Related papers: Estimated VC dimension for risk bounds

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…

Vapnik--Chervonenkis' theorem is a seminal result in machine learning. It establishes sufficient conditions for empirical probabilities to converge to theoretical probabilities, uniformly over families of events. It also provides an…

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…

We provide a negative resolution to a conjecture of Steinke and Zakynthinou (2020a), by showing that their bound on the conditional mutual information (CMI) of proper learners of Vapnik--Chervonenkis (VC) classes cannot be improved from $d…

The VC-dimension is a well-studied and fundamental complexity measure of a set system (or hypergraph) that is central to many areas of machine learning. We establish several new results on the complexity of computing the VC-dimension. In…

Largest theoretical contribution to Neural Networks comes from VC Dimension which characterizes the sample complexity of classification model in a probabilistic view and are widely used to study the generalization error. So far in the…

This paper focuses on understanding how the generalization error scales with the amount of the training data for deep neural networks (DNNs). Existing techniques in statistical learning require computation of capacity measures, such as VC…

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…

Approximation and learning of classifiers of large data sets by neural networks in terms of high-dimensional geometry and statistical learning theory are investigated. The influence of the VC dimension of sets of input-output functions of…

The study of strategic or adversarial manipulation of testing data to fool a classifier has attracted much recent attention. Most previous works have focused on two extreme situations where any testing data point either is completely…

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. However, whether…

Generalization in deep learning has been the topic of much recent theoretical and empirical research. Here we introduce desiderata for techniques that predict generalization errors for deep learning models in supervised learning. Such…

Deep learning methods minimise the empirical risk using loss functions such as the cross entropy loss. When minimising the empirical risk, the generalisation of the learnt function still depends on the performance on the training data, the…

Since its introduction by Vapnik and Chervonenkis in the 1960s, the VC dimension and its variants have played a central role in numerous fields. In this paper, we investigate several variants of the VC dimension and their applications to…

In this paper, we consider the problem of minimizing a linear functional subject to uncertain linear and bilinear matrix inequalities, which depend in a possibly nonlinear way on a vector of uncertain parameters. Motivated by recent results…

The Vapnik-Chervonenkis (VC) dimension measures the complexity of a learning machine, and a low VC dimension leads to good generalization. The recently proposed Minimal Complexity Machine (MCM) learns a hyperplane classifier by minimizing…

In this paper, we uncover a new uncertainty principle that governs the complexity of Boolean functions. This principle manifests as a fundamental trade-off between two central measures of complexity: a combinatorial complexity of its…

The concept of Vapnik-Chervonenkis (VC) density is pivotal across various mathematical fields, including discrete geometry, probability theory and model theory. In this paper, we introduce a topological generalization of VC-density. Let $Y$…

VC-dimension and VC-density are measures of combinatorial complexity of set systems. VC-dimension was first introduced in the context of statistical learning theory, and is tightly related to the sample complexity in PAC learning.…

Delle Rose et al.~(COLT'23) introduced an effective version of the Vapnik-Chervonenkis dimension, and showed that it characterizes improper PAC learning with total computable learners. In this paper, we introduce and study a similar…