Fig. 1: Encoder and decoder models used in variational auto-encoders.
From: Deciphering protein evolution and fitness landscapes with latent space models
Both encoder and decoder models used in this paper are fully connected artificial neural networks with one hidden layer \({\bf{H}}\). The encoder model transforms each protein sequence \({\bf{X}}\) into a distribution \({q}_{{\boldsymbol{\phi }}}({\bf{Z}}| {\bf{X}})\) of \({\bf{Z}}\) in the latent space; the decoder model transforms each point in the latent space \({\bf{Z}}\) into a distribution \({p}_{{\boldsymbol{\theta }}}({\bf{X}}| {\bf{Z}})\) of \({\bf{X}}\) in the protein sequence space. Protein sequences from a multiple sequence alignment with \(L\) amino acids are represented as a \(21\times L\) matrix whose entries are either 0 or 1 based on a one-hot coding scheme. Gaps in sequences are modeled as an extra amino acid type. Therefore, there are 21 amino acid types.
