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Gaussian process regression is a powerful Bayesian nonlinear regression method. Recent research has enabled the capture of many types of observations using non-Gaussian likelihoods. To deal with various tasks in spatial modeling, we benefit…

Machine Learning · Statistics 2025-08-26 Yuta Shikuri

The increased availability of data in recent years has led several authors to ask whether it is possible to use data as a {\em computational} resource. That is, if more data is available, beyond the sample complexity limit, is it possible…

Machine Learning · Computer Science 2013-11-12 Amit Daniely , Nati Linial , Shai Shalev Shwartz

We study the problem of learning halfspaces with Massart noise in the distribution-specific PAC model. We give the first computationally efficient algorithm for this problem with respect to a broad family of distributions, including…

Machine Learning · Computer Science 2020-02-14 Ilias Diakonikolas , Vasilis Kontonis , Christos Tzamos , Nikos Zarifis

We give the first fully polynomial-time algorithm for learning halfspaces with respect to the uniform distribution on the hypercube in the presence of contamination, where an adversary may corrupt some fraction of examples and labels…

Data Structures and Algorithms · Computer Science 2025-11-11 Gautam Chandrasekaran , Adam R. Klivans , Konstantinos Stavropoulos , Arsen Vasilyan

We consider the problem of estimating a rank-one matrix in Gaussian noise under a probabilistic model for the left and right factors of the matrix. The probabilistic model can impose constraints on the factors including sparsity and…

Information Theory · Computer Science 2015-09-16 Alyson K. Fletcher , Sundeep Rangan

We study {\em online} active learning of homogeneous halfspaces in $\mathbb{R}^d$ with adversarial noise where the overall probability of a noisy label is constrained to be at most $\nu$. Our main contribution is a Perceptron-like online…

Machine Learning · Computer Science 2021-06-24 Jie Shen

This chapter considers the computational and statistical aspects of learning linear thresholds in presence of noise. When there is no noise, several algorithms exist that efficiently learn near-optimal linear thresholds using a small amount…

Machine Learning · Computer Science 2020-11-16 Maria-Florina Balcan , Nika Haghtalab

We study the problem of agnostic learning under the Gaussian distribution. We develop a method for finding hard families of examples for a wide class of problems by using LP duality. For Boolean-valued concept classes, we show that the…

Machine Learning · Computer Science 2021-02-09 Ilias Diakonikolas , Daniel M. Kane , Thanasis Pittas , Nikos Zarifis

Noise Contrastive Estimation (NCE) is a popular approach for learning probability density functions parameterized up to a constant of proportionality. The main idea is to design a classification problem for distinguishing training data from…

Machine Learning · Computer Science 2023-03-03 Holden Lee , Chirag Pabbaraju , Anish Sevekari , Andrej Risteski

There are many high dimensional function classes that have fast agnostic learning algorithms when assumptions on the distribution of examples can be made, such as Gaussianity or uniformity over the domain. But how can one be confident that…

Machine Learning · Computer Science 2022-11-22 Ronitt Rubinfeld , Arsen Vasilyan

The problem of learning structural equation models (SEMs) from data is a fundamental problem in causal inference. We develop a new algorithm --- which is computationally and statistically efficient and works in the high-dimensional regime…

Machine Learning · Computer Science 2019-01-30 Asish Ghoshal , Jean Honorio

We consider a reinforcement learning setting in which the deployment environment is different from the training environment. Applying a robust Markov decision processes formulation, we extend the distributionally robust $Q$-learning…

Machine Learning · Computer Science 2024-08-02 Shengbo Wang , Nian Si , Jose Blanchet , Zhengyuan Zhou

We provide sample complexity upper bounds for agnostically learning multivariate Gaussians under the constraint of approximate differential privacy. These are the first finite sample upper bounds for general Gaussians which do not impose…

Machine Learning · Statistics 2020-10-21 Ishaq Aden-Ali , Hassan Ashtiani , Gautam Kamath

System identification is a fundamental problem in control and learning, particularly in high-stakes applications where data efficiency is critical. Classical approaches, such as the ordinary least squares estimator (OLS), achieve an…

Systems and Control · Electrical Eng. & Systems 2025-06-12 Xiong Zeng , Jing Yu , Necmiye Ozay

We study the problem of agnostically learning halfspaces under the Gaussian distribution. Our main result is the {\em first proper} learning algorithm for this problem whose sample complexity and computational complexity qualitatively match…

Machine Learning · Computer Science 2021-02-11 Ilias Diakonikolas , Daniel M. Kane , Vasilis Kontonis , Christos Tzamos , Nikos Zarifis

We consider the problem of computing the best-fitting ReLU with respect to square-loss on a training set when the examples have been drawn according to a spherical Gaussian distribution (the labels can be arbitrary). Let $\mathsf{opt} < 1$…

Machine Learning · Computer Science 2019-11-06 Surbhi Goel , Sushrut Karmalkar , Adam Klivans

We consider the basic problem of learning Single-Index Models with respect to the square loss under the Gaussian distribution in the presence of adversarial label noise. Our main contribution is the first computationally efficient algorithm…

Machine Learning · Computer Science 2025-08-07 Puqian Wang , Nikos Zarifis , Ilias Diakonikolas , Jelena Diakonikolas

We give superpolynomial statistical query (SQ) lower bounds for learning two-hidden-layer ReLU networks with respect to Gaussian inputs in the standard (noise-free) model. No general SQ lower bounds were known for learning ReLU networks of…

Machine Learning · Computer Science 2022-11-15 Sitan Chen , Aravind Gollakota , Adam R. Klivans , Raghu Meka

We study the problem of list-decodable Gaussian mean estimation and the related problem of learning mixtures of separated spherical Gaussians. We develop a set of techniques that yield new efficient algorithms with significantly improved…

Data Structures and Algorithms · Computer Science 2017-11-21 Ilias Diakonikolas , Daniel M. Kane , Alistair Stewart

The problem of learning threshold functions is a fundamental one in machine learning. Classical learning theory implies sample complexity of $O(\xi^{-1} \log(1/\beta))$ (for generalization error $\xi$ with confidence $1-\beta$). The private…

Machine Learning · Computer Science 2022-11-14 Edith Cohen , Xin Lyu , Jelani Nelson , Tamás Sarlós , Uri Stemmer