# On the Latent Variable Interpretation in Sum-Product Networks

@article{Peharz2016OnTL, title={On the Latent Variable Interpretation in Sum-Product Networks}, author={Robert Peharz and Robert Gens and Franz Pernkopf and Pedro M. Domingos}, journal={IEEE Transactions on Pattern Analysis and Machine Intelligence}, year={2016}, volume={39}, pages={2030-2044} }

One of the central themes in Sum-Product networks (SPNs) is the interpretation of sum nodes as marginalized latent variables (LVs. [] Key Method We discuss conditional independencies in augmented SPNs, formally establish the probabilistic interpretation of the sum-weights and give an interpretation of augmented SPNs as Bayesian networks. Based on these results, we find a sound derivation of the EM algorithm for SPNs. Furthermore, the Viterbi-style algorithm for MPE proposed in literature was never proven to…

## 101 Citations

### Bayesian Learning of Sum-Product Networks

- Computer ScienceNeurIPS
- 2019

A well-principled Bayesian framework for SPN structure learning, which consistently and robustly learns SPN structures under missing data, and a natural parametrisation for an important and widely used special case of SPNs.

### Sum–product graphical models

- Computer ScienceMachine Learning
- 2019

The theoretical and practical results demonstrate that jointly exploiting properties of SPNs and GMs is an interesting direction of future research and provide two applications of SPGMs in density estimation with empirical results close to or surpassing state-of-the-art models.

### Parameter and Structure Learning Techniques for Sum Product Networks

- Computer Science
- 2019

A new Bayesian moment matching (BMM) algorithm to learn the parameters for SPNs generatively and a discriminative learning algorithm based on the Extended BaumWelch (EBW) algorithm is presented.

### Structure Inference in Sum-Product Networks using Infinite Sum-Product Trees

- Computer Science
- 2016

This approach is the first correct and successful extension of SPNs to a Bayesian nonparametric model and shows that infinite SPTs can be used successfully to discover SPN structures and outperform infinite Gaussian mixture models in the task of density estimation.

### Sum-Product Network Decompilation

- Computer SciencePGM
- 2020

SPN2BN is proposed, an algorithm that decompiles an SPN into a BN and can be precisely characterized with respect to the compiled BN, and it is established that the compilation-decompilation process is idempotent.

### Collapsed Variational Inference for Sum-Product Networks

- Computer ScienceICML
- 2016

This work proposes a novel deterministic collapsed variational inference algorithm for SPNs that is computationally efficient, easy to implement and at the same time allows us to incorporate prior information into the optimization formulation.

### Maximum A Posteriori Inference in Sum-Product Networks

- Computer ScienceAAAI
- 2018

This work reduces general MAP inference to its special case without evidence and hidden variables and shows that it is NP-hard to approximate the MAP problem to 2nε for fixed 0 ≤ ε < 1, where n is the input size.

### Sum-Product Networks: A Survey

- Computer ScienceIEEE Transactions on Pattern Analysis and Machine Intelligence
- 2022

A survey of SPNs, including their definition, the main algorithms for inference and learning from data, several applications, a brief review of software libraries, and a comparison with related models are offered.

### Explaining Deep Tractable Probabilistic Models: The sum-product network case

- Computer SciencePGM
- 2022

The notion of a context-speciﬁc independence tree (CSI-tree) is considered and an iterative algorithm that converts an SPN to a CSI-tree is presented, which is both interpretable and explainable to the domain expert.

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