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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.
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Fisher's fundamental theorem of natural selection is an idea about genetic variance [1] [2] in population genetics developed by the statistician and evolutionary biologist Ronald Fisher. The proper way of applying the abstract mathematics of the theorem to actual biology has been a matter of some debate, however, it is a true theorem.
where var obs is the observed variance and var bin is the expected variance. The expected variance is calculated with the overall mean of the population. Values of D > 1 are considered to suggest aggregation. D( n − 1 ) is distributed as the chi squared variable with n − 1 degrees of freedom where n is the number of units sampled.
In variational Bayesian methods, the evidence lower bound (often abbreviated ELBO, also sometimes called the variational lower bound [1] or negative variational free energy) is a useful lower bound on the log-likelihood of some observed data.
where is the amplitude of Gaussian, = is exponent relaxation time, is a variance of exponential probability density function. This function cannot be calculated for some values of parameters (for example, =) because of arithmetic overflow.
This demonstrates the errors or new biology that can be missed when using OTUs, since OTUs will include these in the 3% dissimilarity threshold. This is the same real sequence that was sequenced over a hundred times as the above graph.