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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 .
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.
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.
In probability theory and statistics, variance is the expected value of the squared deviation from the mean of a random variable. The standard deviation (SD) ...
In k-nearest neighbor models, a high value of k leads to high bias and low variance (see below). In instance-based learning, regularization can be achieved varying the mixture of prototypes and exemplars. [13] In decision trees, the depth of the tree determines the variance. Decision trees are commonly pruned to control variance. [7]: 307
In statistics, econometrics, and signal processing, an autoregressive (AR) model is a representation of a type of random process; as such, it can be used to describe certain time-varying processes in nature, economics, behavior, etc.
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.
Generally, probabilistic graphical models use a graph-based representation as the foundation for encoding a distribution over a multi-dimensional space and a graph that is a compact or factorized representation of a set of independences that hold in the specific distribution.