Related papers: A Theory of PAC Learnability of Partial Concept Cl…

Monotone learning describes learning processes in which expected performance consistently improves as the amount of training data increases. However, recent studies challenge this conventional wisdom, revealing significant gaps in the…

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…

As learning solutions reach critical applications in social, industrial, and medical domains, the need to curtail their behavior has become paramount. There is now ample evidence that without explicit tailoring, learning can lead to biased,…

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…

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…

We introduce definitions of computable PAC learning for binary classification over computable metric spaces. We provide sufficient conditions for learners that are empirical risk minimizers (ERM) to be computable, and bound the strong…

In real-world applications, the distribution of the data, and our goals, evolve over time. The prevailing theoretical framework for studying machine learning, namely probably approximately correct (PAC) learning, largely ignores time. As a…

Proper learning refers to the setting in which learners must emit predictors in the underlying hypothesis class $H$, and often leads to learners with simple algorithmic forms (e.g. empirical risk minimization (ERM), structural risk…

Probably Approximately Correct (i.e., PAC) learning is a core concept of sample complexity theory, and efficient PAC learnability is often seen as a natural counterpart to the class P in classical computational complexity. But while the…

We study the sample complexity of multiclass prediction in several learning settings. For the PAC setting our analysis reveals a surprising phenomenon: In sharp contrast to binary classification, we show that there exist multiclass…

PAC learning, dating back to Valiant'84 and Vapnik and Chervonenkis'64,'74, is a classic model for studying supervised learning. In the agnostic setting, we have access to a hypothesis set $\mathcal{H}$ and a training set of labeled samples…

We study a variant of Collaborative PAC Learning, in which we aim to learn an accurate classifier for each of the $n$ data distributions, while minimizing the number of samples drawn from them in total. Unlike in the usual collaborative…

In this paper we study the problem of multiclass classification with a bounded number of different labels $k$, in the realizable setting. We extend the traditional PAC model to a) distribution-dependent learning rates, and b) learning rates…

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…

While many classical notions of learnability (e.g., PAC learnability) are distribution-free, utilizing the specific structures of an input distribution may improve learning performance. For example, a product distribution on a…

How quickly can a given class of concepts be learned from examples? It is common to measure the performance of a supervised machine learning algorithm by plotting its "learning curve", that is, the decay of the error rate as a function of…

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…

Over decades traditional information theory of source and channel coding advances toward learning and effective extraction of information from data. We propose to go one step further and offer a theoretical foundation for learning classical…

We study computable probably approximately correct (CPAC) learning, where learners are required to be computable functions. It had been previously observed that the Fundamental Theorem of Statistical Learning, which characterizes PAC…

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…