Related papers: How and Why Did Probability Theory Come About?
This work in progress aims to provide a unified introduction to statistical learning, building up slowly from classical models like the GMM and HMM to modern neural networks like the VAE and diffusion models. There are today many internet…
This paper deals with the problem of estimating the probability that one event was a cause of another in a given scenario. Using structural-semantical definitions of the probabilities of necessary or sufficient causation (or both), we show…
This is a report on the work of Robert Langlands, following his award of the Abel Prize in 2018. It includes his contributions to the general areas of Representation Theory, Automorphic Forms, Number Theory and Arithmetic Geometry. We have…
Classical probability theory supports probability measures, assigning a fixed positive real value to each event, these measures are far from satisfactory in formulating real-life occurrences. The main innovation of this paper is the…
A review is presented of the origin and development of the atomic hypothesis from antiquity till about the first millennium of the common era.
We give a probabilistic analysis of inductive knowledge and belief and explore its predictions concerning knowledge about the future, about laws of nature, and about the values of inexactly measured quantities. The analysis combines a…
This paper argues for a modal view of probability. The syntax and semantics of one particularly strong probability logic are discussed and some examples of the use of the logic are provided. We show that it is both natural and useful to…
This graduate textbook on machine learning tells a story of how patterns in data support predictions and consequential actions. Starting with the foundations of decision making, we cover representation, optimization, and generalization as…
Typicality has always been in the minds of the founding fathers of probability theory when probabilistic reasoning is applied to the real world. However, the role of typicality is not always appreciated. An example is the paper "Foundations…
What is the physical origin of the arrow of time? It is a commonly held belief in the physics community that it relates to the increase of entropy as it appears in the statistical interpretation of the second law of thermodynamics. At the…
The 175th anniversary of the ASA provides an opportunity to look back into the past and peer into the future. What led our forebears to found the association? What commonalities do we still see? What insights might we glean from their…
Recent developments in the mathematical foundations of quantum mechanics have brought the theory closer to that of classical probability and statistics. On the other hand, the unique character of quantum physics sets many of the questions…
Uncertainty enters into human reasoning and inference in at least two ways. It is reasonable to suppose that there will be roles for these distinct uses of uncertainty also in automated reasoning.
The idea that the brain is a probabilistic (Bayesian) inference machine, continuously trying to figure out the hidden causes of its inputs, has become very influential in cognitive (neuro)science over recent decades. Here I present a…
This essay traces the history of three interconnected strands. Firstly, changes in the concept of number, secondly, the study of the qualities of number, which evolved into number theory, and thirdly, the nature of mathematics itself, from…
Combinatorics is a fundamental mathematical discipline as well as an essential component of many mathematical areas, and its study has experienced an impressive growth in recent years. One of the main reasons for this growth is the tight…
This is the introductory paper to the special issue of Topology and Its Applications entirely dedicated to the theory of continuous selections of multivalued mappings. Since the pioneering work of Ernest Michael from 1956 can rightfully be…
The past two decades have witnessed a surge of new research in the analysis of randomized experiments. The emergence of this literature may seem surprising given the widespread use and long history of experiments as the "gold standard" in…
Deep learning algorithms have made incredible strides in the past decade, yet due to their complexity, the science of deep learning remains in its early stages. Being an experimentally driven field, it is natural to seek a theory of deep…
Astronomy is an observationally-led subject where chance discoveries play an important role. A whole range of such discoveries is continually made, from the trivial to the highly significant. What is generally needed is for luck to strike…