Encyclopædia BayesICA
- Bayesian statistics
- "The physics of learning systems"
- Probability is a measure of degree of belief
- Bayes rule tells how beliefs are updated when new observations are made
- Marginalization can be used for prediction and inference about
unknown quantities
- Decisions are based on expected utilities (where expectation is taken
over the current beliefs/probabilities)
- In practice, the integrals are approximated in some way or another
- Ensemble learning
- Bayesian ensemble learning is one type of variational learning
- Misfit between the true posterior and its approximation is measured
by Kullback-Leibler information
- Yields bounds for probability of the data given the model structure
- Close connection to minimum description length principle
- Variational learning
- Calculus of variations refers to optimization problems where the
optimand is a function (as opposed to real number or a vector of
real numbers)
- Methods where a simpler function is fitted to the posterior
- Latent variable models
- Models which postulate unobserved variables to explain
regularities in the observations
- Gaussian linear factor analysis model is one of the simples examples:
unknown factors are assumed to be responsible for the observations
- Pretty much the same as generative models
- Generative models
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- Models which explicitly state how the observations have been generated
by partly or fully unknown factors
- Pretty much the same as latent variable models
- Unsupervised learning
- The goal of unsupervised learning is to extract an efficient
representation of the statistical structure implicit in the
observations
- Generative or latent variable models are common tools
- Minimum description length (MDL) principle
- Principle which states that the most compact explanation for the
observations should be favoured over other explanations
- Description length L(x) of x is measured in bits and is (more or
less) L(x) = -log P(x), where P(x) is the probability of x
- As a learning theory not as well founded theoretically as Bayesian
statistics but can allow intuitive interpretations to various
phenomena in learning
- Bayesian ensemble learning bridges Bayesian statistics and
MDL
Figure caption
Pine trees in winter in Espoo.