Related papers: Domains and Random Variables
Machine learning (ML) has emerged as a powerful tool for tackling complex regression and classification tasks, yet its success often hinges on the quality of training data. This study introduces an ML paradigm inspired by domain knowledge…
This paper offers a new perspective to ease the challenge of domain generalization, which involves maintaining robust results even in unseen environments. Our design focuses on the decision-making process in the final classifier layer.…
All famous machine learning algorithms that comprise both supervised and semi-supervised learning work well only under a common assumption: the training and test data follow the same distribution. When the distribution changes, most…
The theory revision problem is the problem of how best to go about revising a deficient domain theory using information contained in examples that expose inaccuracies. In this paper we present our approach to the theory revision problem for…
In this paper we examine the problem of inference in Bayesian Networks with discrete random variables that have very large or even unbounded domains. For example, in a domain where we are trying to identify a person, we may have variables…
We present a novel, yet rather simple construction within the traditional framework of Scott domains to provide semantics to probabilistic programming, thus obtaining a solution to a long-standing open problem in this area. Unlike current…
Two groups of naturally arising questions in the mathematical theory of domains for denotational semantics are addressed. Domains are equipped with Scott topology and represent data types. Scott continuous functions represent computable…
In probability theory, there is a tendency to treat one random variable with a given distribution as being just as good as any other. By and large this is fine because probability is (mostly) concerned with distributional properties of…
We develop Boolean-valued domain theory and show how the lambda-calculus can be interpreted in using domain-valued random variables. We focus on the reflexive domain construction rather than the language and its semantics. The notion of…
Machine learning systems generally assume that the training and testing distributions are the same. To this end, a key requirement is to develop models that can generalize to unseen distributions. Domain generalization (DG), i.e.,…
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,…
Machine learning models rely on various assumptions to attain high accuracy. One of the preliminary assumptions of these models is the independent and identical distribution, which suggests that the train and test data are sampled from the…
We tackle the problem of conditioning probabilistic programs on distributions of observable variables. Probabilistic programs are usually conditioned on samples from the joint data distribution, which we refer to as deterministic…
Recent advances in statistical inference have significantly expanded the toolbox of probabilistic modeling. Historically, probabilistic modeling has been constrained to (i) very restricted model classes where exact or approximate…
Domain generalization aims to develop a model that can perform well on unseen target domains by learning from multiple source domains. However, recent-proposed domain generalization models usually rely on domain labels, which may not be…
Researchers have been facing a difficult problem that data generation mechanisms could be influenced by internal or external factors leading to the training and test data with quite different distributions, consequently traditional…
Decision theories offer principled methods for making choices under various types of uncertainty. Algorithms that implement these theories have been successfully applied to a wide range of real-world problems, including materials and drug…
We propose a generalization of the random matrix theory following the basic prescription of the recently suggested concept of superstatistics. Spectral characteristics of systems with mixed regular-chaotic dynamics are expressed as weighted…
Categorical random variables are a common staple in machine learning methods and other applications across disciplines. Many times, correlation within categorical predictors exists, and has been noted to have an effect on various algorithm…
This text presents an unified approach of probability and statistics in the pursuit of understanding and computation of randomness in engineering or physical or social system with prediction with generalizability. Starting from elementary…