Related papers: Mathematical Foundations of Probability Theory
This paper examines some methods and ideas underlying the author's successful probabilistic learning systems(PLS), which have proven uniquely effective and efficient in generalization learning or induction. While the emerging principles are…
Probability theory, epistemically interpreted, provides an excellent, if not the best available account of inductive reasoning. This is so because there are general and definite rules for the change of subjective probabilities through…
The aim of this article is to promote the use of probabilistic methods in the study of problems in mathematical general relativity. Two new and simple singularity theorems, whose features are different from the classical singularity…
The aim of this work is to provide a unified framework for ordinal representations of uncertainty lying at the crosswords between possibility and probability theories. Such confidence relations between events are commonly found in monotonic…
Data analysis and machine learning have become an integrative part of the modern scientific methodology, offering automated procedures for the prediction of a phenomenon based on past observations, unraveling underlying patterns in data and…
We present a semantics for adding uncertainty to conditional logics for default reasoning and belief revision. We are able to treat conditional sentences as statements of conditional probability, and express rules for revision such as "If A…
Variational inference uses optimization, rather than integration, to approximate the marginal likelihood, and thereby the posterior, in a Bayesian model. Thanks to advances in computational scalability made in the last decade, variational…
This chapter offers an accessible introduction to the channel-based approach to Bayesian probability theory. This framework rests on algebraic and logical foundations, inspired by the methodologies of programming language semantics. It…
Although not as wide, and popular, as that of quantum mechanics, the investigation of fundamental aspects of statistical mechanics constitutes an important research field in the building of modern physics. Besides the interest for itself,…
This textbook provides a systematic treatment of statistical machine learning for astronomical research through the lens of Bayesian inference, developing a unified framework that reveals connections between modern data analysis techniques…
In spite of its title, the book mostly treats probability theory: the law of large numbers (regarded as a principle); formal definition of a random variable and law of distribution; the misnamed Cauchy distribution; functions now named…
Bayesian Inference is a powerful approach to data analysis that is based almost entirely on probability theory. In this approach, probabilities model {\it uncertainty} rather than randomness or variability. This thesis is composed of a…
In natural-language discourse, related events tend to appear near each other to describe a larger scenario. Such structures can be formalized by the notion of a frame (a.k.a. template), which comprises a set of related events and…
Textbooks on statistics emphasize care and precision, via concepts such as reliability and validity in measurement, random sampling and treatment assignment in data collection, and causal identification and bias in estimation. But how do…
In this paper we study Probability Measures (PM) from a functional point of view: we show that PMs can be considered as functionals (generalized functions) that belong to some functional space endowed with an inner product. This approach…
Machine learning (ML) has become a commodity in our every-day lives. We routinely ask ML empowered smartphones to suggest lovely food places or to guide us through a strange place. ML methods have also become standard tools in many fields…
By probabilistic logic I mean a normative theory of belief that explains how a body of evidence affects one's degree of belief in a possible hypothesis. A new axiomatization of such a theory is presented which avoids a finite additivity…
Probabilistic programs encode stochastic models as ordinary-looking programs with primitives for sampling numbers from predefined distributions and conditioning. Their applications include, among many others, machine learning and modeling…
An a priori semimeasure (also known as "algorithmic probability" or "the Solomonoff prior" in the context of inductive inference) is defined as the transformation, by a given universal monotone Turing machine, of the uniform measure on the…
The philosophical foundations of statistics involve issues in theoretical statistics, such as goals and methods to meet these goals, and interpretation of the meaning of inference using statistics. They are related to the philosophy of…