Related papers: On characterizations of learnability with computab…
Following the wide-spread adoption of machine learning models in real-world applications, the phenomenon of performativity, i.e. model-dependent shifts in the test distribution, becomes increasingly prevalent. Unfortunately, since models…
We demonstrate a compactness result holding broadly across supervised learning with a general class of loss functions: Any hypothesis class $H$ is learnable with transductive sample complexity $m$ precisely when all of its finite…
We study uniform computability properties of PAC learning using Weihrauch complexity. We focus on closed concept classes, which are either represented by positive, by negative or by full information. Among other results, we prove that…
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…
Understanding when learning is possible is a fundamental task in the theory of machine learning. However, many characterizations known from the literature deal with abstract learning as a mathematical object and ignore the crucial question:…
This survey paper gives an overview of various known results on learning classes of Boolean functions in Valiant's Probably Approximately Correct (PAC) learning model and its commonly studied variants.
In response to a 1997 problem of M. Vidyasagar, we state a necessary and sufficient condition for distribution-free PAC learnability of a concept class $\mathscr C$ under the family of all non-atomic (diffuse) measures on the domain…
In Ben-David et al.'s "Learnability Can Be Undecidable," they prove an independence result in theoretical machine learning. In particular, they define a new type of learnability, called Estimating The Maximum (EMX) learnability. They argue…
In language learning in the limit, the most common type of hypothesis is to give an enumerator for a language. This so-called $W$-index allows for naming arbitrary computably enumerable languages, with the drawback that even the membership…
Beyond binary classification, learnability can become a logically fragile notion: in EMX, even the class of all finite subsets of $[0,1]$ is learnable in some models of ZFC and not in others. We argue the paradox is operational. The…
The study of strategic or adversarial manipulation of testing data to fool a classifier has attracted much recent attention. Most previous works have focused on two extreme situations where any testing data point either is completely…
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…
Most models of machine teaching and learning assume the learner makes no errors in its internal deductive inference. However, humans and large language models in few-shot learning regimes are two important examples of learners where this…
We investigate replicable learning algorithms. Ideally, we would like to design algorithms that output the same canonical model over multiple runs, even when different runs observe a different set of samples from the unknown data…
Exchangeable random variables form an important and well-studied generalization of i.i.d. variables, however simple examples show that no nontrivial concept or function classes are PAC learnable under general exchangeable data inputs…
In contrast with standard classification tasks, strategic classification involves agents strategically modifying their features in an effort to receive favorable predictions. For instance, given a classifier determining loan approval based…
Controllability has become a crucial aspect of trustworthy machine learning, enabling learners to meet predefined targets and adapt dynamically at test time without requiring retraining as the targets shift. We provide a formal definition…
In this paper, we consider the problem of replicable realizable PAC learning. We construct a particularly hard learning problem and show a sample complexity lower bound with a close to $(\log|H|)^{3/2}$ dependence on the size of the…
In a companion paper it was shown that the class of constant-depth determinate k-ary recursive clauses is efficiently learnable. In this paper we present negative results showing that any natural generalization of this class is hard to…
The increasing impact of black box models, and particularly of unsupervised ones, comes with an increasing interest in tools to understand and interpret them. In this paper, we consider in particular how to characterise visual groupings…