variational principle - significado y definición. Qué es variational principle
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Qué (quién) es variational principle - definición


Variational principle         
A SCIENTIFIC PRINCIPLE USED WITHIN THE CALCULUS OF VARIATIONS, WHICH DEVELOPS GENERAL METHODS FOR FINDING FUNCTIONS WHICH EXTREMIZE THE VALUE OF QUANTITIES THAT DEPEND UPON THOSE FUNCTIONS
Variational Principle; Variational principles
In science and especially in mathematical studies, a variational principle is one that enables a problem to be solved using calculus of variations, which concerns finding functions that optimize the values of quantities that depend on those functions. For example, the problem of determining the shape of a hanging chain suspended at both ends—a catenary—can be solved using variational calculus, and in this case, the variational principle is the following: The solution is a function that minimizes the gravitational potential energy of the chain.
Variational Bayesian methods         
  • Pictorial illustration of coordinate ascent variational inference algorithm by the duality formula<ref name=Yoon2021/>
MATHEMATICAL METHODS USED IN BAYESIAN INFERENCE AND MACHINE LEARNING
Variational bayes; Variational Bayes; Variational Bayesian method; Variational inference; Variational free energy
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 might be described by a graphical model.
Variational autoencoder         
  • The scheme of the reparameterization trick. The randomness variable <math>{\varepsilon}</math> is injected into the latent space <math>z</math> as external input. In this way, it is possible to backpropagate the gradient without involving stochastic variable during the update.
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  • The basic scheme of a variational autoencoder. The model receives <math>x</math> as input. The encoder compresses it into the latent space. The decoder receives as input the information sampled from the latent space and produces <math>{x'}</math> as similar as possible to <math>x</math>.
DEEP LEARNING GENERATIVE MODEL TO ENCODE DATA REPRESENTATION
Variational autoencoders
In machine learning, a variational autoencoder (VAE), is an artificial neural network architecture introduced by Diederik P. Kingma and Max Welling, belonging to the families of probabilistic graphical models and variational Bayesian methods.