Discriminative Training of Sum-Product Networks by Extended Baum-Welch

We present a discriminative learning algorithm for Sum-Product Networks (SPNs) \citep{poon2011sum} based on the Extended Baum-Welch (EBW) algorithm \citep{baum1970maximization}. We formulate the conditional data likelihood in the SPN framework as a rational function, and we use EBW to monotonically maximize it. We derive the algorithm for SPNs with both discrete and continuous variables. The experiments show that this algorithm performs better than both generative Expectation-Maximization, and discriminative gradient descent on a wide variety of applications. We also demonstrate the robustness of the algorithm in the case of missing features by comparing its performance to Support Vector Machines and Neural Networks.