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Deep neural networks often contain far more parameters than training examples, yet they still manage to generalize well in practice. Classical complexity measures such as VC-dimension or PAC-Bayes bounds usually become vacuous in this…

Machine Learning · Computer Science 2025-08-26 Aviral Dhingra

In machine learning, Domain Adaptation (DA) arises when the distribution gen- erating the test (target) data differs from the one generating the learning (source) data. It is well known that DA is an hard task even under strong assumptions,…

Machine Learning · Statistics 2012-12-12 Pascal Germain , Amaury Habrard , François Laviolette , Emilie Morvant

In many learning theory problems, a central role is played by a hypothesis class: we might assume that the data is labeled according to a hypothesis in the class (usually referred to as the realizable setting), or we might evaluate the…

Machine Learning · Computer Science 2022-11-17 Lunjia Hu , Charlotte Peale

The standard theory of stochastic approximation (SA) is extended to the case when the constraint set is a Riemannian manifold. Specifically, the standard ODE method for analyzing SA schemes is extended to iterations constrained to stay on a…

Optimization and Control · Mathematics 2017-11-30 Suhail M. Shah

We analyze the sample complexity of full-batch Gradient Descent (GD) in the setup of non-smooth Stochastic Convex Optimization. We show that the generalization error of GD, with common choice of hyper-parameters, can be $\tilde \Theta(d/m +…

Machine Learning · Computer Science 2024-04-12 Roi Livni

The existence of evasion attacks during the test phase of machine learning algorithms represents a significant challenge to both their deployment and understanding. These attacks can be carried out by adding imperceptible perturbations to…

Machine Learning · Statistics 2018-06-07 Daniel Cullina , Arjun Nitin Bhagoji , Prateek Mittal

For any family of measurable sets in a probability space, we show that either (i) the family has infinite Vapnik-Chervonenkis (VC) dimension or (ii) for every epsilon > 0 there is a finite partition pi such the pi-boundary of each set has…

Probability · Mathematics 2010-10-22 Terrence M. Adams , Andrew B. Nobel

In this paper, we study the conditional stochastic optimization (CSO) problem which covers a variety of applications including portfolio selection, reinforcement learning, robust learning, causal inference, etc. The sample-averaged gradient…

Machine Learning · Computer Science 2023-12-05 Lie He , Shiva Prasad Kasiviswanathan

Optimal design for linear regression is a fundamental task in statistics. For finite design spaces, recent progress has shown that random designs drawn using proportional volume sampling (PVS) lead to approximation guarantees for A-optimal…

Computation · Statistics 2021-02-02 Arnaud Poinas , Rémi Bardenet

Probabilities of causation (PoCs), such as the probability of necessity and sufficiency (PNS), are important tools for decision making but are generally not point identifiable. Existing work has derived bounds for these quantities using…

Methodology · Statistics 2026-02-20 Tianyuan Cheng , Ruirui Mao , Judea Pearl , Ang Li

Propositional satisfiability (SAT) is one of the most fundamental problems in computer science. The worst-case hardness of SAT lies at the core of computational complexity theory. The average-case analysis of SAT has triggered the…

Discrete Mathematics · Computer Science 2019-05-03 Tobias Friedrich , Anton Krohmer , Ralf Rothenberger , Thomas Sauerwald , Andrew M. Sutton

Query-driven machine learning models have emerged as a promising estimation technique for query selectivities. Yet, surprisingly little is known about the efficacy of these techniques from a theoretical perspective, as there exist…

Machine Learning · Statistics 2026-05-19 Peizhi Wu , Haoshu Xu , Ryan Marcus , Zachary G. Ives

We analyze a simple randomized subgradient method for approximating solutions to stochastic systems of convex functional constraints, the only input to the algorithm being the size of minibatches. By introducing a new notion of what is…

Optimization and Control · Mathematics 2021-08-30 James Renegar , Song Zhou

We study a statistical method to estimate the optimal value, and the optimality gap of a given solution for stochastic optimization as an assessment of the solution quality. Our approach is based on bootstrap aggregating, or bagging,…

Optimization and Control · Mathematics 2022-12-06 Henry Lam , Huajie Qian

We give a fast algorithm for sampling uniform solutions of general constraint satisfaction problems (CSPs) in a local lemma regime. Suppose that the CSP has $n$ variables with domain size at most q, each constraint contains at most k…

Data Structures and Algorithms · Computer Science 2023-03-10 Kun He , Chunyang Wang , Yitong Yin

We present a new general-purpose algorithm for learning classes of $[0,1]$-valued functions in a generalization of the prediction model, and prove a general upper bound on the expected absolute error of this algorithm in terms of a…

Machine Learning · Computer Science 2023-04-25 Peter L. Bartlett , Philip M. Long

This paper takes an initial step to systematically investigate the generalization bounds of algorithms for solving nonconvex-(strongly)-concave (NC-SC/NC-C) stochastic minimax optimization measured by the stationarity of primal functions.…

Optimization and Control · Mathematics 2023-02-08 Siqi Zhang , Yifan Hu , Liang Zhang , Niao He

Explaining how overparametrized neural networks simultaneously achieve low risk and zero empirical risk on benchmark datasets is an open problem. PAC-Bayes bounds optimized using variational inference (VI) have been recently proposed as a…

Machine Learning · Computer Science 2020-03-06 Konstantinos Pitas

We consider convex optimization problems with a possibly nonsmooth objective function in the form of a mathematical expectation. The proposed framework (AN-SPS) employs Sample Average Approximations (SAA) to approximate the objective…

Optimization and Control · Mathematics 2024-10-31 Nataša Krklec Jerinkić , Tijana Ostojić

Sharpness-Aware Minimization (SAM) has emerged as a powerful method for improving generalization in machine learning models by minimizing the sharpness of the loss landscape. However, despite its success, several important questions…

Optimization and Control · Mathematics 2025-03-05 Dimitris Oikonomou , Nicolas Loizou