Discriminative Mixtures of Sparse Latent Fields for Stress Testing
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 sparse latent-variable modeling approach 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.