Deep Latent Variable Models

In our previous blog post, we introduced latent variable models, where the latent variable can be thought of as a feature vector that has been “encoded” efficiently. This encoding turns the feature vector X into a context vector z. Latent variable models sound very GenAI-zy, but they descend from models that quant traders have long been familiar with. No doubt you have heard of PCA or SVD (see Chapter 3 of our book for a primer)? Principal components or singular vectors are ways to represent returns in terms of a small number of variables. These variables are latent, or hidden, because they are inferred from the observed returns themselves, and not observable like the Fama-French factors such as HML or SMB. The benefit of applying these latent factors to model returns is that we need fewer parameters - i.e. dimensional reduction. For example, the covariance matrix of 500 stocks’ returns have 125,250 parameters, whereas its 10-principal-component model has only 5,010 parameters. The methods to find these latent factors are diagonalization of the covariance matrix in the PCA case, or singular value decomposition of the "design" (data) matrix in the SVD case. Read more...