phenomenon of adversarial examples --- maliciously constructed inputs that fool trained machine learning models --- has captured the attention of the research community, especially when the adversary is…

Machine Learning · Computer Science 2019-01-31 Nic Ford , Justin Gilmer , Nicolas Carlini , Dogus Cubuk

Concerning bivariate least squares linear regression, the classical approach pursued for functional models in earlier attempts is reviewed using a new formalism in terms of deviation (matrix) traces. Within the framework of classical error…

Instrumentation and Methods for Astrophysics · Physics 2011-03-08 R. Caimmi

We demonstrate the first algorithms for the problem of regression for generalized linear models (GLMs) in the presence of additive oblivious noise. We assume we have sample access to examples $(x, y)$ where $y$ is a noisy measurement of…

Data Structures and Algorithms · Computer Science 2023-09-29 Ilias Diakonikolas , Sushrut Karmalkar , Jongho Park , Christos Tzamos

Motivated by the construction of tractable robust estimators via convex relaxations, we present conditions on the sample size which guarantee an augmented notion of Restricted Eigenvalue-type condition for Gaussian designs. Such a notion is…

Statistics Theory · Mathematics 2018-12-04 Philip Thompson , Arnak S. Dalalyan

We propose Robust Lasso-Zero, an extension of the Lasso-Zero methodology, initially introduced for sparse linear models, to the sparse corruptions problem. We give theoretical guarantees on the sign recovery of the parameters for a slightly…

Applications · Statistics 2022-03-24 Pascaline Descloux , Claire Boyer , Julie Josse , Aude Sportisse , Sylvain Sardy

We reexamine the classical linear regression model when the model is subject to two types of uncertainty: (i) some of covariates are either missing or completely inaccessible, and (ii) the variance of the measurement error is undetermined…

Statistics Theory · Mathematics 2021-08-05 Shuzhen Yang , Jianfeng Yao

Classical semiparametric inference with missing outcome data is not robust to contamination of the observed data and a single observation can have arbitrarily large influence on estimation of a parameter of interest. This sensitivity is…

Methodology · Statistics 2021-03-02 Eva Cantoni , Xavier de Luna

We study the performance of estimators of a sparse nonrandom vector based on an observation which is linearly transformed and corrupted by additive white Gaussian noise. Using the reproducing kernel Hilbert space framework, we derive a new…

Statistics Theory · Mathematics 2010-09-20 Sebastian Schmutzhard , Alexander Jung , Franz Hlawatsch , Zvika Ben-Haim , Yonina C. Eldar

In this paper, we consider the problem of identifying a linear map from measurements which are subject to intermittent and arbitarily large errors. This is a fundamental problem in many estimation-related applications such as fault…

Systems and Control · Computer Science 2016-08-09 Laurent Bako , Henrik Ohlsson