Related papers: Computing the Vapnik Chervonenkis Dimension for No…

One of the most studied problems in machine learning is finding reasonable constraints that guarantee the generalization of a learning algorithm. These constraints are usually expressed as some simplicity assumptions on the target. For…

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 $r$…

The VC dimension measures the capacity of a learning machine, and a low VC dimension leads to good generalization. While SVMs produce state-of-the-art learning performance, it is well known that the VC dimension of a SVM can be unbounded;…

We study uniform computability properties of PAC learning using Weihrauch complexity. We focus on closed concept classes, which are either represented by positive, by negative or by full information. Among other results, we prove that…

Adversarially robust PAC learning has proved to be challenging, with the currently best known learners [Montasser et al., 2021a] relying on improper methods based on intricate compression schemes, resulting in sample complexity exponential…

Accurate estimates of causal effects play a key role in decision-making across applications such as healthcare, economics, and operations. In the absence of randomized experiments, a common approach to estimating causal effects uses…

Binary classification in the classic PAC model exhibits a curious phenomenon: Empirical Risk Minimization (ERM) learners are suboptimal in the realizable case yet optimal in the agnostic case. Roughly speaking, this owes itself to the fact…

We study the complexity of computing the VC Dimension and Littlestone's Dimension. Given an explicit description of a finite universe and a concept class (a binary matrix whose $(x,C)$-th entry is $1$ iff element $x$ belongs to concept…

Valiant's 1984 paper is widely credited with introducing the PAC learning model, but it, in fact, introduced a different model: unlike PAC learning, the learner receives only positives, may issue membership queries, and must output a…

In a weakly-supervised scenario object detectors need to be trained using image-level annotation alone. Since bounding-box-level ground truth is not available, most of the solutions proposed so far are based on an iterative, Multiple…

We study the task of bandit learning, also known as best-arm identification, under the assumption that the true reward function f belongs to a known, but arbitrary, function class F. We seek a general theory of bandit learnability, akin to…

We study risk-sensitive reinforcement learning in finite discounted MDPs, where a generative model of the MDP is assumed to be available. We consider a family or risk measures called the optimized certainty equivalent (OCE), which includes…

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…

The discovery of causal relationships is a foundational problem in artificial intelligence, statistics, epidemiology, economics, and beyond. While elegant theories exist for accurate causal discovery given infinite data, real-world…

Variational Autoencoders (VAEs) are powerful generative models for learning latent representations. Standard VAEs generate dispersed and unstructured latent spaces by utilizing all dimensions, which limits their interpretability, especially…

We generalize the PAC (probably approximately correct) learning model to the quantum world by generalizing the concepts from classical functions to quantum processes, defining the problem of \emph{PAC learning quantum process}, and study…

In this work we study the quantitative relation between the recursive teaching dimension (RTD) and the VC dimension (VCD) of concept classes of finite sizes. The RTD of a concept class $\mathcal C \subseteq \{0, 1\}^n$, introduced by Zilles…

Understanding 3D scenes semantically and spatially is crucial for the safe navigation of robots and autonomous vehicles, aiding obstacle avoidance and accurate trajectory planning. Camera-based 3D semantic occupancy prediction, which infers…

Cyber-physical systems (CPS) like autonomous vehicles, that utilize learning components, are often sensitive to noise and out-of-distribution (OOD) instances encountered during runtime. As such, safety critical tasks depend upon OOD…

We investigate the VC-dimension of the perceptron and simple two-layer networks like the committee- and the parity-machine with weights restricted to values $\pm1$. For binary inputs, the VC-dimension is determined by atypical pattern sets,…