Related papers: Dual VC Dimension Obstructs Sample Compression by …

We show that if $\mathcal{X}$ is a complete separable metric space and $\mathcal{C}$ is a countable family of Borel subsets of $\mathcal{X}$ with finite VC dimension, then, for every stationary ergodic process with values in $\mathcal{X}$,…

We prove weak duality between two recent convex relaxation methods for bounding the optimal value of a constrained variational problem in which the objective is an integral functional. The first approach, proposed by Valmorbida et al. (IEEE…

Developing simple, sample-efficient learning algorithms for robust classification is a pressing issue in today's tech-dominated world, and current theoretical techniques requiring exponential sample complexity and complicated improper…

The field of deep visual recognition is undergoing a paradigm shift toward universal representations. The Platonic Representation Hypothesis suggests that diverse architectures trained on massive datasets are converging toward a shared,…

Multi-distribution learning is a natural generalization of PAC learning to settings with multiple data distributions. There remains a significant gap between the known upper and lower bounds for PAC-learnable classes. In particular, though…

In 1984, Frankl and Pach proved that, for positive integers $n$ and $d$, the maximum size of a $(d+1)$-uniform set family $\mathcal{F}$ on an $n$-element set with VC-dimension at most $d$ is at most ${n\choose d}$; and they suspected that…

This paper considers completions of COMs (complexes oriented matroids) to ample partial cubes of the same VC-dimension. We show that these exist for OMs (oriented matroids) and CUOMs (complexes of uniform oriented matroids). This implies…

Recent studies show that a reproducing kernel Hilbert space (RKHS) is not a suitable space to model functions by neural networks as the curse of dimensionality (CoD) cannot be evaded when trying to approximate even a single ReLU neuron…

Scientific research and engineering practice often require the modeling and decomposition of nonlinear systems. The Dynamic Mode Decomposition (DMD) is a novel Koopman-based technique that effectively dissects high-dimensional nonlinear…

The problem of distance metric learning is mostly considered from the perspective of learning an embedding space, where the distances between pairs of examples are in correspondence with a similarity metric. With the rise and success of…

The aim of this paper is to provide several novel upper bounds on the excess risk with a primal focus on classification problems. We suggest two approaches and the obtained bounds are represented via the distribution dependent local…

We study the fine-grained uniform convergence behavior of halfspaces beyond worst-case VC bounds. For inhomogeneous halfspaces in $\mathbb{R}^d$ with $d\ge 2$, we show that standard first-order VC bounds are essentially tight: even…

Estimating causal treatment effects in observational settings is frequently compromised by selection bias arising from unobserved confounders. While traditional econometric methods struggle when these confounders are orthogonal to…

We consider the problem of computing the smallest possible distortion for embedding of a given n-point metric space into R^d, where d is fixed (and small). For d=1, it was known that approximating the minimum distortion with a factor better…

Continual learning methods are known to suffer from catastrophic forgetting, a phenomenon that is particularly hard to counter for methods that do not store exemplars of previous tasks. Therefore, to reduce potential drift in the feature…

Motivated by the ever-increasing demands for limited communication bandwidth and low-power consumption, we propose a new methodology, named joint Variational Autoencoders with Bernoulli mixture models (VAB), for performing clustering in the…

Generative models, such as large language models or text-to-image diffusion models, can generate relevant responses to user-given queries. Response-based vector embeddings of generative models facilitate statistical analysis and inference…

We study online learning in the adversarial injection model introduced by [Goel et al. 2017], where a stream of labeled examples is predominantly drawn i.i.d.\ from an unknown distribution $\mathcal{D}$, but may be interspersed with…

Inductive learning is based on inferring a general rule from a finite data set and using it to label new data. In transduction one attempts to solve the problem of using a labeled training set to label a set of unlabeled points, which are…

Learning vectors that capture the meaning of concepts remains a fundamental challenge. Somewhat surprisingly, perhaps, pre-trained language models have thus far only enabled modest improvements to the quality of such concept embeddings.…