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  2. Reparameterization trick - Wikipedia

    en.wikipedia.org/wiki/Reparameterization_trick

    The reparameterization trick (aka "reparameterization gradient estimator") is a technique used in statistical machine learning, particularly in variational inference, variational autoencoders, and stochastic optimization.

  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. Deep backward stochastic differential equation method

    en.wikipedia.org/wiki/Deep_backward_stochastic...

    Deep backward stochastic differential equation method is a numerical method that combines deep learning with Backward stochastic differential equation (BSDE). This method is particularly useful for solving high-dimensional problems in financial derivatives pricing and risk management .

  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. 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 ...

  8. 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

  9. Variational autoencoder - Wikipedia

    en.wikipedia.org/wiki/Variational_autoencoder

    However, variational autoencoders use a neural network as an amortized approach to jointly optimize across data points. This neural network takes as input the data points themselves, and outputs parameters for the variational distribution. As it maps from a known input space to the low-dimensional latent space, it is called the encoder.