The paper investigates how many data samples per domain are needed for effective learning across multiple domains. It derives criteria from learning bounds that reveal an inverse linear relationship between the number of training domains and the required samples per domain, offering theoretical guidance for dataset adequacy and construction. The study also establishes a close link between in-domain learning and out-of-domain generalization through new generalization bounds.
By Hong Zheng
arXiv:2607. 16528v1 Announce Type: new Abstract: We study hierarchical domain generalization as a problem of extrapolation from finite observed regions to an entire instance space, replacing i.
By Chenxiao Yang, Zhiyuan Li, Shai Ben-David, Nathan Srebro
arXiv:2609. 20883v1 Announce Type: new Abstract: Despite the widespread use and success of generative AI techniques today, theoretical guarantees on learning a distribution supported in $d$ dimensions from $n$ samples degrade as $O(n^{-1/\Theta(d)})$, though shown to be minimax optimal.
By Saumya Goyal, Barnab\'as P\'oczos
arXiv:2606. 28309v1 Announce Type: cross Abstract: Binary classification from positive-only samples is a variant of PAC learning in which the learner receives i.
By Shai Ben-David, Farnam Mansouri, Anay Mehrotra, Manolis Zampetakis
arXiv:2608.30246v1 Announce Type: cross
Abstract: The fundamental theorem of statistical learning states that, under suitable measurability assumptions, finite Vapnik--Chervonenkis (VC) dimension gua...
By Mateus Jesus de Arruda Campos, Gabriel Fernandes, Vinicius de Oliveira Rodrigues
arXiv:2609.39512v1 Announce Type: new
Abstract: The small-sample learning problem remains a fundamental challenge in machine learning because limited training data lead to unstable model estimation a...
By Hong Zheng
arXiv:2603. 23561v4 Announce Type: replace-cross Abstract: In the realm of machine learning theory, to prevent unnatural coding schemes between teacher and learner, No-Clash Teaching Dimension was introduced as provably optimal complexity measure for collusion-free teaching.
By Jiahua Liu, Benchong Li
arXiv:2604. 24749v2 Announce Type: replace Abstract: While the optimal sample complexity of binary classification in terms of the VC dimension is well-established, determining the optimal sample complexity of multiclass classification has remained open.
By Chirag Pabbaraju
The paper introduces a unified framework for dataset condensation (DC) that generalizes existing methods by using discrepancy measures to quantify the distance between probability distributions. It extends the traditional goal of DC—creating a small synthetic dataset that preserves generalization—to include additional objectives such as robustness and privacy. The framework positions DC as a formal approximation problem, broadening its applicability across different machine learning regimes.
By Tong Chen, Raghavendra Selvan
arXiv:2511. 02644v2 Announce Type: replace Abstract: We study computable probably approximately correct (CPAC) learning, where learners are required to be computable functions.
By David Kattermann, Lothar Sebastian Krapp
arXiv:2607. 24732v1 Announce Type: cross Abstract: Motivated by learning from heterogeneous and overlapping data providers, we study a stylized model of distribution learning from restricted conditional samples.
By Jon Kleinberg, Amin Saberi, Xizhi Tan, Grigoris Velegkas
arXiv:2303. 18031v2 Announce Type: replace-cross Abstract: In real-world applications, a machine learning model is required to handle an open-set recognition (OSR), where unknown classes appear during the inference, in addition to a domain shift, where the data distribution differs between the training and inference phases.
By Masashi Noguchi, Shinichi Shirakawa