Related papers: A Theory of Universal Learning
Machine learning researchers and practitioners steadily enlarge the multitude of successful learning models. They achieve this through in-depth theoretical analyses and experiential heuristics. However, there is no known general-purpose…
We consider the problem of PAC-learning decision trees, i.e., learning a decision tree over the n-dimensional hypercube from independent random labeled examples. Despite significant effort, no polynomial-time algorithm is known for learning…
We informally call a stochastic process learnable if it admits a generalization error approaching zero in probability for any concept class with finite VC-dimension (IID processes are the simplest example). A mixture of learnable processes…
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…
We use the PAC-Bayesian theory for 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-Bayesian bounds) and explicit…
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…
We generalize the PAC (probably approximately correct) learning model to the quantum world by generalizing the concepts from classical functions to quantum processes, defining the problem of \emph{PAC learning quantum process}, and study…
Statistical learning theory chiefly studies restricted hypothesis classes, particularly those with finite Vapnik-Chervonenkis (VC) dimension. The fundamental quantity of interest is the sample complexity: the number of samples required to…
Transfer learning has received a lot of attention in the machine learning community over the last years, and several effective algorithms have been developed. However, relatively little is known about their theoretical properties,…
Supervised learning aims to train a classifier under the assumption that training and test data are from the same distribution. To ease the above assumption, researchers have studied a more realistic setting: out-of-distribution (OOD)…
This paper surveys quantum learning theory: the theoretical aspects of machine learning using quantum computers. We describe the main results known for three models of learning: exact learning from membership queries, and Probably…
This paper proposes a data-driven systematic, consistent and non-exhaustive approach to Model Selection, that is an extension of the classical agnostic PAC learning model. In this approach, learning problems are modeled not only by a…
A Machine can only learn if it is biased in some way. Typically the bias is supplied by hand, for example through the choice of an appropriate set of features. However, if the learning machine is embedded within an {\em environment} of…
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…
Here we study the comparative power of classical and quantum learners for generative modelling within the Probably Approximately Correct (PAC) framework. More specifically we consider the following task: Given samples from some unknown…
Transformation invariances are present in many real-world problems. For example, image classification is usually invariant to rotation and color transformation: a rotated car in a different color is still identified as a car. Data…
Statistical learning theory and the Probably Approximately Correct (PAC) criterion are the common approach to mathematical learning theory. PAC is widely used to analyze learning problems and algorithms, and have been studied thoroughly.…
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 explore questions dealing with the learnability of models of choice over time. We present a large class of preference models defined by a structural criterion for which we are able to obtain an exponential improvement over previously…
Learning curves are a concept from social sciences that has been adopted in the context of machine learning to assess the performance of a learning algorithm with respect to a certain resource, e.g., the number of training examples or the…