Related papers: Knowledge from Probability
An inductive logic can be formulated in which the elements are not propositions or probability distributions, but information systems. The logic is complete for information systems with binary hypotheses, i.e., it applies to all such…
Knowledge constitutes the accumulated understanding and experience that humans use to gain insight into the world. In deep learning, prior knowledge is essential for mitigating shortcomings of data-driven models, such as data dependence,…
We develop a systematic approach to quantum probability as a theory of rational betting in quantum gambles. In these games of chance the agent is betting in advance on the outcomes of several (finitely many) incompatible measurements. One…
Controversy about the significance of underdetermination of theories persists in the philosophy and conduct of science. The issue has practical import when research is used to inform decision making, because scientific uncertainty yields…
I discuss the meaning of probability in the Everett-Wheeler interpretation of quantum mechanics, together with the problem of defining histories. To resolve these, I propose an understanding of probability arising from a form of temporal…
The goal of machine learning is to find models that minimize prediction error on data that has not yet been seen. Its operational paradigm assumes access to a dataset $S$ and articulates a scheme for evaluating how well a given model…
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…
Prediction in quantum cosmology requires a specification of the universe's quantum dynamics and its quantum state. We expect only a few general features of the universe to be predicted with probabilities near unity conditioned on the…
Bayesian probability theory is used as a framework to develop a formalism for the scientific method based on principles of inductive reasoning. The formalism allows for precise definitions of the key concepts in theories of physics and also…
Forecasting has always been at the forefront of decision making and planning. The uncertainty that surrounds the future is both exciting and challenging, with individuals and organisations seeking to minimise risks and maximise utilities.…
Bayesian statistics is based on the subjective definition of probability as {\it ``degree of belief''} and on Bayes' theorem, the basic tool for assigning probabilities to hypotheses combining {\it a priori} judgements and experimental…
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…
A fundamental problem in science is how to make logical inferences from scientific data. Mere data does not suffice since additional information is necessary to select a domain of models or hypotheses and thus determine the likelihood of…
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…
Consider a predictor who ranks eventualities on the basis of past cases: for instance a search engine ranking webpages given past searches. Resampling past cases leads to different rankings and the extraction of deeper information. Yet a…
Many policies allocate harms or benefits that are uncertain in nature: they produce distributions over the population in which individuals have different probabilities of incurring harm or benefit. Comparing different policies thus involves…
Mathematics is a limited component of solutions to real-world problems, as it expresses only what is expected to be true if all our assumptions are correct, including implicit assumptions that are omnipresent and often incorrect.…
Note: Published now as a chapter in "Handbook of the History and Philosophy of Mathematical Practice" (Springer Nature, editor B. Sriraman, https://doi.org/10.1007/978-3-030-19071-2_105-1). The application of mathematical probability theory…
Human reasoning often involves working over limited information to arrive at probabilistic conclusions. In its simplest form, this involves making an inference that is not strictly entailed by a premise, but rather only likely given the…
The invariant response was defined from a formulation of the fluctuation-response theorem in the space of probability distributions. An inequality is here conjectured which sets the mutual information as an upper bound to the invariant…