A Unified Approach for Learning the Parameters of Sum-Product Networks
This work provides a unified framework for parameter learning in SPNs, which is incremental as it builds on existing methods but offers new insights and algorithms for a specific machine learning model.
The paper tackles the problem of learning parameters for Sum-Product Networks (SPNs) by proving their equivalence to mixtures of trees and formulating the optimization as a signomial program, resulting in two algorithms (SMA and CCCP) that avoid projection operations and show equivalence between CCCP and EM for SPNs.
We present a unified approach for learning the parameters of Sum-Product networks (SPNs). We prove that any complete and decomposable SPN is equivalent to a mixture of trees where each tree corresponds to a product of univariate distributions. Based on the mixture model perspective, we characterize the objective function when learning SPNs based on the maximum likelihood estimation (MLE) principle and show that the optimization problem can be formulated as a signomial program. We construct two parameter learning algorithms for SPNs by using sequential monomial approximations (SMA) and the concave-convex procedure (CCCP), respectively. The two proposed methods naturally admit multiplicative updates, hence effectively avoiding the projection operation. With the help of the unified framework, we also show that, in the case of SPNs, CCCP leads to the same algorithm as Expectation Maximization (EM) despite the fact that they are different in general.