US stock market interaction network as learned by the Boltzmann Machine

We study historical dynamics of joint equilibrium distribution of stock returns in the US stock market using the Boltzmann distribution model being parametrized by external fields and pairwise couplings. Within Boltzmann learning framework for statistical inference, we analyze historical behavior of the parameters inferred using exact and approximate learning algorithms. Since the model and inference methods require use of binary variables, effect of this mapping of continuous returns to the discrete domain is studied. Properties of distributions of external fields and couplings as well as industry sector clustering structure are studied for different historical dates and moving window sizes. We show that discrepancies between them might be used as a precursor of financial instabilities.