# Top-Down Bayesian Posterior Sampling for Sum-Product Networks

arXiv: https://arxiv.org/abs/2406.12353 · HTML: https://mlsanity.com/paper/2406.12353/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 34 references that are in the map.
- First posted on arXiv 18 Jun 2024.

## Builds on (most cited first, 10 of 10)

- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [OpenML: networked science in machine learning](https://mlsanity.com/paper/1407.7722/) (2014)
- [On the Latent Variable Interpretation in Sum-Product Networks](https://mlsanity.com/paper/1601.06180/) (2016)
- [A Unified Approach for Learning the Parameters of Sum-Product Networks](https://mlsanity.com/paper/1601.00318/) (2016)
- [Bayesian Learning of Sum-Product Networks](https://mlsanity.com/paper/1905.10884/) (2019)
- [SPPL: Probabilistic Programming with Fast Exact Symbolic Inference](https://mlsanity.com/paper/2010.03485/) (2020)
- [Automatic Bayesian Density Analysis](https://mlsanity.com/paper/1807.09306/) (2018)
- [Online Structure Learning for Sum-Product Networks with Gaussian Leaves](https://mlsanity.com/paper/1701.05265/) (2017)
- [Learning Deep Generative Spatial Models for Mobile Robots](https://mlsanity.com/paper/1610.02627/) (2016)
- [Optimisation of Overparametrized Sum-Product Networks](https://mlsanity.com/paper/1905.08196/) (2019)

## Abstract (arXiv)

Sum-product networks (SPNs) are probabilistic models characterized by exact and fast evaluation of fundamental probabilistic operations. Its superior computational tractability has led to applications in many fields, such as machine learning with time constraints or accuracy requirements and real-time systems. The structural constraints of SPNs supporting fast inference, however, lead to increased learning-time complexity and can be an obstacle to building highly expressive SPNs. This study aimed to develop a Bayesian learning approach that can be efficiently implemented on large-scale SPNs. We derived a new full conditional probability of Gibbs sampling by marginalizing multiple random variables to expeditiously obtain the posterior distribution. The complexity analysis revealed that our sampling algorithm works efficiently even for the largest possible SPN. Furthermore, we proposed a hyperparameter tuning method that balances the diversity of the prior distribution and optimization efficiency in large-scale SPNs. Our method has improved learning-time complexity and demonstrated computational speed tens to more than one hundred times faster and superior predictive performance in numerical experiments on more than 20 datasets.