Discriminative Mixtures of Sparse Latent Fields for Risk Management

We describe a simple and efficient approach to learning structures of sparse high-dimensional latent variable models. Standard algorithms either learn structures of specific predefined forms, or estimate sparse graphs in the data space ignoring the possibility of the latent variables. In contrast, our method learns rich dependencies and allows for latent variables that may confound the relations between the observations. We extend the model to conditional mixtures with side information and non-Gaussian marginal distributions of the observations. We then show that our model may be used for learning sparse latent variable structures corresponding to multiple unknown states, and for uncovering features useful for explaining and predicting structural changes. We apply the model to real-world financial data with heavy-tailed marginals covering the low- and high- market volatility periods of 2005-2011. We show that our method tends to give rise to significantly higher likelihoods of test data than standard network learning methods exploiting the sparsity assumption. We also demonstrate that our approach may be practical for financial stress-testing and visualization of dependencies between financial instruments.