Related papers: PAC Verification of Statistical Algorithms

Many quantitative properties of probabilistic programs can be characterized as least fixed points, but verifying their lower bounds remains a challenging problem. We present a new approach to lower-bound verification that exploits and…

A fundamental result of statistical learnig theory states that a concept class is PAC learnable if and only if it is a uniform Glivenko-Cantelli class if and only if the VC dimension of the class is finite. However, the theorem is only…

In this paper, we investigate the question: Given a small number of datapoints, for example N = 30, how tight can PAC-Bayes and test set bounds be made? For such small datasets, test set bounds adversely affect generalisation performance by…

This paper proposes a data-driven systematic, consistent and non-exhaustive approach to Model Selection, that is an extension of the classical agnostic PAC learning model. In this approach, learning problems are modeled not only by a…

We prove an impossibility result for conditional Probably Approximately Correct (PAC)-efficient reasoning in large language models. While recent work has established marginal PAC efficiency guarantees for composite models that switch…

We establish fundamental and general techniques for formal verification of quantum protocols. Quantum protocols are novel communication schemes involving the use of quantum-mechanical phenomena for representation, storage and transmission…

We consider the problem of predicting as well as the best linear combination of d given functions in least squares regression under L^\infty constraints on the linear combination. When the input distribution is known, there already exists…

This paper investigates the algorithmic safety verification problem of infinite-state parameterized concurrent programs over a rich set of communication topologies. The goal is to automatically produce a proof of correctness in the form of…

This paper is about the recent notion of computably probably approximately correct learning, which lies between the statistical learning theory where there is no computational requirement on the learner and efficient PAC where the learner…

In machine learning applications, predictive models are trained to serve future queries across the entire data distribution. Real-world data often demands excessively complex models to achieve competitive performance, however, sacrificing…

We study the problem of learning robust classifiers where the classifier will receive a perturbed input. Unlike robust PAC learning studied in prior work, here the clean data and its label are also adversarially chosen. We formulate this…

$ \newcommand{\eps}{\varepsilon} $In learning theory, the VC dimension of a concept class $C$ is the most common way to measure its "richness." In the PAC model $$ \Theta\Big(\frac{d}{\eps} + \frac{\log(1/\delta)}{\eps}\Big) $$ examples are…

Recent advances in the binary classification setting by Hanneke [2016b] and Larsen [2023] have resulted in optimal PAC learners. These learners leverage, respectively, a clever deterministic subsampling scheme and the classic heuristic of…

Intermediate-scale quantum devices are becoming more reliable, and may soon be harnessed to solve useful computational tasks. At the same time, common classical methods used to verify their computational output become intractable due to a…

Quantum computers promise to efficiently solve not only problems believed to be intractable for classical computers, but also problems for which verifying the solution is also considered intractable. This raises the question of how one can…

Predictive parity (PP), also known as sufficiency, is a core definition of algorithmic fairness essentially stating that model outputs must have the same interpretation of expected outcomes regardless of group. Testing and satisfying PP is…

We address an inherent difficulty in welfare-theoretic fair machine learning by proposing an equivalently axiomatically-justified alternative and studying the resulting computational and statistical learning questions. Welfare metrics…

Minimising upper bounds on the population risk or the generalisation gap has been widely used in structural risk minimisation (SRM) -- this is in particular at the core of PAC-Bayesian learning. Despite its successes and unfailing surge of…

Gaussian Processes (GPs) are a generic modelling tool for supervised learning. While they have been successfully applied on large datasets, their use in safety-critical applications is hindered by the lack of good performance guarantees. To…

The aim of this paper is to generalize the PAC-Bayesian theorems proved by Catoni in the classification setting to more general problems of statistical inference. We show how to control the deviations of the risk of randomized estimators. A…