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Low-rank matrix recovery problems involving high-dimensional and heterogeneous data appear in applications throughout statistics and machine learning. The contribution of this paper is to establish the fundamental limits of recovery for a…

Machine Learning · Statistics 2022-03-22 Joshua K. Behne , Galen Reeves

We study the query complexity of sampling from high-dimensional Gaussian distributions using gradient information. In the standard oracle model, exact gradients expose only matrix-vector products with the precision matrix, leading to…

Data Structures and Algorithms · Computer Science 2026-05-28 Jingbo Liu

We present a differentially private learner for halfspaces over a finite grid $G$ in $\mathbb{R}^d$ with sample complexity $\approx d^{2.5}\cdot 2^{\log^*|G|}$, which improves the state-of-the-art result of [Beimel et al., COLT 2019] by a…

Machine Learning · Computer Science 2020-11-04 Haim Kaplan , Yishay Mansour , Uri Stemmer , Eliad Tsfadia

We consider the problem of PAC learning the most valuable item from a pool of $n$ items using sequential, adaptively chosen plays of subsets of $k$ items, when, upon playing a subset, the learner receives relative feedback sampled according…

Machine Learning · Computer Science 2020-02-20 Aadirupa Saha , Aditya Gopalan

In his breakthrough paper, Raz showed that any parity learning algorithm requires either quadratic memory or an exponential number of samples [FOCS'16, JACM'19]. A line of work that followed extended this result to a large class of learning…

Machine Learning · Computer Science 2023-10-13 Xin Lyu , Avishay Tal , Hongxun Wu , Junzhao Yang

A novel matrix approximation problem is considered herein: observations based on a few fully sampled columns and quasi-polynomial structural side information are exploited. The framework is motivated by quantum chemistry problems wherein…

Signal Processing · Electrical Eng. & Systems 2023-05-23 Jeongmin Chae , Praneeth Narayanamurthy , Selin Bac , Shaama Mallikarjun Sharada , Urbashi Mitra

We study the collaborative PAC learning problem recently proposed in Blum et al.~\cite{BHPQ17}, in which we have $k$ players and they want to learn a target function collaboratively, such that the learned function approximates the target…

Machine Learning · Computer Science 2018-10-15 Jiecao Chen , Qin Zhang , Yuan Zhou

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 study the sample complexity of learning an $\varepsilon$-optimal policy in an average-reward Markov decision process (MDP) under a generative model. For weakly communicating MDPs, we establish the complexity bound…

Machine Learning · Computer Science 2025-02-25 Matthew Zurek , Yudong Chen

We give noise-robust, Probably Approximately Correct (PAC) guarantees of global $\varepsilon$-optimality for the Variational Quantum Eigensolver under explicit geometric conditions. For periodic ansatzes with bounded generators -- yielding…

Quantum Physics · Physics 2025-11-19 Benjamin Asch

During recent years the interest of optimization and machine learning communities in high-probability convergence of stochastic optimization methods has been growing. One of the main reasons for this is that high-probability complexity…

We study the problem of learning adversarially robust halfspaces in the distribution-independent setting. In the realizable setting, we provide necessary and sufficient conditions on the adversarial perturbation sets under which halfspaces…

Machine Learning · Computer Science 2020-05-18 Omar Montasser , Surbhi Goel , Ilias Diakonikolas , Nathan Srebro

We revisit the problem of learning mixtures of spherical Gaussians. Given samples from mixture $\frac{1}{k}\sum_{j=1}^{k}\mathcal{N}(\mu_j, I_d)$, the goal is to estimate the means $\mu_1, \mu_2, \ldots, \mu_k \in \mathbb{R}^d$ up to a…

Machine Learning · Computer Science 2022-10-07 Mingda Qiao , Guru Guruganesh , Ankit Singh Rawat , Avinava Dubey , Manzil Zaheer

We initiate the study of tolerant adversarial PAC-learning with respect to metric perturbation sets. In adversarial PAC-learning, an adversary is allowed to replace a test point $x$ with an arbitrary point in a closed ball of radius $r$…

Machine Learning · Statistics 2023-02-16 Hassan Ashtiani , Vinayak Pathak , Ruth Urner

Continuous-variable systems enable key quantum technologies in computation, communication, and sensing. Bosonic Gaussian states emerge naturally in various such applications, including gravitational-wave and dark-matter detection. A…

We study the task of testable learning of general -- not necessarily homogeneous -- halfspaces with adversarial label noise with respect to the Gaussian distribution. In the testable learning framework, the goal is to develop a…

Machine Learning · Computer Science 2024-09-02 Ilias Diakonikolas , Daniel M. Kane , Sihan Liu , Nikos Zarifis

We study monotonicity testing of functions $f \colon \{0,1\}^d \to \{0,1\}$ using sample-based algorithms, which are only allowed to observe the value of $f$ on points drawn independently from the uniform distribution. A classic result by…

Data Structures and Algorithms · Computer Science 2024-08-21 Hadley Black

In this paper we consider the problem of learning an $\epsilon$-optimal policy for a discounted Markov Decision Process (MDP). Given an MDP with $S$ states, $A$ actions, the discount factor $\gamma \in (0,1)$, and an approximation threshold…

Machine Learning · Computer Science 2020-12-25 Zihan Zhang , Yuan Zhou , Xiangyang Ji

Recently, several studies consider the stochastic optimization problem but in a heavy-tailed noise regime, i.e., the difference between the stochastic gradient and the true gradient is assumed to have a finite $p$-th moment (say being upper…

Optimization and Control · Mathematics 2023-05-23 Zijian Liu , Zhengyuan Zhou

We revisit the problem of robust linear regression under Gaussian covariates with an unknown covariance matrix of condition number $\kappa$. For this fundamental problem, significant gaps remain in our understanding of the trade-offs among…

Data Structures and Algorithms · Computer Science 2026-05-19 Deeksha Adil , Jarosław Błasiok , Hongjie Chen , Deepak Narayanan Sridharan