# A Unified Approach for Learning the Parameters of Sum-Product Networks

arXiv: https://arxiv.org/abs/1601.00318 · HTML: https://mlsanity.com/paper/1601.00318/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Jan 2016.

## Built on by (most cited first, 24 of 24)

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- [Top-Down Bayesian Posterior Sampling for Sum-Product Networks](https://mlsanity.com/paper/2406.12353/) (2024)
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## Abstract (arXiv)

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.