Related papers: Learning the Hypotheses Space from data: Learning …
In the classic point location problem, one is given an arbitrary dataset $X \subset \mathbb{R}^d$ of $n$ points with query access to an unknown halfspace $f : \mathbb{R}^d \to \{0,1\}$, and the goal is to learn the label of every point in…
We apply the PAC-Bayes theory to the setting of learning-to-optimize. To the best of our knowledge, we present the first framework to learn optimization algorithms with provable generalization guarantees (PAC-bounds) and explicit trade-off…
The increased availability of data in recent years has led several authors to ask whether it is possible to use data as a {\em computational} resource. That is, if more data is available, beyond the sample complexity limit, is it possible…
Meta-learning can successfully acquire useful inductive biases from data. Yet, its generalization properties to unseen learning tasks are poorly understood. Particularly if the number of meta-training tasks is small, this raises concerns…
The classical PAC sample complexity bounds are stated for any Empirical Risk Minimizer (ERM) and contain an extra logarithmic factor $\log(1/{\epsilon})$ which is known to be necessary for ERM in general. It has been recently shown by…
The basic problem in the PAC model of computational learning theory is to determine which hypothesis classes are efficiently learnable. There is presently a dearth of results showing hardness of learning problems. Moreover, the existing…
We consider the relationship between learnability of a "base class" of functions on a set $X$, and learnability of a class of statistical functions derived from the base class. For example, we refine results showing that learnability of a…
Classic supervised learning involves algorithms trained on $n$ labeled examples to produce a hypothesis $h \in \mathcal{H}$ aimed at performing well on unseen examples. Meta-learning extends this by training across $n$ tasks, with $m$…
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…
A classical result in learning theory shows the equivalence of PAC learnability of binary hypothesis classes and the finiteness of VC dimension. Extending this to the multiclass setting was an open problem, which was settled in a recent…
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…
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…
Data-driven algorithms can adapt their internal structure or parameters to inputs from unknown application-specific distributions, by learning from a training sample of inputs. Several recent works have applied this approach to problems in…
Learning curves are a fundamental primitive in supervised learning, describing how an algorithm's performance improves with more data and providing a quantitative measure of its generalization ability. Formally, a learning curve plots the…
We initiate the study of tolerant adversarial PAC-learning with respect to metric perturbation sets. In adversarial PAC-learning, an adversary is allowed to replace a test point $x$ with an arbitrary point in a closed ball of radius $r$…
We study the problem of binary classification from the point of view of learning convex polyhedra in Hilbert spaces, to which one can reduce any binary classification problem. The problem of learning convex polyhedra in finite-dimensional…
We present new PAC-Bayesian generalisation bounds for learning problems with unbounded loss functions. This extends the relevance and applicability of the PAC-Bayes learning framework, where most of the existing literature focuses on…
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…
We introduce a novel technique for verification and model synthesis of sequential programs. Our technique is based on learning a regular model of the set of feasible paths in a program, and testing whether this model contains an incorrect…
Probably the most important problem in machine learning is the preliminary biasing of a learner's hypothesis space so that it is small enough to ensure good generalisation from reasonable training sets, yet large enough that it contains a…