Related papers: Domains and Random Variables
Abstract Contextuality is a property of systems of random variables. The identity of a random variable in a system is determined by its joint distribution with all other random variables in the same context. When context changes, a variable…
We present two theorems concerned with algorithmic randomness and differentiability of functions of several variables. Firstly, we prove an effective form of the Rademacher's Theorem: we show that computable randomness implies…
We provide a formal, simple and intuitive theory of rational decision making including sequential decisions that affect the environment. The theory has a geometric flavor, which makes the arguments easy to visualize and understand. Our…
In combinatorics, the probabilistic method is a very powerful tool to prove the existence of combinatorial objects with interesting and useful properties. Explicit constructions of objects with such properties are often very difficult, or…
This paper covers two topics: first an introduction to Algorithmic Complexity Theory: how it defines probability, some of its characteristic properties and past successful applications. Second, we apply it to problems in A.I. - where it…
This contribution proposes a new approach towards developing a class of probabilistic methods for classifying attributed graphs. The key concept is random attributed graph, which is defined as an attributed graph whose nodes and edges are…
Bayesian network is a complete model for the variables and their relationships, it can be used to answer probabilistic queries about them. A Bayesian network can thus be considered a mechanism for automatically applying Bayes' theorem to…
The purpose of this article is to formulate a number of probabilistic hidden-variable theorems, to provide proofs in some cases, and counterexamples to some conjectured relationships. The first theorem is the fundamental one. It asserts the…
This book introduces to the theory of probabilities from the beginning. Assuming that the reader possesses the normal mathematical level acquired at the end of the secondary school, we aim to equip him with a solid basis in probability…
In this paper we describe a theory of a cumulative distribution function on a space with an order from a probability measure defined in this space. This distribution function plays a similar role to that played in the classical case.…
It is argued from several points of view that quantum probabilities might play a role in statistical settings. New approaches toward quantum foundations have postulates that appear to be equally valid in macroscopic settings. One such…
Domain randomization (DR) is a successful technique for learning robust policies for robot systems, when the dynamics of the target robot system are unknown. The success of policies trained with domain randomization however, is highly…
The risk of occurrence of atypical phenomena is a cross-cutting concern in several areas, such as engineering, climatology, finance, actuarial, among others. Extreme value theory is the natural tool to approach this theme. Many of these…
Domain randomization in reinforcement learning is an established technique for increasing the robustness of control policies trained in simulation. By randomizing environment properties during training, the learned policy can become robust…
Domain generalization aims at training machine learning models to perform robustly across different and unseen domains. Several recent methods use multiple datasets to train models to extract domain-invariant features, hoping to generalize…
Some tools and ideas are interchanged between random matrix theory and multivariate statistics. In the context of the random matrix theory, classes of spherical and generalised Wishart random matrix ensemble, containing as particular cases…
The ability to build a model on a source task and subsequently adapt such model on a new target task is a pervasive need in many astronomical applications. The problem is generally known as transfer learning in machine learning, where…
Given a universe of discourse X-a domain of possible outcomes-an experiment may consist of selecting one of its elements, subject to the operation of chance, or of observing the elements, subject to imprecision. A priori uncertainty about…
We provide an analysis of theory ladenness in machine learning in science, where "theory", that we call "domain theory", refers to the domain knowledge of the scientific discipline where ML is used. By constructing an account of ML models…
How can probabilities make sense in a deterministic many-worlds theory? We address two facets of this problem: why should rational agents assign subjective probabilities to branching events, and why should branching events happen with…