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We study the problem of PAC learning $\gamma$-margin halfspaces in the presence of Massart noise. Without computational considerations, the sample complexity of this learning problem is known to be $\widetilde{\Theta}(1/(\gamma^2…

Machine Learning · Computer Science 2025-01-17 Ilias Diakonikolas , Nikos Zarifis

Deconvolution is a statistical inverse problem to estimate the distribution of a random variable based on its noisy observations. Despite the extensive studies on the topic, deconvolution with unknown noise distribution remains as a…

Statistics Theory · Mathematics 2020-04-06 Devavrat Shah , Dogyoon Song

In this paper, we propose two algorithms for solving linear inverse problems when the observations are corrupted by Poisson noise. A proper data fidelity term (log-likelihood) is introduced to reflect the Poisson statistics of the noise. On…

Applications · Statistics 2011-03-14 François-Xavier Dupé , Jalal Fadili , Jean-Luc Starck

We propose a Fourier-based approach for optimization of several clustering algorithms. Mathematically, clusters data can be described by a density function represented by the Dirac mixture distribution. The density function can be smoothed…

Machine Learning · Computer Science 2019-09-24 Soheil Mehrabkhani

We provide high-probability sample complexity guarantees for exact structure recovery and accurate predictive learning using noise-corrupted samples from an acyclic (tree-shaped) graphical model. The hidden variables follow a…

Machine Learning · Statistics 2021-02-18 Konstantinos E. Nikolakakis , Dionysios S. Kalogerias , Anand D. Sarwate

We show how any PAC learning algorithm that works under the uniform distribution can be transformed, in a blackbox fashion, into one that works under an arbitrary and unknown distribution $\mathcal{D}$. The efficiency of our transformation…

Machine Learning · Statistics 2023-03-31 Guy Blanc , Jane Lange , Ali Malik , Li-Yang Tan

We describe a slightly sub-exponential time algorithm for learning parity functions in the presence of random classification noise. This results in a polynomial-time algorithm for the case of parity functions that depend on only the first…

Machine Learning · Computer Science 2007-05-23 Avrim Blum , Adam Kalai , Hal Wasserman

We study the efficient learnability of low-degree polynomial threshold functions (PTFs) in the presence of a constant fraction of adversarial corruptions. Our main algorithmic result is a polynomial-time PAC learning algorithm for this…

Data Structures and Algorithms · Computer Science 2024-04-02 Ilias Diakonikolas , Daniel M. Kane , Vasilis Kontonis , Sihan Liu , Nikos Zarifis

We propose a supervised learning algorithm for machine learning applications. Contrary to the model developing in the classical methods, which treat training, validation, and test as separate steps, in the presented approach, there is a…

Machine Learning · Computer Science 2019-09-24 Soheil Mehrabkhani

We study the computational complexity of adversarially robust proper learning of halfspaces in the distribution-independent agnostic PAC model, with a focus on $L_p$ perturbations. We give a computationally efficient learning algorithm and…

Machine Learning · Computer Science 2020-07-31 Ilias Diakonikolas , Daniel M. Kane , Pasin Manurangsi

We say that a classifier is \emph{adversarially robust} to perturbations of norm $r$ if, with high probability over a point $x$ drawn from the input distribution, there is no point within distance $\le r$ from $x$ that is classified…

Data Structures and Algorithms · Computer Science 2025-05-21 Jane Lange , Arsen Vasilyan

We study distribution-free property testing and learning problems where the unknown probability distribution is a product distribution over $\mathbb{R}^d$. For many important classes of functions, such as intersections of halfspaces,…

Data Structures and Algorithms · Computer Science 2021-11-17 Nathaniel Harms , Yuichi Yoshida

This paper considers the deconvolution problem in the case where the target signal is multidimensional and no information is known about the noise distribution. More precisely, no assumption is made on the noise distribution and no samples…

Statistics Theory · Mathematics 2021-02-18 Elisabeth Gassiat , Sylvain Le Corff , Luc Lehéricy

We study the problem of PAC learning homogeneous halfspaces in the presence of Tsybakov noise. In the Tsybakov noise model, the label of every sample is independently flipped with an adversarially controlled probability that can be…

Machine Learning · Computer Science 2020-10-06 Ilias Diakonikolas , Daniel M. Kane , Vasilis Kontonis , Christos Tzamos , Nikos Zarifis

We consider noisy observations of a distribution with unknown support. In the deconvolution model, it has been proved recently [19] that, under very mild assumptions, it is possible to solve the deconvolution problem without knowing the…

Statistics Theory · Mathematics 2024-06-21 Jérémie Capitao-Miniconi , Elisabeth Gassiat , Luc Lehéricy

Mixtures of Gaussian (or normal) distributions arise in a variety of application areas. Many heuristics have been proposed for the task of finding the component Gaussians given samples from the mixture, such as the EM algorithm, a…

Probability · Mathematics 2007-05-23 Sanjeev Arora , Ravi Kannan

We study the problem of PAC learning halfspaces with Massart noise. Given labeled samples $(x, y)$ from a distribution $D$ on $\mathbb{R}^{d} \times \{ \pm 1\}$ such that the marginal $D_x$ on the examples is arbitrary and the label $y$ of…

Machine Learning · Computer Science 2021-11-09 Ilias Diakonikolas , Daniel M. Kane

Supervised deep learning has become the method of choice for image denoising. It involves the training of neural networks on large datasets composed of pairs of noisy and clean images. However, the necessity of training data that are…

Computer Vision and Pattern Recognition · Computer Science 2025-07-10 Sébastien Herbreteau , Michael Unser

Nonnegative matrix factorization (NMF) is a popular method for audio spectral unmixing. While NMF is traditionally applied to off-the-shelf time-frequency representations based on the short-time Fourier or Cosine transforms, the ability to…

Machine Learning · Statistics 2018-11-07 Pierre Ablin , Dylan Fagot , Herwig Wendt , Alexandre Gramfort , Cédric Févotte

Tabular learning transforms raw features into optimized spaces for downstream tasks, but its effectiveness deteriorates under distribution shifts between training and testing data. We formalize this challenge as the Distribution Shift…

Machine Learning · Computer Science 2025-08-28 Wangyang Ying , Nanxu Gong , Dongjie Wang , Xinyuan Wang , Arun Vignesh Malarkkan , Vivek Gupta , Chandan K. Reddy , Yanjie Fu