Inductive probability attempts to give the probability of future events based on past events. It is the basis for inductive reasoning, and gives the mathematical basis for learning and the perception of patterns. It is a source of knowledge about the world.
There are three sources of knowledge: inference, communication, and deduction. Communication relays information found using other methods. Deduction establishes new facts based on existing facts. Inference establishes new facts from data. Its basis is Bayes' theorem.
Information describing the world is written in a language. For example, a simple mathematical language of propositions may be chosen. Sentences may be written down in this language as strings of characters. But in the computer it is possible to encode these sentences as strings of bits (1s and 0s). Then the language may be encoded so that the most commonly used sentences are the shortest. This internal language implicitly represents probabilities of statements.
Occam's razor says the "simplest theory, consistent with the data is most likely to be correct". The "simplest theory" is interpreted as the representation of the theory written in this internal language. The theory with the shortest encoding in this internal language is most likely to be correct.
Probability and statistics was focused on probability distributions and tests of significance. Probability was formal, well defined, but limited in scope. In particular its application was limited to situations that could be defined as an experiment or trial, with a well defined population.
Bayes's theorem is named after Rev. Thomas Bayes 1701–1761. Bayesian inference broadened the application of probability to many situations where a population was not well defined. But Bayes' theorem always depended on prior probabilities, to generate new probabilities. It was unclear where these prior probabilities should come from.
Ray Solomonoff developed algorithmic probability which gave an explanation for what randomness is and how patterns in the data may be represented by computer programs, that give shorter representations of the data circa 1964.
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Minimum message length (MML) is a Bayesian information-theoretic method for statistical model comparison and selection. It provides a formal information theory restatement of Occam's Razor: even when models are equal in their measure of fit-accuracy to the observed data, the one generating the most concise explanation of data is more likely to be correct (where the explanation consists of the statement of the model, followed by the lossless encoding of the data using the stated model).
Inductive probability attempts to give the probability of future events based on past events. It is the basis for inductive reasoning, and gives the mathematical basis for learning and the perception of patterns. It is a source of knowledge about the world. There are three sources of knowledge: inference, communication, and deduction. Communication relays information found using other methods. Deduction establishes new facts based on existing facts. Inference establishes new facts from data. Its basis is Bayes' theorem.
La longueur de description minimale ou LDM (MDL pour Minimum Description Length en anglais) est un concept inventé par Jorma Rissanen en 1978 et utilisé en théorie de l'information et en compression de données. Le principe est basé sur l'affirmation suivante : toute régularité dans un ensemble de données peut être utilisée afin de compresser l'information, c'est-à-dire l'exprimer à l'aide d'un nombre réduit de symboles. Théorie de l'information Jorma Rissanen, « Modeling by shortest data description », Automatica, vol 14, No 5, pp.
Discrete mathematics is a discipline with applications to almost all areas of study. It provides a set of indispensable tools to computer science in particular. This course reviews (familiar) topics a
The course introduces the foundations on which programs and programming languages are built. It introduces syntax, types and semantics as building blocks that together define the properties of a progr
Introduction aux techniques de l'Intelligence Artificielle, complémentée par des exercices de programmation qui montrent les algorithmes et des exemples de leur application à des problèmes pratiques.
Explore le raisonnement incertain, les réseaux bayésiens et la résolution stochastique, soulignant l'importance de la logique probabiliste et de l'enlèvement.
Explore les modèles génératifs, la régression logistique et la distribution gaussienne pour approximer les probabilités postérieures et optimiser les performances du modèle.