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We study the problem of PAC learning halfspaces on $\mathbb{R}^d$ with Massart noise under the Gaussian distribution. In the Massart model, an adversary is allowed to flip the label of each point $\mathbf{x}$ with unknown probability…

Machine Learning · Computer Science 2021-11-09 Ilias Diakonikolas , Daniel M. Kane , Vasilis Kontonis , Christos Tzamos , Nikos Zarifis

We study the improper learning of multi-layer neural networks. Suppose that the neural network to be learned has $k$ hidden layers and that the $\ell_1$-norm of the incoming weights of any neuron is bounded by $L$. We present a kernel-based…

Machine Learning · Computer Science 2015-10-14 Yuchen Zhang , Jason D. Lee , Michael I. Jordan

Function approximation based on data drawn randomly from an unknown distribution is an important problem in machine learning. The manifold hypothesis assumes that the data is sampled from an unknown submanifold of a high dimensional…

Machine Learning · Computer Science 2024-08-20 H. N. Mhaskar , Ryan O'Dowd

We give a $2^{\tilde{O}(\sqrt{n}/\epsilon)}$-time algorithm for properly learning monotone Boolean functions under the uniform distribution over $\{0,1\}^n$. Our algorithm is robust to adversarial label noise and has a running time nearly…

Data Structures and Algorithms · Computer Science 2023-03-29 Jane Lange , Ronitt Rubinfeld , Arsen Vasilyan

We study feature learning in a compositional variant of kernel ridge regression in which the predictor is applied to a learnable linear transformation of the input. When the response depends on the input only through a low-dimensional…

Statistics Theory · Mathematics 2026-02-17 Yunlu Chen , Yang Li , Keli Liu , Feng Ruan

We consider a new construction of locality-sensitive hash functions for Hamming space that is \emph{covering} in the sense that is it guaranteed to produce a collision for every pair of vectors within a given radius $r$. The construction is…

Data Structures and Algorithms · Computer Science 2016-01-08 Rasmus Pagh

Obtaining reliable, adaptive confidence sets for prediction functions (hypotheses) is a central challenge in sequential decision-making tasks, such as bandits and model-based reinforcement learning. These confidence sets typically rely on…

Machine Learning · Statistics 2022-06-20 Parnian Kassraie , Jonas Rothfuss , Andreas Krause

Asymmetric kernels naturally exist in real life, e.g., for conditional probability and directed graphs. However, most of the existing kernel-based learning methods require kernels to be symmetric, which prevents the use of asymmetric…

Machine Learning · Computer Science 2022-02-04 Mingzhen He , Fan He , Lei Shi , Xiaolin Huang , Johan A. K. Suykens

Several recent works [DHLNSY25, CPPS25a, CPPS25b] have studied a model of property testing of Boolean functions under a \emph{relative-error} criterion. In this model, the distance from a target function $f: \{0,1\}^n \to \{0,1\}$ that is…

Computational Complexity · Computer Science 2026-03-24 Xi Chen , Anindya De , Yizhi Huang , Shivam Nadimpalli , Rocco A. Servedio , Tianqi Yang

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

Conditional expectiles are becoming an increasingly important tool in finance as well as in other areas of applications. We analyse a support vector machine type approach for estimating conditional expectiles and establish learning rates…

Machine Learning · Statistics 2017-02-28 Muhammad Farooq , Ingo Steinwart

Polynomial approximations to boolean functions have led to many positive results in computer science. In particular, polynomial approximations to the sign function underly algorithms for agnostically learning halfspaces, as well as…

Computational Complexity · Computer Science 2014-12-09 Mark Bun , Thomas Steinke

A remarkable recent paper by Rubinfeld and Vasilyan (2022) initiated the study of \emph{testable learning}, where the goal is to replace hard-to-verify distributional assumptions (such as Gaussianity) with efficiently testable ones and to…

Machine Learning · Computer Science 2022-11-28 Aravind Gollakota , Adam R. Klivans , Pravesh K. Kothari

Despite their many appealing properties, kernel methods are heavily affected by the curse of dimensionality. For instance, in the case of inner product kernels in $\mathbb{R}^d$, the Reproducing Kernel Hilbert Space (RKHS) norm is often…

Machine Learning · Computer Science 2021-11-09 Michael Celentano , Theodor Misiakiewicz , Andrea Montanari

Deep reinforcement learning excels in numerous large-scale practical applications. However, existing performance analyses ignores the unique characteristics of continuous-time control problems, is unable to directly estimate the…

Machine Learning · Computer Science 2024-03-08 Shuyu Yin , Qixuan Zhou , Fei Wen , Tao Luo

In this paper we study how the choice of loss functions of non-convex optimization problems affects their robustness and optimization landscape, through the study of noisy matrix sensing. In traditional regression tasks, mean squared error…

Machine Learning · Computer Science 2026-01-06 Xinyuan Song , Ziye Ma

We give the first tester-learner for halfspaces that succeeds universally over a wide class of structured distributions. Our universal tester-learner runs in fully polynomial time and has the following guarantee: the learner achieves error…

Machine Learning · Computer Science 2023-05-22 Aravind Gollakota , Adam R. Klivans , Konstantinos Stavropoulos , Arsen Vasilyan

We introduce a nonparametric algorithm to learn interaction kernels of mean-field equations for 1st-order systems of interacting particles. The data consist of discrete space-time observations of the solution. By least squares with…

Machine Learning · Statistics 2020-10-30 Quanjun Lang , Fei Lu

Lokshtanov et al.~[STOC 2017] introduced \emph{lossy kernelization} as a mathematical framework for quantifying the effectiveness of preprocessing algorithms in preserving approximation ratios. \emph{$\alpha$-approximate reduction rules}…

Data Structures and Algorithms · Computer Science 2021-06-29 Fredrik Manne , Geevarghese Philip , Saket Saurabh , Prafullkumar Tale

I study the problem of learning a Lipschitz function with corrupted binary signals. The learner tries to learn a $L$-Lipschitz function $f: [0,1]^d \rightarrow [0, L]$ that the adversary chooses. There is a total of $T$ rounds. In each…

Machine Learning · Computer Science 2024-02-02 Shiliang Zuo