  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.
