A Unified Approach for Learning the Parameters of Sum-Product Networks
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.
This paper derives methods to train SPNs starting from a perspective very different from methods established in literature. SPN training is viewed as a signomial program, and different approximate solutions to this problem are proposed. A theoretical and experimental analysis shows that the best method, called concave-convex procedure (CCCP), is equivalent to the already established Expectation Maximization for SPNs.  
The single contribution of the paper which is relevant in practice is an alternative derivation of an existing method (Expectation Maximization for learning SPN weights). While this is an interesting result, I think that it does not grant alone a publication in NIPS since it's hard to imagine how this can contribute to better theoretical understanding or practical applications of SPNs.   The interpretation of SPNs as mixtures of tree structured SPNs, which is reported as a novelty by the authors, was actually first derived in  [Dennis and Vantura, Greedy Structure Search for Sum-Product Networks, 2015].  The paper is overall well written, clearly structured and the derivation of the results is really interesting. My main concern, as detailed above, is that in my opinion the potential impact of this paper is low, and the novelty is also somewhat limited due to the fact that the interpretation of SPN as mixture of trees was already given in [Dennis and Vantura, Greedy Structure Search for Sum-Product Networks, 2015] and that this is basically just an alternative derivation of EM. So, I think the paper is (in the current form) a bit under the threshold for NIPS.    The experiment section is also not surprising, since basically it takes a SPN which is not trained, but in which weights are initialized with heuristic methods, and trains them with EM - which naturally improves a bit the log likelihood.   The title "unified approach" is misleading, since not all learning methods for SPNs are covered by this approach - in particular, the hard-gradient and hardEM methods that have been used successfully in the past (see [Discriminative Learning of Sum-Product Networks, Gens and Domingos, NIPS 2012]).   Small remark - in line 311: it is not always true that size is smaller in LearnSPN for 20News and AD (see line 574).  Overall, an interesting paper in terms of original derivation of results which have potential for future development, but the results are not novel enough, in my opinion, to grant publication at NIPS.