Variational Autoencoder for Non-Negative Matrix Factorization with Exogenous Inputs Applied to Financial Data Modelling

Multi-variate time series that arise in financial data, for example, are likely to be driven by underlying lower dimensional latent variables. Extracting such latent spaces can be useful in representing the data efficiently and as a means of explaining aspects of the system from which they are generated. Here, we study an extension to the Variational Autoencoder model specifically cast in a probabilistic setting to deal with positive valued data to extract a non-negative matrix factorization model (NMF) in a probabilistic setting (PAE-NMF). To model financial data, where information about some underlying macroeconomic system may be observed, we extend the PAE-NMF model to include exogenous variables (PAE-XNMF). We present the learning algorithm for this model and illustrate its operation on financial data of constituents of the FTSE100 index and a set of relevant macroeconomic variables. We show an example of the latent space detecting a sharp transition around the Brexit event that is not readily apparent on any of the individual time series.