In linear algebra and functional analysis, the min-max theorem, or variational theorem, or Courant–Fischer–Weyl min-max principle, is a result that gives a variational characterization of eigenvalues of compact Hermitian operators on Hilbert spaces.It can be viewed as the starting point of many results of similar nature. This article first discusses the finite-dimensional case …

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.. Variational autoencoders are often associated with the autoencoder model because of its architectural affinity, but with significant …

Mar 19, 2018 · A variational autoencoder (VAE) provides a probabilistic manner for describing an observation in latent space. Thus, rather than building an encoder which outputs a single value to describe each latent state attribute, we'll formulate our encoder to describe a probability distribution for each latent attribute.

May 14, 2020 · In variational autoencoders, inputs are mapped to a probability distribution over latent vectors, and a latent vector is then sampled from that distribution. The decoder becomes more robust at decoding latent vectors as a result.

Feb 05, 2021 · We introduce Bayesian convolutional neural networks with variational inference, a variant of convolutional neural networks (CNNs), in which the intractable posterior probability distributions over weights are inferred by Bayes by Backprop.We demonstrate how our proposed variational inference method achieves performances equivalent to frequentist inference in …

Jan 19, 2021 · Variational classifiers usually define a “layer” or “block”, which is an elementary circuit architecture that gets repeated to build the variational circuit. Our circuit layer consists of an arbitrary rotation on every qubit, as well as CNOTs that entangle each qubit with its neighbour.

May 03, 2020 · Variational AutoEncoder. Author: fchollet Date created: 2020/05/03 Last modified: 2020/05/03 Description: Convolutional Variational AutoEncoder (VAE) trained on MNIST digits. ... Define the VAE as a Model with a custom train_step. class VAE (keras. Model): ...

Aug 27, 2010 · It is then shown that these balances follow as the Euler equations of incremental variational principles that govern the multi-field problems. These principles make the proposed formulation extremely compact and provide a perfect base for the finite element implementation, including features such as the symmetry of the monolithic tangent matrices.

One key component of variational autoencoders is variational inference. Variational inference is like a Bayesian extension of the expectation-maximization (EM) algorithm. One of the weaknesses of GMMs is that we have to choose K, the number of clusters, and if we choose wrong our model doesn't perform well.

Apr 03, 2017 · A variational "E" step where we compute the values latent variables (or more directly the responsibility) based upon the current parameter estimates of the mixture components. A variational "M" step where we estimate the parameters of the distributions for each mixture component based upon the values of all the latent variables. Conclusion