Algorithmic Statistics, Prediction and Machine Learning

Milovanov, Alexey

doi:10.4230/lipics.stacs.2016.54

Cited by 1 publication

(2 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Let us note that in a more general setting [25] where we consider several strings as outcomes of the repeated experiment (with independent trials) and look for a model that explains all of them, a similar result is not true: not every probability distribution can be transformed into a uniform one.…”

Section: Optimality Deficiencymentioning

confidence: 99%

“…Though theorem 11 looks like a technical statement, it has important consequences; it implies that the two approaches based on randomness and optimality deficiencies remain equivalent in the case of bounded class of descriptions. The proof technique can be also used to prove Epstein-Levin theorem [11], as explained in [31]; similar technique was used by A. Milovanov in [25] where a common model for several strings is considered.…”

Section: Randomness and Optimality Deficiencies: Restricted Casementioning

confidence: 99%

See 1 more Smart Citation

Algorithmic Statistics: Forty Years Later

Vereshchagin

Shen

2016

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Algorithmic statistics has two different (and almost orthogonal) motivations. From the philosophical point of view, it tries to formalize how the statistics works and why some statistical models are better than others. After this notion of a "good model" is introduced, a natural question arises: it is possible that for some piece of data there is no good model? If yes, how often these bad (non-stochastic) data appear "in real life"?Another, more technical motivation comes from algorithmic information theory. In this theory a notion of complexity of a finite object (=amount of information in this object) is introduced; it assigns to every object some number, called its algorithmic complexity (or Kolmogorov complexity). Algorithmic statistic provides a more fine-grained classification: for each finite object some curve is defined that characterizes its behavior. It turns out that several different definitions give (approximately) the same curve. 1 In this survey we try to provide an exposition of the main results in the field (including full proofs for the most important ones), as well as some historical comments. We assume that the reader is familiar with the main notions of algorithmic information (Kolmogorov complexity) theory. An exposition can be found in [44, chapters 1, 3, 4] Montpellier, 161 rue Ada, 34095, France 1 Road-map: Section 2 considers the notion of (α, β)-stochasticity; Section 3 considers two-part descriptions and the so-called "minimal description length principle"; Section 4 gives one more approach: we consider the list of objects of bounded complexity and measure how far some object is from the end of the list, getting some natural class of "standard descriptions" as a by-product; finally, Section 5 establishes a connection between these notions and resource-bounded complexity. The rest of the paper deals with an attempts to make theory close to practice by considering restricted classes of description (Section 6) and strong models (Section 7).

show abstract

Section: Optimality Deficiencymentioning

confidence: 99%

Section: Randomness and Optimality Deficiencies: Restricted Casementioning

confidence: 99%