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  2. Reparameterization trick - Wikipedia

    en.wikipedia.org/wiki/Reparameterization_trick

    In this way, it is possible to backpropagate the gradient without involving stochastic variable during the update. The scheme of a variational autoencoder after the reparameterization trick. In Variational Autoencoders (VAEs), the VAE objective function, known as the Evidence Lower Bound (ELBO), is given by:

  3. Variational Bayesian methods - Wikipedia

    en.wikipedia.org/wiki/Variational_Bayesian_methods

    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 ...

  4. Malliavin calculus - Wikipedia

    en.wikipedia.org/wiki/Malliavin_calculus

    Malliavin introduced Malliavin calculus to provide a stochastic proof that Hörmander's condition implies the existence of a density for the solution of a stochastic differential equation; Hörmander's original proof was based on the theory of partial differential equations. His calculus enabled Malliavin to prove regularity bounds for the ...

  5. Variational message passing - Wikipedia

    en.wikipedia.org/wiki/Variational_message_passing

    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

  6. Calculus of variations - Wikipedia

    en.wikipedia.org/wiki/Calculus_of_Variations

    The calculus of variations (or variational calculus) is a field of mathematical analysis that uses variations, which are small changes in functions and functionals, to find maxima and minima of functionals: mappings from a set of functions to the real numbers.

  7. Bayesian experimental design - Wikipedia

    en.wikipedia.org/wiki/Bayesian_experimental_design

    In numerous publications on Bayesian experimental design, it is (often implicitly) assumed that all posterior probabilities will be approximately normal. This allows for the expected utility to be calculated using linear theory, averaging over the space of model parameters. [2]

  8. t-distributed stochastic neighbor embedding - Wikipedia

    en.wikipedia.org/wiki/T-distributed_stochastic...

    t-distributed stochastic neighbor embedding (t-SNE) is a statistical method for visualizing high-dimensional data by giving each datapoint a location in a two or three-dimensional map. It is based on Stochastic Neighbor Embedding originally developed by Geoffrey Hinton and Sam Roweis, [ 1 ] where Laurens van der Maaten and Hinton proposed the t ...

  9. Stochastic calculus - Wikipedia

    en.wikipedia.org/wiki/Stochastic_calculus

    The main flavours of stochastic calculus are the Itô calculus and its variational relative the Malliavin calculus. For technical reasons the Itô integral is the most useful for general classes of processes, but the related Stratonovich integral is frequently useful in problem formulation (particularly in engineering disciplines). The ...