相关论文: PAC Learning, VC Dimension, and the Arithmetic Hie…

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…

We propose an algorithm combining calibrated prediction and generalization bounds from learning theory to construct confidence sets for deep neural networks with PAC guarantees---i.e., the confidence set for a given input contains the true…

Finite semisimple group algebras for which all the minimal ideals are easily computable dimension (ECD) are characterized and some lower bounds for the minimum Hamming distance of group codes in these algebras are offered. Examples…

Two different views on machine learning problem: Applied learning (machine learning with business applications) and Agnostic PAC learning are formalized and compared here. I show that, under some conditions, the theory of PAC Learnable…

This paper presents an extension of the classical agnostic PAC learning model in which learning problems are modelled not only by a Hypothesis Space $\mathcal{H}$, but also by a Learning Space $\mathbb{L}(\mathcal{H})$, which is a cover of…

To date, the tightest upper and lower-bounds for the active learning of general concept classes have been in terms of a parameter of the learning problem called the splitting index. We provide, for the first time, an efficient algorithm…

Bounds on the risk play a crucial role in statistical learning theory. They usually involve as capacity measure of the model studied the VC dimension or one of its extensions. In classification, such "VC dimensions" exist for models taking…

We provide some background on the category of classifiable $\mathrm{C}^*$-algebras, whose objects are infinite-dimensional, simple, separable, unital $\mathrm{C}^*$-algebras that have finite nuclear dimension and satisfy the universal…

Replicability, introduced by (Impagliazzo et al. STOC '22), is the notion that algorithms should remain stable under a resampling of their inputs (given access to shared randomness). While a strong and interesting notion of stability, the…

Learning is a process wherein a learning agent enhances its performance through exposure of experience or data. Throughout this journey, the agent may encounter diverse learning environments. For example, data may be presented to the leaner…

We consider the problem of learning rules from a data set that support a proof of a given query, under Valiant's PAC-Semantics. We show how any backward proof search algorithm that is sufficiently oblivious to the contents of its knowledge…

Static program analysis today takes an analytical approach which is quite suitable for a well-scoped system. Data- and control-flow is taken into account. Special cases such as pointers, procedures, and undefined behavior must be handled. A…

We study an abstract framework for interactive learning called interactive estimation in which the goal is to estimate a target from its "similarity'' to points queried by the learner. We introduce a combinatorial measure called…

How many bits of information are revealed by a learning algorithm for a concept class of VC-dimension $d$? Previous works have shown that even for $d=1$ the amount of information may be unbounded (tend to $\infty$ with the universe size).…

In this note we study the computational complexity of feedback arc set counting problems in directed graphs, highlighting some subtle yet common properties of counting classes. Counting the number of feedback arc sets of cardinality $k$ and…

Multiclass neural networks are a common tool in modern unsupervised domain adaptation, yet an appropriate theoretical description for their non-uniform sample complexity is lacking in the adaptation literature. To fill this gap, we propose…

In this paper we use finite vector spaces (finite dimension, over finite fields) as a non-standard computational model of linear logic. We first define a simple, finite PCF-like lambda-calculus with booleans, and then we discuss two finite…

We consider the problem of learning generalized first-order representations of concepts from a single example. To address this challenging problem, we augment an inductive logic programming learner with two novel algorithmic contributions.…

A central goal in the cognitive sciences is the development of numerical models for mental representations of object concepts. This paper introduces Variational Interpretable Concept Embeddings (VICE), an approximate Bayesian method for…

A recent line of work has shown a qualitative equivalence between differentially private PAC learning and online learning: A concept class is privately learnable if and only if it is online learnable with a finite mistake bound. However,…