相关论文: Computing the Vapnik Chervonenkis Dimension for No…

Vision-Language Models (VLMs) are increasingly pivotal for generalist robot manipulation, enabling tasks such as physical reasoning, policy generation, and failure detection. However, their proficiency in these high-level applications often…

Standard value function approaches to finding policies for Partially Observable Markov Decision Processes (POMDPs) are generally considered to be intractable for large models. The intractability of these algorithms is to a large extent a…

In this paper we present a novel model checking approach to finite-time safety verification of black-box continuous-time dynamical systems within the framework of probably approximately correct (PAC) learning. The black-box dynamical…

We present the first PAC optimal algorithm for Bayes-Adaptive Markov Decision Processes (BAMDPs) in continuous state and action spaces, to the best of our knowledge. The BAMDP framework elegantly addresses model uncertainty by incorporating…

In this paper, a mathematical theory of learning is proposed that has many parallels with information theory. We consider Vapnik's General Setting of Learning in which the learning process is defined to be the act of selecting a hypothesis…

In many applications of relational learning, the available data can be seen as a sample from a larger relational structure (e.g. we may be given a small fragment from some social network). In this paper we are particularly concerned with…

In this paper we study the approximate learnability of valuations commonly used throughout economics and game theory for the quantitative encoding of agent preferences. We provide upper and lower bounds regarding the learnability of…

This paper addresses the ``curse of dimensionality'' in the loss valuation of credit risk models. A dimension reduction methodology based on the Bayesian filter and smoother is proposed. This methodology is designed to achieve a fast and…

We give an algorithm that learns arbitrary Boolean functions of $k$ arbitrary halfspaces over $\mathbb{R}^n$, in the challenging distribution-free Probably Approximately Correct (PAC) learning model, running in time $2^{\sqrt{n} \cdot (\log…

We study the generalization capabilities of Group Convolutional Neural Networks (GCNNs) with ReLU activation function by deriving upper and lower bounds for their Vapnik-Chervonenkis (VC) dimension. Specifically, we analyze how factors such…

One of the earliest conjectures in computational learning theory-the Sample Compression conjecture-asserts that concept classes (equivalently set systems) admit compression schemes of size linear in their VC dimension. To-date this…

We propose a new sufficient dimension reduction approach designed deliberately for high-dimensional classification. This novel method is named maximal mean variance (MMV), inspired by the mean variance index first proposed by Cui, Li and…

We investigate the feasibility of sample average approximation (SAA) for general stochastic optimization problems, including two-stage stochastic programming without the relatively complete recourse assumption. Instead of analyzing problems…

We consider the problem of learning an unknown subset $N_\text{target}$ of a domain in an online setting. In each round $t$, the learner predicts a set of items ${N}_t$ and receives one of two types of feedback, each with equal probability:…

In this paper we develop a $C^0$-conforming virtual element method (VEM) for a class of second-order quasilinear elliptic PDEs in two dimensions. We present a posteriori error analysis for this problem and derive a residual based error…

Feature selection involes identifying the most relevant subset of input features, with a view to improving generalization of predictive models by reducing overfitting. Directly searching for the most relevant combination of attributes is…

The empirical risk minimization (ERM) principle has been highly impactful in machine learning, leading both to near-optimal theoretical guarantees for ERM-based learning algorithms as well as driving many of the recent empirical successes…

Machine unlearning seeks to remove the influence of particular data or class from trained models to meet privacy, legal, or ethical requirements. Existing unlearning methods tend to forget shallowly: phenomenon of an unlearned model pretend…

The VC dimension of the Ising perceptron with binary patterns is calculated by numerical enumerations for system sizes N <= 31. It is significantly larger than N/2. The data suggest that there is probably no well defined asymptotic…

A critical set in an $n \times n$ Latin square is a minimal set of entries that uniquely identifies it among all Latin squares of the same size. It is conjectured by Nelder in 1979, and later independently by Mahmoodian, and Bate and van…