Related papers: Equivalences between learning of data and probabil…

In many learning theory problems, a central role is played by a hypothesis class: we might assume that the data is labeled according to a hypothesis in the class (usually referred to as the realizable setting), or we might evaluate the…

In this paper, we propose a learning algorithm that enables a model to quickly exploit commonalities among related tasks from an unseen task distribution, before quickly adapting to specific tasks from that same distribution. We investigate…

On-line learning of probability distributions is analyzed from the field theoretical point of view. We can obtain an optimal on-line learning algorithm, since renormalization group enables us to control the number of degrees of freedom of a…

We consider the problem of learning models for risk-sensitive reinforcement learning. We theoretically demonstrate that proper value equivalence, a method of learning models which can be used to plan optimally in the risk-neutral setting,…

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…

Transfer learning involves taking information and insight from one problem domain and applying it to a new problem domain. Although widely used in practice, theory for transfer learning remains less well-developed. To address this, we prove…

In this paper, a mathematical theory of learning is proposed that has many parallels with information theory. We consider Vapnik's General Setting of Learning in which the learning process is defined to be the act of selecting a hypothesis…

Designing models that are both expressive and preserve known invariances of tasks is an increasingly hard problem. Existing solutions tradeoff invariance for computational or memory resources. In this work, we show how to leverage…

We introduce a new embarrassingly parallel parameter learning algorithm for Markov random fields with untied parameters which is efficient for a large class of practical models. Our algorithm parallelizes naturally over cliques and, for…

Two different views on machine learning problem: Applied learning (machine learning with business applications) and Agnostic PAC learning are formalized and compared here. I show that, under some conditions, the theory of PAC Learnable…

Statistical learning theory is the foundation of machine learning, providing theoretical bounds for the risk of models learned from a (single) training set, assumed to issue from an unknown probability distribution. In actual deployment,…

Use of machine learning to perform database operations, such as indexing, cardinality estimation, and sorting, is shown to provide substantial performance benefits. However, when datasets change and data distribution shifts, empirical…

Domain similarity measures can be used to gauge adaptability and select suitable data for transfer learning, but existing approaches define ad hoc measures that are deemed suitable for respective tasks. Inspired by work on curriculum…

Algorithmic statistics considers the following problem: given a binary string $x$ (e.g., some experimental data), find a "good" explanation of this data. It uses algorithmic information theory to define formally what is a good explanation.…

The equivalence of realizable and agnostic learnability is a fundamental phenomenon in learning theory. With variants ranging from classical settings like PAC learning and regression to recent trends such as adversarially robust learning,…

Prior work of Gavryushkin, Khoussainov, Jain and Stephan investigated what algebraic structures can be realised in worlds given by a positive (= recursively enumerable) equivalence relation which partitions the natural numbers into…

The purpose of this paper is to look into how central notions in statistical learning theory, such as realisability, generalise under the assumption that train and test distribution are issued from the same credal set, i.e., a convex set of…

The inability of artificial neural networks to assess the uncertainty of their predictions is an impediment to their widespread use. We distinguish two types of learnable uncertainty: model uncertainty due to a lack of training data and…

The modeling of probability distributions, specifically generative modeling and density estimation, has become an immensely popular subject in recent years by virtue of its outstanding performance on sophisticated data such as images and…

In this paper, we aim at establishing an approximation theory and a learning theory of distribution regression via a fully connected neural network (FNN). In contrast to the classical regression methods, the input variables of distribution…