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The reparameterization trick (aka "reparameterization gradient estimator") is a technique used in statistical machine learning, particularly in variational inference, variational autoencoders, and stochastic optimization.
Variational Bayesian methods are a family of techniques for approximating intractable integrals arising in Bayesian inference and machine learning.They are typically used in complex statistical models consisting of observed variables (usually termed "data") as well as unknown parameters and latent variables, with various sorts of relationships among the three types of random variables, as ...
Expectation propagation (EP) is a technique in Bayesian machine learning. [1]EP finds approximations to a probability distribution. [1] It uses an iterative approach that uses the factorization structure of the target distribution. [1]
Variational free energy is a function of observations and a probability density over their hidden causes. This variational density is defined in relation to a probabilistic model that generates predicted observations from hypothesized causes. In this setting, free energy provides an approximation to Bayesian model evidence. [10]
The likelihood estimate needs to be as large as possible; because it's a lower bound, getting closer improves the approximation of the log likelihood. By substituting in the factorized version of , (), parameterized over the hidden nodes as above, is simply the negative relative entropy between and plus other terms independent of if is defined as
In variational Bayesian methods, the evidence lower bound (often abbreviated ELBO, also sometimes called the variational lower bound [1] or negative variational free energy) is a useful lower bound on the log-likelihood of some observed data.
To optimize this model, one needs to know two terms: the "reconstruction error", and the Kullback–Leibler divergence (KL-D). Both terms are derived from the free energy expression of the probabilistic model, and therefore differ depending on the noise distribution and the assumed prior of the data, here referred to as p-distribution.
Devising a good model for the data is central in Bayesian inference. In most cases, models only approximate the true process, and may not take into account certain factors influencing the data. [2] In Bayesian inference, probabilities can be assigned to model parameters. Parameters can be represented as random variables. Bayesian inference uses ...