Related papers: On computable learning of continuous features

In this short note we observe that the sample complexity of PAC machine learning of various concepts, including learning the maximum (EMX), can be exactly determined when the support of the probability measures considered as models…

The standard definition of PAC learning (Valiant 1984) requires learners to succeed under all distributions -- even ones that are intractable to sample from. This stands in contrast to samplable PAC learning (Blum, Furst, Kearns, and Lipton…

The Fundamental Theorem of Statistical Learning states that a hypothesis space is PAC learnable if and only if its VC dimension is finite. For the agnostic model of PAC learning, the literature so far presents proofs of this theorem that…

We prove risk bounds for binary classification in high-dimensional settings when the sample size is allowed to be smaller than the dimensionality of the training set observations. In particular, we prove upper bounds for both 'compressive…

The problem of attempting to learn the mapping between data and labels is the crux of any machine learning task. It is, therefore, of interest to the machine learning community on practical as well as theoretical counts to consider the…

The goal of a learning algorithm is to receive a training data set as input and provide a hypothesis that can generalize to all possible data points from a domain set. The hypothesis is chosen from hypothesis classes with potentially…

We study contrastive learning under the PAC learning framework. While a series of recent works have shown statistical results for learning under contrastive loss, based either on the VC-dimension or Rademacher complexity, their algorithms…

An active learner is given a class of models, a large set of unlabeled examples, and the ability to interactively query labels of a subset of these examples; the goal of the learner is to learn a model in the class that fits the data well.…

We propose a general theorem providing upper bounds for the risk of an empirical risk minimizer (ERM).We essentially focus on the binary classification framework. We extend Tsybakov's analysis of the risk of an ERM under margin type…

The universal learning framework has been developed to obtain guarantees on the learning rates that hold for any fixed distribution, which can be much faster than the ones uniformly hold over all the distributions. Given that the Empirical…

The well-known empirical risk minimization (ERM) principle is the basis of many widely used machine learning algorithms, and plays an essential role in the classical PAC theory. A common description of a learning algorithm's performance is…

Learning from quantum data presents new challenges to the paradigm of learning from data. This typically entails the use of quantum learning models to learn quantum processes that come with enough subtleties to modify the theoretical…

We compute that the index set of PAC-learnable concept classes is $m$-complete $\Sigma^0_3$ within the set of indices for all concept classes of a reasonable form. All concept classes considered are computable enumerations of computable…

We study the problem of reducing adversarially robust learning to standard PAC learning, i.e. the complexity of learning adversarially robust predictors using access to only a black-box non-robust learner. We give a reduction that can…

This paper contributes to the study of CPAC learnability -- a computable version of PAC learning -- by solving three open questions from recent papers. Firstly, we prove that every improperly CPAC learnable class is contained in a class…

We present a formal proof in Lean of probably approximately correct (PAC) learnability of the concept class of decision stumps. This classic result in machine learning theory derives a bound on error probabilities for a simple type of…

Conditional Value at Risk (CVaR) is a family of "coherent risk measures" which generalize the traditional mathematical expectation. Widely used in mathematical finance, it is garnering increasing interest in machine learning, e.g., as an…

The Fundamental Theorem of PAC Learning asserts that learnability of a concept class $H$ is equivalent to the $\textit{uniform convergence}$ of empirical error in $H$ to its mean, or equivalently, to the problem of $\textit{density…

Considering a probability distribution over parameters is known as an efficient strategy to learn a neural network with non-differentiable activation functions. We study the expectation of a probabilistic neural network as a predictor by…

We introduce the problem of learning conditional averages in the PAC framework. The learner receives a sample labeled by an unknown target concept from a known concept class, as in standard PAC learning. However, instead of learning the…