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In machine learning, a variational autoencoder (VAE) is an artificial neural network architecture introduced by Diederik P. Kingma and Max Welling. [1] It is part of the families of probabilistic graphical models and variational Bayesian methods .
More generally, other distributions can be used than the Bernoulli distribution, such as the gaussian noise: = +, (,) where = and =, with and being the mean and variance of the -th output neuron. The reparameterization trick can be applied to all such cases, resulting in the variational dropout method.
An autoencoder is a type of artificial neural network used to learn efficient codings of unlabeled data (unsupervised learning).An autoencoder learns two functions: an encoding function that transforms the input data, and a decoding function that recreates the input data from the encoded representation.
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 ...
Orthogonal initialization has been generalized to layer-sequential unit-variance (LSUV) initialization. It is a data-dependent initialization method, and can be used in convolutional neural networks. It first initializes weights of each convolution or fully connected layer with orthonormal matrices.
This naturally leads to the idea of training another network that performs "encoding", creating an autoencoder out of the encoder-generator pair. Already in the original paper, [ 1 ] the authors noted that "Learned approximate inference can be performed by training an auxiliary network to predict z {\displaystyle z} given x {\displaystyle x} ".
LDM consists of a variational autoencoder (VAE), a modified U-Net, and a text encoder. The VAE encoder compresses the image from pixel space to a smaller dimensional latent space, capturing a more fundamental semantic meaning of the image. Gaussian noise is iteratively applied to the compressed latent representation during forward diffusion.
Algorithms for calculating variance play a major role in computational statistics.A key difficulty in the design of good algorithms for this problem is that formulas for the variance may involve sums of squares, which can lead to numerical instability as well as to arithmetic overflow when dealing with large values.