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A structured list of resources about Sum-Product Networks (SPNs)
https://github.com/arranger1044/awesome-spn
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A structured list of resources about Sum-Product Networks (SPNs)
Host: GitHub
URL: https://github.com/arranger1044/awesome-spn
Owner: arranger1044
Created: 2016-07-10T16:53:03.000Z (about 8 years ago)
Default Branch: master
Last Pushed: 2021-01-05T03:17:57.000Z (over 3 years ago)
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Topics: code, literature, spn, sum-product-networks
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- Readme: README.md
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README

        # Discontinued

**awesome-spn** has been **discontinued** as of 01/01/2021!

Please visit and contribute to the [website](https://arranger1044.github.io/probabilistic-circuits/) and [repo](https://github.com/arranger1044/probabilistic-circuits/) on **probabilistic circuits**

# Awesome Sum-Product Networks

**awesome-spn** is a curated and structured list of resources about

*Sum-Product Networks* (SPNs), tractable deep density estimators.

This includes (even not formally published) research papers sorted by year and topics as well as

links to tutorials and code and other related Tractable Probabilistic

Models (TPMs). It is inspired by the

[SPN page](http://spn.cs.washington.edu/) at the Washington University.

## Licence and Contributing

[![CC0](http://i.creativecommons.org/p/zero/1.0/88x31.png)](http://creativecommons.org/publicdomain/zero/1.0/)

**awesome-spn** is released under Public Domain. Feel free to complete

and/or correct any of these

lists. [Pull requests](https://github.com/arranger1044/awesome-spn/pulls)

are very welcome!

## Table of Contents

   * [Papers](#papers)

      * [Year](#year)

        * [2020](#2020)

        * [2019](#2019)

        * [2018](#2018)

        * [2017](#2017)

        * [2016](#2016)

        * [2015](#2015)

        * [2014](#2014)

        * [2013](#2013)

        * [2012](#2012)

        * [2011](#2011)

      * [Topic](#topics)

        * [Survey](#survey)

        * [Weight Learning](#weight-learning)

        * [Structure Learning](#structure-learning)

        * [Representation Learning](#representation-learning)

        * [Modeling](#modeling)

        * [Applications](#applications)

        * [Theory](#theory)

        * [Hardware](#hardware)

   * [Related Works](#related-works) 

      * [Arithmetic Circuits](#arithmetic-circuits)

      * [Other TPMs](#other-tpms)

      * [Exploiting Sum-Product Theorem](#Exploiting-Sum-Product-Theorem)

   * [Resources](#resources)

      * [Dataset](#dataset)

      * [Code](#code)

      * [Talks and Tutorials](#talks-and-tutorials)

      * [Blog posts](#blog-posts)

   * [References](#resources)

        

## Papers

Sorted by [year](#year) or [topics](#topics) 

### Year

#### 2020

   - [[Paris2020](#paris2020)]

     [**Sum-product networks: A survey**](https://arxiv.org/abs/2004.01167) *preprint* [`survey`](#survey)

#### 2019

   - [[Trapp2019](#trapp2019)]

     [**Bayesian Learning of Sum-Product Networks**](https://papers.nips.cc/paper/8864-bayesian-learning-of-sum-product-networks.pdf) *NeurIPS 2019* [`structure-learning`](#structure-learning) 

   - [[Tan2019](#tan2019)]

     [**Hierarchical Decompositional Mixtures of Variational Autoencoders**](http://proceedings.mlr.press/v97/tan19b/tan19b.pdf) *ICML 2019* [`modeling`](#modeling)

   - [[Peharz2019](#peharz2019)]

     [**Random Sum-Product Networks: A Simple and Effective Approach to Probabilistic Deep Learning**](https://arxiv.org/abs/1806.01910) *UAI 2019* [`modeling`](#modeling) [`weight learning`](#weight-learning)

   - [[Stelzner2019](#stelzner2019)] [**Faster Attend-Infer-Repeat with Tractable Probabilistic Models**](http://proceedings.mlr.press/v97/stelzner19a/stelzner19a.pdf) *ICML 2019* [`applications`](#applications)

   - [[Shao2019](#shao2019)] [**Conditional Sum-Product Networks: Imposing Structure on Deep Probabilistic Architectures**](https://arxiv.org/pdf/1905.08550.pdf) *preprint* [`modeling`](#modeling)

   - [[Vergari2019](#vergari2019)] [**Automatic Bayesian Density Analysis**](https://www.researchgate.net/publication/326621815_Automatic_Bayesian_Density_Analysis) *AAAI 2019* [`modeling`](#modeling)

   - [[Butz2019](#butz2019)] [**Deep Convolutional Sum-Product Networks**](https://www.aaai.org/Papers/AAAI/2019/AAAI-ButzC.3622.pdf) *AAAI 2019* [`modeling`](#modeling)

   - [[Molina2019](#molina2019)] [**SPFlow: An Easy and Extensible Library for Deep Probabilistic Learning using Sum-Product Networks**](https://arxiv.org/abs/1901.03704) *preprint* [`applications`](#applications)

   - [[Wolfshaar2019](#wolfshaar2019)] [**Deep Convolutional Sum-Product Networks for Probabilistic Image Representations**](https://arxiv.org/pdf/1902.06155.pdf) *preprint* [`modeling`](#modeling)

#### 2018

   - [[Jaini2018b](#jaini2018b)] [**Deep Homogeneous Mixture Models: Representation, Separation, and Approximation**](http://papers.nips.cc/paper/7944-deep-homogeneous-mixture-models-representation-separation-and-approximation) *NeurIPS 2018* [`modeling`](#modeling)

   - [[Ko2018](#ko2018)] [**Deep Compression of Sum-Product Networks on Tensor Networks**](https://arxiv.org/abs/1811.03963) *preprint* [`modeling`](#modeling)

   - [[Sommer2018](#sommer2018)] [**Automatic Mapping of the Sum-Product Network Inference Problem to FPGA-Based Accelerators**](https://ieeexplore.ieee.org/document/8615710) *ICCD2018* [`hardware`](#hardware)

   - [[Trapp2018](#trapp2018)] [**Learning Deep Mixtures of Gaussian Process Experts Using Sum-Product Networks**](https://www.researchgate.net/publication/327621399_Learning_Deep_Mixtures_of_Gaussian_Process_Experts_Using_Sum-Product_Networks) *Workshop on Tractable Probabilistic Models* [`modeling`](#modeling)

   - [[Vergari2018b](#vergari2018b)] [**Visualizing and Understanding Sum-Product Networks**](https://arxiv.org/abs/1608.08266) *Machine Learning Journal* [`representation learning`](#representation-learning)

   - [[Bueff2018](#bueff2018)]

     [**Tractable Querying and Learning in Hybrid Domains via Sum-Product Networks**](https://arxiv.org/abs/1807.05464) *preprint* [`structure-learning`](#structure-learning)

   - [[Rashwan2018b](#rashwan2018b)]

     [**Online Structure Learning for Feed-Forward and Recurrent Sum-Product Networks**](http://papers.nips.cc/paper/7926-online-structure-learning-for-feed-forward-and-recurrent-sum-product-networks.pdf) *NIPS 2018* [`structure-learning`](#structure-learning)

   - [[Rashwan2018a](#rashwan2018a)]

     [**Discriminative Training of Sum-Product Networks by Extended Baum-Welch**](http://pgm2018.utia.cz/data/proc/rashwan18a.pdf) *PGM 2018* [`weight-learning`](#weight-learning)

   - [[Jaini2018a](#jaini2018a)]

     [**Prometheus: Directly Learning Acyclic Directed Graph Structures for Sum-Product Networks**](http://pgm2018.utia.cz/data/proc/jaini18a.pdf) *PGM 2018* [`structure-learning`](#structure-learning)

   - [[Conaty2018](#conaty2018)]

     [**Cascading Sum-Product Networks using Robustness**](http://pgm2018.utia.cz/data/proc/conaty18a.pdf) *PGM 2018*  [`applications`](#applications)

   - [[Joshi2018](#joshi2018)]

     [**Exact, Tractable Inference in the Sigma Cognitive Architecture via Sum-Product Networks**](http://www.cogsys.org/papers/ACSvol6/article08.pdf) *Advances in Cognitive Systems 2018*  [`applications`](#applications

   - [[Ratajczak2018](#ratajczak2018)]

     [**Sum-Product Networks for Sequence Labeling**](https://arxiv.org/abs/1807.02324) *arXiv preprint* [`applications`](#applications) [`modeling`](#modeling)

   - [[Butz2018b](#butz2018b)]

     [**An Empirical Study of Methods for SPN Learning and Inference**](http://proceedings.mlr.press/v72/butz18a/butz18a.pdf) *PGM 2018* [`structure-learning`](#structure-learning)

   - [[Butz2018a](#butz2018a)]

     [**Efficient Examination of Soil Bacteria Using Probabilistic Graphical Models**](https://link.springer.com/chapter/10.1007/978-3-319-92058-0_30) *IEA-AIE 2018*  [`applications`](#applications)

   - [[Sharir2018](#sharir2018)]

     [**Sum-Product-Quotient Networks**](https://arxiv.org/abs/1710.04404) *AISTATS 2018*

     [`modeling`](#modeling)

   - [[Zheng2018](#zheng2018)]

     [**Learning Graph-Structured Sum-Product Networks for Probabilistic Semantic Maps**](https://arxiv.org/abs/1709.08274) *AAAI 2018*

     [`modeling`](#modeling) [`applications`](#applications)

   - [[Mei2018](#mei2018)] [**Maximum A Posteriori Inference in Sum-Product Networks**](https://arxiv.org/abs/1708.04846) *AAAI 2018* [`theory`](#theory)

   - [[Vergari2018a](#vergari2018a)]

     [**Sum-Product Autoencoding: Encoding and Decoding Representations with Sum-Product Networks**](http://www.di.uniba.it/~ndm/pubs/vergari18aaai.pdf) *AAAI 2018*

     [`representation learning`](#representation-learning)

   - [[Molina2018](#molina2018)]

     [**Mixed Sum-Product Networks: A Deep Architecture for Hybrid Domains**](http://www.ml.informatik.tu-darmstadt.de/papers/molina2018aaai_mspns.pdf) *AAAI 2018*

     [`modeling`](#modeling)

     

#### 2017

   

   - [[Dennis2017b](#dennis2017b)]

     [**Autoencoder-Enhanced Sum-Product Networks**](http://ieeexplore.ieee.org/document/8260779/) *ICMLA 2017* [`modeling`](#modeling)

   - [[Dennis2017a](#dennis2017a)]

     [**Online Structure-Search for Sum-Product Networks**](http://ieeexplore.ieee.org/document/8260628/) *ICMLA 2017*  [`structure-learning`](#structure-learning)

   - [[DiMauro2017](#dimauro2017)]

     [**Alternative Variable Splitting Methods to Learn Sum-Product Networks**](https://www.researchgate.net/profile/Esposito_Floriana/publication/319504310_Alternative_variable_splitting_methods_to_learn_Sum-Product_Networks/links/59afcc050f7e9bf3c72920bb/Alternative-variable-splitting-methods-to-learn-Sum-Product-Networks.pdf) *AIxIA 2017*

     [`structure-learning`](#structure-learning)

   - [[Desana2017](#desana2017)]

     [**Sum-Product Graphical Models**](https://arxiv.org/abs/1708.06438)

     *arXiv* [`modeling`](#modeling)

   - [[Pronobis2017b](#pronobis2017b)] [**LibSPN: A Library for Learning and Inference with Sum-Product Networks and TensorFlow**](http://padl.ws/papers/Paper%2043.pdf) *PADL@ICML 2017* [`code`](#code)

   - [[Friesen2017](#friesen2017)] [**Unifying Sum-Product Networks and Submodular Fields**](http://padl.ws/papers/Paper%201.pdf) *PADL@ICML 2017* [`applications`](#applications) [`modeling`](#modeling)

   - [[Pronobis2017a](#pronobis2017a)] [**Deep Spatial Affordance Hierarchy: Spatial Knowledge Representation for Planning in Large-scale Environments**](http://www.ece.rochester.edu/projects/rail/ssrr2017/contributions/rao_rss17_ssrr_ws.pdf) *SSRR 2017* [`applications`](#applications)

   - [[Rathke2017](#rathke2017)] [**Locally Adaptive Probabilistic Models for Global Segmentation of Pathological OCT Scans**](https://ipa.math.uni-heidelberg.de/dokuwiki/Papers/Rathke2017.pdf) *MICCAI 2017* [`applications`](#applications)

   - [[Trapp2017](#trapp2017)] [**Safe Semi-Supervised Learning of Sum-Product Networks**](http://auai.org/uai2017/proceedings/papers/108.pdf) *UAI 2017* [`weight learning`](#weight-learning)

   - [[Mauà2017](#mauà2017)] [**Credal Sum-Product Networks**](http://pure.qub.ac.uk/portal/files/128951275/maua17.pdf) *ISIPTA 2017* [`modeling`](#modeling)

   - [[Conaty2017](#conaty2017)] [**Approximation Complexity of Maximum A Posteriori Inference in Sum-Product Networks**](https://arxiv.org/abs/1703.06045) *UAI 2017* [`theory`](#theory)

   - [[Zhao2017](#zhao2017)] [**Efficient Computation of Moments in Sum-Product Networks**](https://arxiv.org/abs/1702.04767) *NIPS 2017* [`weight-learning`](#weight-learning)

   - [[Vergari2017](#vergari2017)] [**Encoding and Decoding Representations with Sum- and Max-Product Networks**](https://openreview.net/forum?id=rkndY2VYx) *ICLR 2017 - Workshop* [`representation learning`](#representation-learning)

   - [[Hsu2017](#hsu2017)] [**Online Structure Learning for Sum-Product Networks with Gaussian Leaves**](https://openreview.net/pdf?id=S1QefL5ge) *ICLR 2017 - Workshop* [`structure-learning`](#structure-learning)

   - [[Gens2017](#gens2017)] [**Compositional Kernel Machines**](https://openreview.net/pdf?id=S1Bm3T_lg) *ICLR 2017 - Workshop* [`modeling`](#modeling)

   - [[Molina2017](#molina2017)] [**Poisson Sum-Product Networks: A Deep Architecture for Tractable Multivariate Poisson Distributions**](http://www-ai.cs.uni-dortmund.de/auto?self=$Publication_ewtkrvss1s) *AAAI2017* [`modeling`](#modeling)

  

  

#### 2016

   - [[Sguerra2016](#sguerra2016)] [**Image Classification Using Sum-Product Networks for Autonomous Flight of Micro Aerial Vehicles**](http://ieeexplore.ieee.org/abstract/document/7839576/) *BRACIS 2016* [`applications`](#applications)

   - [[Trapp2016](#trapp2016)] [**Structure Inference in Sum-Product Networks using Infinite Sum-Product Trees**](https://drive.google.com/file/d/0B3WHb3BabixAVWFVaDEzdThSbk0/view) *Practical Bayesian Nonparametrics* [`structure-learning`](#structure-learning)

   - [[Melibari2016c](#melibari2016c)] [**Dynamic Sum-Product Networks for Tractable Inference on Sequence Data**](http://arxiv.org/abs/1511.04412)

   *PGM2016* [`modeling`](#modeling) [`structure-learning`](#structure-learning)

   - [[Jaini2016](#jaini2016)]

     [**Online Algorithms for Sum-Product Networks with Continuous Variables**](http://jmlr.org/proceedings/papers/v52/jaini16.pdf)

     *PGM2016* [`weight-learning`](#weight-learning)

   - [[Desana2016](#desana2016)]

     [**Learning Arbitrary Sum-Product Network Leaves with Expectation-Maximization**](http://arxiv.org/abs/1604.07243)

     *arXiv* [`weight-learning`](#weight-learning)

   - [[Peharz2016](#peharz2016)]

     [**On the Latent Variable Interpretation in Sum-Product Networks**](http://arxiv.org/abs/1601.06180)

     *arXiv* [`theory`](#theory)	 [`weight-learning`](#weight-learning)

   - [[Zhao2016b](#zhao2016b)]

       [**A unified approach for learning the parameters of sum-product networks**](http://arxiv.org/abs/1601.00318)    *NIPS 2016* [`weight-learning`](#weight-learning)

   - [[Yuan2016](#yuan2016)]

     [**Modeling Spatial Layout for Scene Image Understanding Via a Novel Multiscale Sum-Product Network**](http://www.sciencedirect.com/science/article/pii/S0957417416303591)

     *Expert Systems and Applications* [`applications`](#applications)

   - [[Rahman2016](#rahman2016)]

     [**Merging Strategies for Sum-Product Networks: From Trees to Graphs**](http://www.hlt.utdallas.edu/~vgogate/papers/uai16.pdf)

     *UAI2016* [`structure-learning`](#structure-learning)

   - [[Friesen2016](#friesen2016)]

     [**The Sum-Product Theorem: A Foundation for Learning Tractable Models**](http://homes.cs.washington.edu/~pedrod/papers/mlc16.pdf)

     *ICML2016* [`theory`](#theory)

   - [[Zhao2016a](#zhao2016a)]

     [**Collapsed Variational Inference for Sum-Product Networks**](http://jmlr.org/proceedings/papers/v48/zhaoa16.pdf)

     *ICML2016*	 [`weight-learning`](#weight-learning)

   - [[Rashwan2016](#rashwan2016)]

     [**Online and Distributed Bayesian Moment Matching for Parameter Learning in Sum-Product Networks**](http://www.jmlr.org/proceedings/papers/v51/rashwan16.pdf)

     *AISTATS2016* [`weight-learning`](#weight-learning)

   - [[Krakovna2016](#krakovna2016)]

     [**A Minimalistic Approach to Sum-Product Network Learning for Real Applications**](http://arxiv.org/abs/1602.04259)

     *ICLR2016* [`structure-learning`](#structure-learning)

   - [[Melibari2016b](#melibari2016b)]

     [**Sum-Product-Max Networks for Tractable Decision Making**](http://trust.sce.ntu.edu.sg/aamas16/pdfs/p1419.pdf)

     *AAMAS2016* [`modeling`](#modeling)

   - [[Melibari2016a](#melibari2016a)] [**Decision Sum-Product-Max Networks**](https://cs.uwaterloo.ca/~mmelibar/publications/melibari-aaai2016.pdf)

     *AAAI2016*	 [`modeling`](#modeling)	  [`structure-learning`](#structure-learning)

   - [[Nath2016](#nath2016)]

     [**Learning Tractable Probabilistic Models for Fault Localization**](http://homes.cs.washington.edu/~pedrod/papers/aaai16.pdf)

     *AAAI2016* [`applications`](#applications)

#### 2015

   - [[Peharz2015b](#peharz2015b)]

     [**Foundations of Sum-Product Networks for Probabilistic Modeling**](https://www.researchgate.net/profile/Robert_Peharz/publication/273000973_Foundations_of_Sum-Product_Networks_for_Probabilistic_Modeling/links/54f49ff00cf2f28c1362088b.pdf)

     *Thesis* [`theory`](#theory)

   - [[Wang2015](#wang2015)]

     [**Hierarchical Spatial Sum-Product Networks for action recognition in Still Images**](http://arxiv.org/abs/1511.05292)

     *arXiv* [`applications`](#applications)	 

   - [[Amer2015](#amer2015)]

     [**Sum Product Networks for Activity Recognition**](http://web.engr.oregonstate.edu/~sinisa/research/publications/PAMI_SPN.pdf)

     *TPAMI2015* [`applications`](#applications)

   - [[Li2015](#li2015)]

     [**Combining Sum-Product Network and Noisy-OrModel for Ontology Matching**](http://disi.unitn.it/~pavel/om2015/papers/om2015_TSpaper1.pdf)

     *OM2015* [`applications`](#applications)

   - [[Vergari2015](#vergari2015)]

     [**Simplifying, Regularizing and Strengthening Sum-Product Network Structure Learning**](http://www.di.uniba.it/~vergari/papers/Simplifying,%20Regularizing%20and%20Strengthening%20Sum-Product%20Network%20Structure%20Learning.pdf)

     *ECML-PKDD2015*  [`structure-learning`](#structure-learning)

   - [[Dennis2015](#dennis2015)]

     [**Greedy Structure Search for Sum-Product Networks**](http://www.ijcai.org/Proceedings/15/Papers/136.pdf) *IJCAI2015*	  [`structure-learning`](#structure-learning)

   - [[Friesen2015](#friesen2015)]

     [**Recursive Decomposition for Nonconvex Optimization**](https://www.cs.washington.edu/node/11282)

     *IJCAI2015*	 [`theory`](#theory)

   - [[Niepert2015](#niepert2015)]

     [**Learning and Inference in Tractable Probabilistic Knowledge Bases**](http://homes.cs.washington.edu/~pedrod/papers/uai15.pdf)

     *UAI2015* [`modeling`](#modeling)

   - [[Adel2015](#adel2015)]

     [**Learning the Structure of Sum-Product Networks via an SVD-based Algorithm**](http://auai.org/uai2015/proceedings/papers/83.pdf)

     *UAI2015*  [`structure-learning`](#structure-learning)

   - [[Zhao2015](#zhao2015)]

     [**On the Relationship between Sum-Product Networks and Bayesian Networks**](http://jmlr.org/proceedings/papers/v37/zhaoc15.pdf)

     *ICML2015* [`theory`](#theory)

   - [[Peharz2015a](#peharz2015a)]

     [**On Theoretical Properties of Sum-Product Networks**](http://www.jmlr.org/proceedings/papers/v38/peharz15.pdf)

     *AISTATS2015* [`theory`](#theory)

   - [[Nath2015](#nath2015)]

     [**Learning Relational Sum-Product Networks**](http://homes.cs.washington.edu/~pedrod/papers/aaai15.pdf)

     *AAAI2015* [`modeling`](#modeling)

#### 2014

   - [[Martens2014](#martens2014)]

     [**On the Expressive Efficiency of Sum Product Networks**](http://arxiv.org/abs/1411.7717)

     *arXiv* [`theory`](#theory)

   - [[Cheng2014](#cheng2014)]

     [**Language Modeling with Sum-Product Networks**](http://spn.cs.washington.edu/papers/is14.pdf)

     *INTERSPEECH2014* [`modeling`](#modeling) [`applications`](#applications)

   - [[Peharz2014a](#peharz2014a)]

     [**Modeling Speech with Sum-Product Networks: Application to Bandwidth Extension**](http://spn.cs.washington.edu/papers/icassp14.pdf)

     *ICASSP2014* [`applications`](#applications)

   - [[Lee2014](#lee2014)]

     [**Non-Parametric Bayesian Sum-Product Networks**](http://spn.cs.washington.edu/papers/ltpm2014_paper_6.pdf)

     *LTPM2014*  [`structure-learning`](#structure-learning)

   - [[Ratajczak2014](#ratajczak2014)]

     [**Sum-Product Networks for Structured Prediction: Context-Specific Deep Conditional Random Fields**](https://www.spsc.tugraz.at/biblio/ratajczak20143046)

     *LTPM2014* [`applications`](#applications)

   - [[Nath2014](#nath2014)]

     [**Learning Tractable Statistical Relational Models**](http://spn.cs.washington.edu/papers/ltpm2014_paper_4.pdf)

     *LTPM2014* [`modeling`](#modeling)

   - [[Peharz2014b](#peharz2014b)]

     [**Learning Selective Sum-Product Networks**](http://spn.cs.washington.edu/papers/ltpm2014_paper_9.pdf)

     *LTPM2014* [`weight-learning`](#weight-learning) [`modeling`](#modeling)

   - [[Rooshenas2014](#rooshenas2014)]

     [**Learning Sum-Product Networks with Direct and Indirect Interactions**](http://ix.cs.uoregon.edu/~lowd/icml14rooshenas.pdf)

     *ICML2014*  [`structure-learning`](#structure-learning)

#### 2013

   - [[Lee2013](#lee2013)]

     [**Online Incremental Structure Learning of Sum-Product Networks**](https://bi.snu.ac.kr/Publications/Conferences/International/ICONIP2013_SWLee.pdf)

     *ICONIP2013*	  [`structure-learning`](#structure-learning)

   - [[Peharz2013](#peharz2013)]

     [**Greedy Part-Wise Learning of Sum-Product Networks**](https://www.spsc.tugraz.at/sites/default/files/MergeSPN.pdf) 

     *ECML-PKDD2013*  [`structure-learning`](#structure-learning)

   - [[Gens2013](#gens2013)]

     [**Learning the Structure of Sum-Product Networks**](http://jmlr.org/proceedings/papers/v28/gens13.pdf)

     *ICML2013*  [`structure-learning`](#structure-learning)

#### 2012

   - [[Gens2012](#gens2012)]

     [**Discriminative Learning of Sum-Product Networks**](http://spn.cs.washington.edu/papers/dspn.pdf)

     *NIPS2012* [`weight-learning`](#weight-learning)

   - [[Dennis2012](#dennis2012)]

     [**Learning the Architecture of Sum-Product Networks Using Clustering on Variables**](http://papers.nips.cc/paper/4544-learning-the-architecture-of-sum-product-networks-using-clustering-on-variables.pdf)

     *NIPS2012*  [`structure-learning`](#structure-learning)

   - [[Stuhlmueller2012](#stuhlmueller2012)]

     [**Dynamic Programming Algorithm for Inference in Recursive Probabilistic Programs**](http://arxiv.org/abs/1206.3555)

     *StaRAI2012* [`modeling`](#modeling)

   - [[Amer2012](#amer2012)]

     [**Sum-product Networks for Modeling Activities with Stochastic Structure**](http://web.engr.oregonstate.edu/~sinisa/research/publications/cvpr12_SPN.pdf)

     *CVPR2012* [`applications`](#applications)

#### 2011

    

   - [[Delalleau2011](#dellaleau2011)]

     [**Shallow vs. Deep Sum-Product Networks**](http://papers.nips.cc/paper/4350-shallow-vs-deep-sum-product-networks.pdf)

     *NIPS2011* [`theory`](#theory)

   - [[Poon2011](#poon2011)]

     [**Sum-Product Networks: A New Deep Architecture**](http://spn.cs.washington.edu/papers/spn.pdf)

     *UAI2011* [`modeling`](#modeling) [`weight-learning`](#weight-learning)

    

### Topics

#### Survey

   - [[Paris2020](#paris2020)]

     [**Sum-product networks: A survey**](https://arxiv.org/abs/2004.01167) `survey`

     

#### Weight Learning

   - [[Peharz2019](#peharz2019)]

     [**Random Sum-Product Networks: A Simple and Effective Approach to Probabilistic Deep Learning**](https://arxiv.org/abs/1806.01910) `RAT-SPNs`

   - [[Rashwan2018a](#rashwan2018a)]

     [**Discriminative Training of Sum-Product Networks by Extended Baum-Welch**](http://pgm2018.utia.cz/data/proc/rashwan18a.pdf) `EBW SPN`

   - [[Trapp2017](#trapp2017)] 

     [**Safe Semi-Supervised Learning of Sum-Product Networks**]() `semi supervised`

   - [[Zhao2017](#zhao2017)] 

     [**Efficient Computation of Moments in Sum-Product Networks**](https://arxiv.org/abs/1702.04767) `ADF`

   - [[Jaini2016](#jaini2016)]

     [**Online Algorithms for Sum-Product Networks with Continuous Variables**](http://jmlr.org/proceedings/papers/v52/jaini16.pdf) `OBMM`

   - [[Desana2016](#desana2016)]

     [**Learning Arbitrary Sum-Product Network Leaves with Expectation-Maximization**](http://arxiv.org/abs/1604.07243) `EM`

   - [[Zhao2016b](#zhao2016b)]

       [**A unified approach for learning the parameters of sum-product networks**](http://arxiv.org/abs/1601.00318) `CCCP`

   - [[Zhao2016a](#zhao2016a)]

     [**Collapsed Variational Inference for Sum-Product Networks**](http://jmlr.org/proceedings/papers/v48/zhaoa16.pdf) `variational method`

   - [[Rashwan2016](#rashwan2016)]

  [**Online and Distributed Bayesian Moment Matching for Parameter Learning in Sum-Product Networks**](http://www.jmlr.org/proceedings/papers/v51/rashwan16.pdf)

  `OBMM` `EGD`

   - [[Peharz2014b](#peharz2014b)]

     [**Learning Selective Sum-Product Networks**](http://spn.cs.washington.edu/papers/ltpm2014_paper_9.pdf)

     `ML` `SSPN`

   - [[Poon2011](#poon2011)]

   [**Sum-Product Networks: A New Deep Architecture**](http://spn.cs.washington.edu/papers/spn.pdf) `EM` `Hard EM` `SGD`

   - [[Gens2012](#gens2012)]

   [**Discriminative Learning of Sum-Product Networks**](http://spn.cs.washington.edu/papers/dspn.pdf)

   `disc Hard EM` `disc Hard SGD`

#### Structure Learning

   - [[Trapp2019](#trapp2019)]

     [**Bayesian Learning of Sum-Product Networks**](https://papers.nips.cc/paper/8864-bayesian-learning-of-sum-product-networks.pdf) `bayesian structure learning` 

   - [[Bueff2018](#bueff2018)]

     [**Tractable Querying and Learning in Hybrid Domains via Sum-Product Networks**](https://arxiv.org/abs/1807.05464) `WMI-SPN`

   - [[Rashwan2018b](#rashwan2018b)]

     [**Online Structure Learning for Feed-Forward and Recurrent Sum-Product Networks**](http://papers.nips.cc/paper/7926-online-structure-learning-for-feed-forward-and-recurrent-sum-product-networks.pdf) `RSPN`

   - [[Jaini2018a](#jaini2018a)]

     [**Prometheus: Directly Learning Acyclic Directed Graph Structures for Sum-Product Networks**](http://pgm2018.utia.cz/data/proc/jaini18a.pdf) `Prometheus`

   - [[Butz2018b](#butz2018b)]

     [**An Empirical Study of Methods for SPN Learning and Inference**](http://proceedings.mlr.press/v72/butz18a/butz18a.pdf) `PP` 

   - [[Dennis2017a](#dennis2017a)]

     [**Online Structure-Search for Sum-Product Networks**](http://ieeexplore.ieee.org/document/8260628/) 

   - [[DiMauro2017](#dimauro2017)] `online SEARCHSPN`

     [**Alternative Variable Splitting Methods to Learn Sum-Product Networks**](https://www.researchgate.net/profile/Esposito_Floriana/publication/319504310_Alternative_variable_splitting_methods_to_learn_Sum-Product_Networks/links/59afcc050f7e9bf3c72920bb/Alternative-variable-splitting-methods-to-learn-Sum-Product-Networks.pdf) `RGVS` `EBVS`

   - [[Hsu2017](#hsu2017)] [**Online Structure Learning for Sum-Product Networks with Gaussian Leaves**](https://openreview.net/pdf?id=S1QefL5ge)  `online structure learning`

   - [[Trapp2016](#trapp2016)] [**Structure Inference in Sum-Product Networks using Infinite Sum-Product Trees**](https://drive.google.com/file/d/0B3WHb3BabixAVWFVaDEzdThSbk0/view) `infiniteSPT` `Bayesian nonparametrics`

   - [[Melibari2016c](#melibari2016c)]

     [**Dynamic Sum-Product Networks for Tractable Inference on Sequence Data**](http://arxiv.org/abs/1511.04412) `hill-climbing`

   - [[Rahman2016](#rahman2016)]

     [**Merging Strategies for Sum-Product Networks: From Trees to Graphs**](http://www.hlt.utdallas.edu/~vgogate/papers/uai16.pdf)

     `pruning` `dagSPN`

   - [[Vergari2015](#vergari2015)]

     [**Simplifying, Regularizing and Strengthening Sum-Product Network Structure Learning**](http://www.di.uniba.it/~vergari/papers/Simplifying,%20Regularizing%20and%20Strengthening%20Sum-Product%20Network%20Structure%20Learning.pdf)

     `LearnSPN-b` `LearnSPN-bt` `LearnSPN-btb`

   - [[Dennis2015](#dennis2015)]

     [**Greedy Structure Search for Sum-Product Networks**](http://www.ijcai.org/Proceedings/15/Papers/136.pdf) `dagSPN`

   - [[Adel2015](#adel2015)]

     [**Learning the Structure of Sum-Product Networks via an SVD-based Algorithm**](http://auai.org/uai2015/proceedings/papers/83.pdf)

     `SPN-SVD` `DSPN-SVD`

   - [[Nath2015](#nath2015)]

     [**Learning Relational Sum-Product Networks**](http://homes.cs.washington.edu/~pedrod/papers/aaai15.pdf) `relational`

   - [[Lee2014](#lee2014)]

     [**Non-Parametric Bayesian Sum-Product Networks**](http://spn.cs.washington.edu/papers/ltpm2014_paper_6.pdf) `non-parametrics`

   - [[Peharz2014b](#peharz2014b)] [**Learning Selective Sum-Product Networks**](http://spn.cs.washington.edu/papers/ltpm2014_paper_9.pdf) `SSPN`

   - [[Rooshenas2014](#rooshenas2014)] [**Learning Sum-Product Networks with Direct and Indirect Interactions**](http://ix.cs.uoregon.edu/~lowd/icml14rooshenas.pdf) `ID-SPN`

   - [[Lee2013](#lee2013)]

     [**Online Incremental Structure Learning of Sum-Product Networks**](https://bi.snu.ac.kr/Publications/Conferences/International/ICONIP2013_SWLee.pdf)

   - [[Peharz2013](#peharz2013)]

     [**Greedy Part-Wise Learning of Sum-Product Networks**](https://www.spsc.tugraz.at/sites/default/files/MergeSPN.pdf) `bottom-up`

   - [[Gens2013](#gens2013)]

  [**Learning the Structure of Sum-Product Networks**](http://jmlr.org/proceedings/papers/v28/gens13.pdf) `top-down` `LearnSPN`

   - [[Dennis2012](#dennis2012)]

     [**Learning the Architecture of Sum-Product Networks Using Clustering on Variables**](http://papers.nips.cc/paper/4544-learning-the-architecture-of-sum-product-networks-using-clustering-on-variables.pdf)

     `top-down``k-means`

#### Representation Learning

   - [[Vergari2018a](#vergari2018a)]

     [**Sum-Product Autoencoding: Encoding and Decoding Representations with Sum-Product Networks**](http://www.di.uniba.it/~ndm/pubs/vergari18aaai.pdf) `SPAE`

   - [[Vergari2017](#vergari2017)] [**Encoding and Decoding Representations with Sum- and Max-Product Networks**](https://openreview.net/forum?id=rkndY2VYx) `decoding`

   - [[Vergari2018b](#vergari2018b)] [**Visualizing and Understanding Sum-Product Networks**](https://arxiv.org/abs/1608.08266) `embeddings`

     

#### Modeling

   - [[Tan2019](#tan2019)]

     [**Hierarchical Decompositional Mixtures of Variational Autoencoders**](http://proceedings.mlr.press/v97/tan19b/tan19b.pdf) `SPVAE`

   - [[Peharz2019](#peharz2019)]

     [**Random Sum-Product Networks: A Simple and Effective Approach to Probabilistic Deep Learning**](https://arxiv.org/abs/1806.01910) `RAT-SPNs`

   - [[Vergari2019](#vergari2019)] [**Automatic Bayesian Density Analysis**](https://www.researchgate.net/publication/326621815_Automatic_Bayesian_Density_Analysis) `ABDA`

   - [[Shao2019](#shao2019)] [**Conditional Sum-Product Networks: Imposing Structure on Deep Probabilistic Architectures**](https://arxiv.org/pdf/1905.08550.pdf) `CSPN`

   - [[Wolfshaar2019](#wolfshaar2019)] [**Deep Convolutional Sum-Product Networks for Probabilistic Image Representations**](https://arxiv.org/pdf/1902.06155.pdf) `WickerSPN`

   - [[Butz2019](#butz2019)] [**Deep Convolutional Sum-Product Networks**](https://www.aaai.org/Papers/AAAI/2019/AAAI-ButzC.3622.pdf) `DCSPN`

   - [[Jaini2018b](#jaini2018b)] [**Deep Homogeneous Mixture Models: Representation, Separation, and Approximation**](http://papers.nips.cc/paper/7944-deep-homogeneous-mixture-models-representation-separation-and-approximation) `SPN-CG`

   - [[Ko2018](#ko2018)] [**Deep Compression of Sum-Product Networks on Tensor Networks**](https://arxiv.org/abs/1811.03963) `tSPN`

   - [[Trapp2018](#trapp2018)] [**Learning Deep Mixtures of Gaussian Process Experts Using Sum-Product Networks**](https://www.researchgate.net/publication/327621399_Learning_Deep_Mixtures_of_Gaussian_Process_Experts_Using_Sum-Product_Networks) `SPN-GP`

   - [[Ratajczak2018](#ratajczak2018)]

     [**Sum-Product Networks for Sequence Labeling**](https://arxiv.org/abs/1807.02324) `SPN-HO-LC-CRF` `SPN-HO-MEMM`

   - [[Zheng2018](#zheng2018)]

     [**Learning Graph-Structured Sum-Product Networks for Probabilistic Semantic Maps**](https://arxiv.org/abs/1709.08274)

     `GraphSPN`

   - [[Molina2018](#molina2018)]

     [**Mixed Sum-Product Networks: A Deep Architecture for Hybrid Domains**](http://www.ml.informatik.tu-darmstadt.de/papers/molina2018aaai_mspns.pdf) `MSPN`

   - [[Sharir2018](#sharir2018)]

     [**Sum-Product-Quotient Networks**](https://arxiv.org/abs/1710.04404) `SPQN`

   - [[Dennis2017b](#dennis2017b)]

     [**Autoencoder-Enhanced Sum-Product Networks**](http://ieeexplore.ieee.org/document/8260779/) `AESPN`

   - [[Desana2017](#desana2017)]

     [**Sum-Product Graphical Models**](https://arxiv.org/abs/1708.06438)

     `SPGM`

   - [[Mauà2017](#mauà2017)] [**Credal Sum-Product Networks**](http://pure.qub.ac.uk/portal/files/128951275/maua17.pdf) `CSPN`

   - [[Gens2017](#gens2017)] [**Compositional Kernel Machines**](https://openreview.net/pdf?id=S1Bm3T_lg) `CKM`

   - [[Friesen2017](#friesen2017)] [**Unifying Sum-Product Networks and Submodular Fields**](http://padl.ws/papers/Paper%201.pdf) `SSPN`

   - [[Molina2017](#molina2017)] [**Poisson Sum-Product Networks: A Deep Architecture for Tractable Multivariate Poisson Distributions**](http://www-ai.cs.uni-dortmund.de/auto?self=$Publication_ewtkrvss1s) `Poisson SPNs`

   - [[Melibari2016c](#melibari2016c)] [**Dynamic Sum-Product Networks for Tractable Inference on Sequence Data**](http://arxiv.org/abs/1511.04412) `dynamic-SPN`

   - [[Melibari2016b](#melibari2016b)]

     [**Sum-Product-Max Networks for Tractable Decision Making**](http://trust.sce.ntu.edu.sg/aamas16/pdfs/p1419.pdf) `decision-diagram`

   - [[Melibari2016a](#melibari2016a)]

     [**Decision Sum-Product-Max Networks**](https://cs.uwaterloo.ca/~mmelibar/publications/melibari-aaai2016.pdf) `decision-diagram`

   - [[Friesen2015](#friesen2015)]

     [**Recursive Decomposition for Nonconvex Optimization**](https://www.cs.washington.edu/node/11282) `opt`

   - [[Niepert2015](#niepert2015)]

     [**Learning and Inference in Tractable Probabilistic Knowledge Bases**](http://homes.cs.washington.edu/~pedrod/papers/uai15.pdf) `relational`

   - [[Nath2015](#nath2015)]

     [**Learning Relational Sum-Product Networks**](http://homes.cs.washington.edu/~pedrod/papers/aaai15.pdf) `relational`

   - [[Nath2014](#nath2014)]

     [**Learning Tractable Statistical Relational Models**](http://spn.cs.washington.edu/papers/ltpm2014_paper_4.pdf)

   `relational`

   - [[Peharz2014b](#peharz2014b)] [**Learning Selective Sum-Product Networks**](http://spn.cs.washington.edu/papers/ltpm2014_paper_9.pdf) `SSPN`

   - [[Stuhlmueller2012](#stuhlmueller2012)]

     [**Dynamic Programming Algorithm for Inference in Recursive Probabilistic Programs**](http://arxiv.org/abs/1206.3555)

     `FSPN`

   - [[Poon2011](#poon2011)]

   [**Sum-Product Networks: A New Deep Architecture**](http://spn.cs.washington.edu/papers/spn.pdf) `SPN`

#### Applications

   - [[Stelzner2019](#stelzner2019)] [**Faster Attend-Infer-Repeat with Tractable Probabilistic Models**](http://proceedings.mlr.press/v97/stelzner19a/stelzner19a.pdf) `SuPAIR`

   - [[Conaty2018](#conaty2018)]

     [**Cascading Sum-Product Networks using Robustness**](http://pgm2018.utia.cz/data/proc/conaty18a.pdf) `Cascaded CSPN`

   - [[Joshi2018](#joshi2018)]

     [**Exact, Tractable Inference in the Sigma Cognitive Architecture via Sum-Product Networks**](http://www.cogsys.org/papers/ACSvol6/article08.pdf) `cognitive architectures`

   - [[Ratajczak2018](#ratajczak2018)]

     [**Sum-Product Networks for Sequence Labeling**](https://arxiv.org/abs/1807.02324)

     `speech`

   - [[Butz2018a](#butz2018a)]

     [**Efficient Examination of Soil Bacteria Using Probabilistic Graphical Models**](https://link.springer.com/chapter/10.1007/978-3-319-92058-0_30)  

   - [[Zheng2018](#zheng2018)]

     [**Learning Graph-Structured Sum-Product Networks for Probabilistic Semantic Maps**](https://arxiv.org/abs/1709.08274)

     `semantic mapping in robotics`

   - [[Pronobis2017a](#pronobis2017a)] [**Deep Spatial Affordance Hierarchy: Spatial Knowledge Representation for Planning in Large-scale Environments**](http://www.ece.rochester.edu/projects/rail/ssrr2017/contributions/rao_rss17_ssrr_ws.pdf) *SSRR 2017* `robot control`

   - [[Rathke2017](#rathke2017)] [**Locally Adaptive Probabilistic Models for Global Segmentation of Pathological OCT Scans**](https://ipa.math.uni-heidelberg.de/dokuwiki/Papers/Rathke2017.pdf) *MICCAI 2017* `segmentation`

   - [[Friesen2017](#friesen2017)] [**Submodular Sum-Product Networks for Scene Understanding**](https://openreview.net/pdf?id=ryEGFD9gl) *OpenReview@ICLR 2017* `segmentation`

   - [[Sguerra2016](#sguerra2016)] 

     [**Image Classification Using Sum-Product Networks for Autonomous Flight of Micro Aerial Vehicles**](http://ieeexplore.ieee.org/abstract/document/7839576/) `image-classification` `ID-Spn`

   - [[Yuan2016](#yuan2016)]

     [**Modeling Spatial Layout for Scene Image Understanding Via a Novel Multiscale Sum-Product Network**](http://www.sciencedirect.com/science/article/pii/S0957417416303591)

     `cv` `segmentation`

   - [[Nath2016](#nath2016)]

     [**Learning Tractable Probabilistic Models for Fault Localization**](http://homes.cs.washington.edu/~pedrod/papers/aaai16.pdf)

   - [[Wang2015](#wang2015)]

     [**Hierarchical Spatial Sum-Product Networks for action recognition in Still Images**](http://arxiv.org/abs/1511.05292)      `cv` `activity-recognition`

   - [[Amer2015](#amer2015)]

     [**Sum Product Networks for Activity Recognition**](http://web.engr.oregonstate.edu/~sinisa/research/publications/PAMI_SPN.pdf)

     `cv` `activity-recognition`

   - [[Li2015](#li2015)] [**Combining Sum-Product Network and Noisy-OrModel for Ontology Matching**](http://disi.unitn.it/~pavel/om2015/papers/om2015_TSpaper1.pdf) `sem-web`

   - [[Cheng2014](#cheng2014)]

     [**Language Modeling with Sum-Product Networks**](http://spn.cs.washington.edu/papers/is14.pdf)

     `sequence`

   - [[Ratajczak2014](#ratajczak2014)]

     [**Sum-Product Networks for Structured Prediction: Context-Specific Deep Conditional Random Fields**](https://www.spsc.tugraz.at/biblio/ratajczak20143046)

     `speech`

   - [[Peharz2014a](#peharz2014a)]

     [**Modeling Speech with Sum-Product Networks: Application to Bandwidth Extension**](http://spn.cs.washington.edu/papers/icassp14.pdf) `speech`

   - [[Amer2012](#amer2012)]

     [**Sum-product Networks for Modeling Activities with Stochastic Structure**](http://web.engr.oregonstate.edu/~sinisa/research/publications/cvpr12_SPN.pdf)

     `cv``activity-recognition`

	 

#### Theory

   - [[Mei2018](#mei2018)] [**Maximum A Posteriori Inference in Sum-Product Networks**](https://arxiv.org/abs/1708.04846) `MAP inference`

   - [[Conaty2017](#conaty2017)] [**Approximation Complexity of Maximum A Posteriori Inference in Sum-Product Networks**](https://arxiv.org/abs/1703.06045) `MAP inference`

   - [[Zhao2016b](#zhao2016b)]

      [**A Unified Approach for Learning the Parameters of Sum-Product Networks**](https://arxiv.org/abs/1601.00318) `CCCP`

   - [[Peharz2016](#peharz2016)]

     [**On the Latent Variable Interpretation in Sum-Product Networks**](http://arxiv.org/abs/1601.06180) `EM`

   - [[Friesen2016](#friesen2016)]

     [**The Sum-Product Theorem: A Foundation for Learning Tractable Models**](http://homes.cs.washington.edu/~pedrod/papers/mlc16.pdf)

     `opt` `sum-prod-theorem`

   - [[Peharz2015b](#peharz2015b)]

     [**Foundations of Sum-Product Networks for Probabilistic Modeling**](https://www.researchgate.net/profile/Robert_Peharz/publication/273000973_Foundations_of_Sum-Product_Networks_for_Probabilistic_Modeling/links/54f49ff00cf2f28c1362088b.pdf)

   - [[Friesen2015](#friesen2015)]

     [**Recursive Decomposition for Nonconvex Optimization**](https://www.cs.washington.edu/node/11282)

     `opt` `sum-prod-theorem`

   - [[Zhao2015](#zhao2015)]

     [**On the Relationship between Sum-Product Networks and Bayesian Networks**](http://jmlr.org/proceedings/papers/v37/zhaoc15.pdf)

   - [[Peharz2015a](#peharz2015a)] [**On Theoretical Properties of Sum-Product Networks**](http://www.jmlr.org/proceedings/papers/v38/peharz15.pdf)

   - [[Martens2014](#martens2014)]

     [**On the Expressive Efficiency of Sum Product Networks**](http://arxiv.org/abs/1411.7717) `depth`

   - [[Delalleau2011](#dellaleau2011)]

     [**Shallow vs. Deep Sum-Product Networks**](http://papers.nips.cc/paper/4350-shallow-vs-deep-sum-product-networks.pdf)     `depth`

#### Hardware

  - [[Sommer2018](#sommer2018)] [**Automatic Mapping of the Sum-Product Network Inference Problem to FPGA-Based Accelerators**](https://ieeexplore.ieee.org/document/8615710) `FPGA`

	 

## Related Works

### Arithmetic Circuits

   - [[Darwiche2003](#darwiche2003)]

     [**A Differential Approach to Inference in Bayesian Networks**](Advances

     in Neural Information Processing Systems 2011) *J. ACM 2003*

   - [[Lowd2013](#lowd2013)]

     [**Learning Markov Networks With Arithmetic Circuits**](http://ix.cs.uoregon.edu/~lowd/aistats13lowd.pdf)

     *AISTATS 2013*

   - [[Rooshenas2016](#rooshenas2016)]

     [**Discriminative Structure Learning of Arithmetic Circuits**](http://www.jmlr.org/proceedings/papers/v51/rooshenas16.pdf)

     *AISTATS 2016*

   - [[Choi2017](#Choi2017)]

     [**On Relaxing Determinism in Arithmetic Circuits**](http://proceedings.mlr.press/v70/choi17a/choi17a.pdf)

     *ICML 2017*

     

### Other TPMs

   - [[Livni2013](#livni2013)]

     [**A Provably Efficient Algorithm for Training Deep Networks**](http://arxiv.org/abs/1304.7045)

     *arXiv 2013*

### Exploiting Sum-Product Theorem

   - [[Gens2017](#gens2017)] 

     [**Compositional Kernel Machines**](https://openreview.net/pdf?id=S1Bm3T_lg)

     *ICLR 2017 - Workshop*

## Resources

### Dataset

   - 20 commonly used

     [datasets for density estimation](https://github.com/arranger1044/DEBD) as in [[Lowd2013](#lowd2013)][[Gens2013](#gens2013)][[Rooshenas2014](#rooshenas2014)][[Vergari2015](#vergari2015)][[Adel2015](#adel2015)][[Zhao2016a](#zhao2016a)][[Rooshenas2016](#rooshenas2016)]

### Code

   - [[Trapp2019](#trapp2019)] [**BayesianSumProductNetworks.jl**](https://github.com/trappmartin/BayesianSumProductNetworks) Julia implementation of Bayesian structure and parameter learning. 

   - [[Molina2019](#molina2019)] [**SPFlow**](https://github.com/SPFlow/SPFlow) an open-source Python library providing a simple interface to inference, learning, and manipulation routines for SPNs `python3`

   - [[Mai2018](#mei2018)] [**MAP inference**](https://github.com/shtechair/maxspn) routines and experiments in  `Go` 

   - [[Vergari2018](#vergari2018)] [**SPAE**](https://github.com/arranger1044/spae) encoding and decoding embeddings from SPNs in `python3`

   - [[Molina2018](#molina2018)] [**MSPN**](https://github.com/alejandromolinaml/MSPN) learning SPNs in hybrid domains in `python3` 

   - [[Zheng2018](#zheng2018)] [**GraphSPN**](https://github.com/zkytony/graphspn) a general framework for probabilistic structured prediction. `python3`

   - [[DiMauro2017](#dimauro2017)] [**alt-vs-spyn**](https://github.com/fabriziov/alt-vs-spyn) `dockerized` `python3` implementation of structure learning variants

   - [[Desana2017](#desana2017)] [**SPGM**](https://github.com/ocarinamat/SumProductGraphMod) implementation in `C++`

   - [[Pronobis2017b](#pronobis2017b)] [**LibSPN**](http://www.libspn.org/) tensorflow implementation with bindings in `python3`

   - [**SumProductNetworks.jl**](https://github.com/trappmartin/SumProductNetworks.jl) Software package for SPNs. `julia`

   - [[Hsu2017](#hsu2017)] [**Tachyon**](https://github.com/KalraA/Tachyon) structure and parameter learning in `python3`

   - [[Hsu2017](#hsu2017)] Online structure learning for [**continuous leaf**](https://github.com/whsu/spn) SPNs `python3` 

   - [[Peharz2016](#peharz2016)] Weight learning by the correct [**EM algorithm**](https://github.com/smatmo/LatentSPN) in `C++` 

   - [[Zhao2016a, Zhao2016b](#zhao2016b)] Parameter optimization using MLE and Bayesian approach

      [**spn-opt**](http://www.cs.cmu.edu/~hzhao1/papers/ICML2016/spn_release.zip) `C++`  

   - [[Vergari2018b](#vergari2018b)]

     [**spyn-repr**](https://github.com/arranger1044/spyn-repr)

     extracting embeddings from SPNs `python3`

   - [[Vergari2015](#vergari2015)] [**spyn**](https://github.com/arranger1044/spyn) LearnSPN-B/T/B and SPN

     inference routines in Python `python3` 

   - [[Rooshenas2014](#rooshenas2014)] ID-SPN and inference routines

     on ACs implemented in the

     [**Libra Toolkit**](http://libra.cs.uoregon.edu/) `Ocaml`  

   - [[Peharz2014a](#peharz2014a)]

     [**ABE-SPN**](https://www.spsc.tugraz.at/tools/artificial-bandwidth-extension-sum-product-networks)

     Artificial Bandwidth-Extension with Sum-Product Networks `MATLAB` `C++`  

   - [**GoSPN**](https://github.com/RenatoGeh/gospn) implementing

     LearnSPN in Go `Go` 

   - [[Cheng2014](#cheng2014)]

      [**lmspn**](https://github.com/stakok/lmspn) Language modeling

      with SPNs `C++` `CUDA`

   - [**C++/Cuda porting**](https://github.com/vseledkin/SumProductNetwork)

      of Poon's architecture `C++` `CUDA`  

   - [**Python porting**](https://github.com/vseledkin/Sum-Product-Networks)

      of Poon's architecture `python2`  

   - [[Gens2013](#gens2013)]

      [**LearnSPN**](http://spn.cs.washington.edu/learnspn/) `Java`

   - [[Poon2011](#poon2011)] Code to **train** [**Poon's architecture

      weigths by EM**](http://spn.cs.washington.edu/spn/) `Java` `MPI`

### Talks and Tutorials

   - Di Mauro and Vergari [**Learning Sum-Product Networks**](http://people.idsia.ch/~alessandro/pgm/DiMauroVergari.pdf)

     tutorial at PGM'16 _2016_

   - Poupart P. **Deep Learning, Sum-Product Networks** [**Part I**](https://www.youtube.com/watch?v=eF0APeEIJNw)

     [**Part II**](https://www.youtube.com/watch?v=9-1YE_N-lnw) _2015_

   - Hernàndez-Lobato, J. M. [**An Introduction to Sum-Product Networks**](https://jmhldotorg.files.wordpress.com/2013/11/slidescambridgesumproductnetworks2013.pdf) _2013_  

   - Gens, R. [**Learning the Structure of Sum-Product Networks**](http://spn.cs.washington.edu/talks/Gens_SLSPN_ICML2013.pdf)

     [[Gens2013](#gens2013)] _2013_  

   - Gens, R.  [**Discriminative Learning of Sum-Product Networks**](http://videolectures.net/nips2012_gens_discriminative_learning/) [[Gens2012]](#gens2012) _2012_

   - Poon,

     H. [**Sum-Product Networks: A New Deep Architecture**](http://spn.cs.washington.edu/talks/spn11.pdf)

     [[Poon2011](#poon2011)] _2011_

### Blog Posts

   - [**Tensor-Based Sum-Product Networks: Part I**](http://jostosh.github.io/spn01/), _Jos van de Wolfshaar_, June 11, 2019. 

   - [**Tensor-Based Sum-Product Networks: Part II**](http://jostosh.github.io/spn02/), _Jos van de Wolfshaar_, July 10, 2019.

## References

* 


[Adel2015]


_Adel, Tameem and Balduzzi, David and Ghodsi, Ali_


**Learning the Structure of Sum-Product Networks via an SVD-based Algorithm**


Uncertainty in Artificial Intelligence 2015

* 

[Amer2012]


_Amer, Mohamed and Todorovic, Sinisa_


**Sum-Product Networks for Modeling Activities with Stochastic Structure**


2012 IEEE Conference on CVPR

* 

[Amer2015]


_Amer, Mohamed and Todorovic, Sinisa_


**Sum Product Networks for Activity Recognition**


IEEE Transactions on Pattern Analysis and Machine Intelligence

* 

[Bueff2018]


_Bueff, Andreas and Spelchert, Stefanie and Belle, Vaishak_


**Tractable Querying and Learning in Hybrid Domains via Sum-Product Networks**


preprint

* 

[Butz2018a]


_Butz, Cory J. and dos Santos André E. and Oliveira Jhonatan S. and Stavrinides John_


**Efficient Examination of Soil Bacteria Using Probabilistic Graphical Models**


International Conference on Industrial, Engineering and Other Applications of Applied Intelligent Systems 2018

* 

[Butz2018b]


_Butz, Cory J. and Oliveira Jhonatan S. and dos Santos André E., Teixeira, A. L. and  Poupart, P. and Kalra, A._


**An Empirical Study of Methods for SPN Learning and Inference**


PGM 2018

* 

[Butz2019]


_Butz, Cory J and Oliveira, Jhonatan S. and dos Santos,  André E. and Teixeira, André L._


**Deep Convolutional Sum-Product Networks**


AAAI 2019

* 

[Cheng2014]


_Cheng, Wei-Chen and Kok, Stanley and Pham, Hoai Vu and Chieu, Hai Leong and Chai, Kian Ming Adam_


**Language modeling with Sum-Product Networks**


INTERSPEECH 2014

* 

[Choi2017]


_Cheng, Arthur and Darwiche, Adnan_


**On Relaxing Determinism in Arithmetic Circuits**


ICML 2017

* 

[Conaty2017]


_Conaty, Diarmaid and Deratani Mauá, Denis and de Campos, Cassio P._


**Approximation Complexity of Maximum A Posteriori Inference in Sum-Product Networks**


UAI 2017

* 

[Conaty2018]


_Conaty, Diarmaid and Del Rincon, Jesus Martinez and de Campos, Cassio P._


**Cascading Sum-Product Networks using Robustness**


PGM 2018

* 

[Darwiche2003]


_Darwiche, Adnan_


**A Differential Approach to Inference in Bayesian Networks**


Journal of the ACM 2003

* 

[Dellaleau2011]


_Delalleau, Olivier and Bengio, Yoshua_


**Shallow vs. Deep Sum-Product Networks**


Advances in Neural Information Processing Systems 2011

* 

[Dennis2012]


_Dennis, Aaron and Ventura, Dan_


**Learning the Architecture of Sum-Product Networks Using Clustering on Varibles**


Advances in Neural Information Processing Systems 25

* 

[Dennis2015]


_Dennis, Aaron and Ventura, Dan_


**Greedy Structure Search for Sum-product Networks**


International Joint Conference on Artificial Intelligence 2015

* 

[Dennis2017a]


_Dennis, Aaron and Ventura, Dan_


**Online Structure-Search for Sum-Product Networks**


16th IEEE International Conference on Machine Learning and Applications (ICMLA) 2017

* 

[Dennis2017b]


_Dennis, Aaron and Ventura, Dan_


**Autoencoder-Enhanced Sum-Product Networks**


16th IEEE International Conference on Machine Learning and Applications (ICMLA) 2017

* 

[Desana2016]


_Desana, Mattia and Schn{\"{o}}rr Christoph_


**Learning Arbitrary Sum-Product Network Leaves with Expectation-Maximization**


arxiv.org/abs/1604.07243

* [Desana2017]


_Desana, Mattia and Schn{\"{o}}rr Christoph_


**Sum-Product Graphical Models**


arxiv.org/abs/1708.06438

* [DiMauro2017]


_Di Mauro, Nicola and Esposito, Floriana and Ventola, Fabrizio Giuseppe and Vergari, Antonio_


**Alternative variable splitting methods to learn Sum-Product Networks**


Proceedings of the 16th International Conference of the Italian Association for Artificial Intelligence (AI*IA 2017)

* [Friesen2015]


_Friesen, Abram L. and Domingos, Pedro_


**Recursive Decomposition for Nonconvex Optimization**


Proceedings of the 24th International Joint Conference on Artificial Intelligence

* [Friesen2016]


_Friesen, Abram L. and Domingos, Pedro_


**The Sum-Product Theorem: A Foundation for Learning Tractable Models**


ICML 2016

* [Friesen2017]


_Friesen, Abram L. and Domingos, Pedro_


**Unifying Sum-Product Networks and Submodular Fields**


Principled Approaches to Deep Learning Workshop at ICML 2017

* [Gens2012]


_Gens, Robert and Domingos, Pedro_


**Discriminative Learning of Sum-Product Networks**


NIPS 2012

* 

[Gens2013]


_Gens, Robert and Domingos, Pedro_


**Learning the Structure of Sum-Product Networks**


ICML 2013

* 

[Gens2017]


_Gens, Robert and Domingos, Pedro_


**Compositional Kernel Machines**


ICLR 2017 - Workshop Track

* 

[Hsu2017]


_Hsu, Wilson and Kalra, Agastya and Poupart, Pascal_


**Online Structure Learning for Sum-Product Networks with Gaussian Leaves**


ICLR 2017 - Workshop Track

* 

[Jaini2016]


_Jaini, Priyank and Rashwan, Abdullah and Zhao, Han and Liu, Yue and

Banijamali, Ershad and Chen, Zhitang and Poupart, Pascal_


**Online Algorithms for Sum-Product Networks with Continuous Variables**


International Conference on Probabilistic Graphical Models 2016

* 

[Jaini2018a]


_Jaini, Priyank and Ghose Amur and Poupart, Pascal_


**Prometheus: Directly Learning Acyclic Directed Graph Structures for Sum-Product Networks**


PGM 2018

[Jaini2018b]


_Jaini, Priyank and Poupart, Pascal and Yu, Yaoliang_


**Deep Homogeneous Mixture Models: Representation, Separation, and Approximation**


NIPS 2018

* 

[Joshi2018]


_Joshi, Himanshu, Paul S. Rosenbloom, and Volkan Ustun_


**Exact, Tractable Inference in the Sigma Cognitive Architecture via Sum-Product Networks**


Advances in Cognitive Systems 6 (2018)

* 

[Ko2018]


_Ko, Ching-Yun and Chen, Cong and Zhang, Yuke and Batselier, Kim and Wong, Ngai_


**Deep Compression of Sum-Product Networks on Tensor Networks**


arXiv 2018

* 

[Krakovna2016]


_Krakovna, Viktoriya and Looks, Moshe_


**A Minimalistic Approach to Sum-Product Network Learning for Real Applications**


ICLR 2016

* 

[Lee2013]


_Lee, Sang-Woo and Heo, Min-Oh and Zhang, Byoung-Tak_


**Online Incremental Structure Learning of Sum-Product Networks**


ICONIP 2013

* 

[Lee2014]


_Lee, Sang-Woo and Watkins, Christopher and Zhang, Byoung-Tak_


**Non-Parametric Bayesian Sum-Product Networks**


Workshop on Learning Tractable Probabilistic Models 2014

* 

[Li2015]


_Weizhuo Li_


**Combining sum-product network and noisy-or model for ontology matching**


Proceedings of the 10th International Workshop on Ontology Matching

* 

[Livni2013]


_Livni, Roi and Shalev-Shwartz, Shai and Shamir, Ohad_


**A Provably Efficient Algorithm for Training Deep Networks**


arXiv 2013

* 

[Lowd2013]


_Lowd, Daniel and Rooshenas, Amirmohammad_


**Learning Markov Networks With Arithmetic Circuits**


Proceedings of the 16th International Conference on Artificial Intelligence and Statistics 2013

* 

[Martens2014]


_Martens, James and Medabalimi, Venkatesh_


**On the Expressive Efficiency of Sum Product Networks**


arXiv/1411.7717

* 

[Mauà2017]


_Mauá, Deratani Denis and Cozman Fabio Gagliardi and Conaty, Diarmaid and de Campos, Cassio P._


**Credal Sum-Product Networks**


ISIPTA 2017

* 

[Mei2018]


_Mei, Jun and Jiang, Yong and Tu, Kewei_


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


AAAI 2018

* 

[Melibari2016a]


_Melibari, Mazen and Poupart, Pascal and Doshi, Prashant_


**Decision Sum-Product-Max Networks**


Proceedings of the 30th AAAI Conference on Artificial Intelligence (AAAI 2016)

* 

[Melibari2016b]


_Melibari, Mazen and Poupart, Pascal and Doshi, Prashant_


**Sum-Product-Max Networks for Tractable Decision Making**


Proceedings of the 2016 International Conference on Autonomous Agents & Multiagent Systems

* 

[Melibari2016c]


_Melibari, Mazen and Poupart, Pascal and Doshi, Prashant and

Trimponias, George_


**Dynamic Sum-Product Networks for Tractable Inference on Sequence Data**


International Conference on Probabilistic Graphical Models 2016

* 

[Molina2017]


_Molina, Alejandro and Natarajan, Sriraam and Kersting, Kristian_


**Poisson Sum-Product Networks: A Deep Architecture for Tractable Multivariate Poisson Distributions**


Proceedings of the 31st AAAI Conference on Artificial Intelligence (AAAI 2017)

* 

[Molina2018]


_Molina, Alejandro and Vergari, Antonio and Di Mauro, Nicola and Natarajan, Sriraam and Esposito, Floriana and Kersting, Kristian_


**Mixed Sum-Product Networks: A Deep Architecture for Hybrid Domains**


Proceedings of the 32nd AAAI Conference on Artificial Intelligence (AAAI 2018)

* 

[Molina2019]


_Molina, Alejandro and Vergari, Antonio and Stelzner, Karl and Peharz, Robert and Subramani, Pranav and Di Mauro, Nicola and Poupart, Pascal and Kersting, Kristian_


**SPFlow: An Easy and Extensible Library for Deep Probabilistic Learning using Sum-Product Networks**


arXiv:1901.03704

* 

[Nath2014]


_Nath, Aniruddh and Domingos, Pedro_


**Learning Tractable Statistical Relational Models**


Workshop on Learning Tractable Probabilistic Models

* 

[Nath2015]


_Nath, Aniruddh and Domingos, Pedro_


**Learning Relational Sum-Product Networks**


Proceedings of the 29th AAAI Conference on Artificial Intelligence (AAAI 2015)

* 

[Nath2016]


_Nath, Aniruddh and Domingos, Pedro_


**Learning Tractable Probabilistic Models for Fault Localization**


Proceedings of the 30th AAAI Conference on Artificial Intelligence (AAAI 2016)

* 

[Niepert2015]


_Niepert, Mathias and Domingos, Pedro_


**Learning and Inference in Tractable Probabilistic Knowledge Bases**


UAI 2015

* 

[Paris2020]


_París, Iago and Sánchez-Cauce, Raquel and Díez, Francisco Javier_


**Sum-product networks: A survey**


arXiv:2004.01167

* 

[Peharz2013]


_Peharz, Robert and Geiger, Bernhard and Pernkopf, Franz_


**Greedy Part-Wise Learning of Sum-Product Networks**


ECML-PKDD 2013

* 

[Peharz2014a]


_Peharz, Robert and Kapeller, Georg and Mowlaee, Pejman and Pernkopf, Franz_


**Modeling Speech with Sum-Product Networks: Application to Bandwidth Extension**


ICASSP2014

* 

[Peharz2014b]


_Robert Peharz and Gens, Robert and Domingos, Pedro_


**Learning Selective Sum-Product Networks**


Workshop on Learning Tractable Probabilistic Models 2014

* 

[Peharz2015a]


_Robert Peharz and Tschiatschek, Sebastian and Pernkopf, Franz and Domingos, Pedro_


**On Theoretical Properties of Sum-Product Networks**


Proceedings of the 18th International Conference on Artificial Intelligence and Statistics

* 

[Peharz2015b]


_Peharz, Robert_


**Foundations of Sum-Product Networks for Probabilistic Modeling**


PhD Thesis

* 

[Peharz2016]


_Robert Peharz and Robert Gens and Franz Pernkopf and Pedro Domingos_


**On the Latent Variable Interpretation in Sum-Product Networks**


arxiv.org/abs/1601.06180

* 

[Peharz2019]


_Robert Peharz and Antonio Vergari and Karl Stelzner and Alejandro Molina and Martin Trapp and Xiaoting Shao and  Kristian Kersting and Zoubin Ghahramani_


**Random Sum-Product Networks: A Simple and Effective Approach to Probabilistic Deep Learning**


UAI 2019

* 

[Poon2011]


_Poon, Hoifung and Domingos, Pedro_


**Sum-Product Network: a New Deep Architecture**


UAI 2011

* 

[Pronobis2017a]


_Pronobis, A. and Riccio, F. and Rao, R.~P.~N._


**Deep Spatial Affordance Hierarchy: Spatial Knowledge Representation for Planning in Large-scale Environments**


SSRR 2017

* 

[Pronobis2017b]


_Pronobis, A. and Ranganath, A. and Rao, R.~P.~N._


**LibSPN: A Library for Learning and Inference with Sum-Product Networks and TensorFlow**


Principled Approaches to Deep Learning Workshop at ICML 2017

* 

[Rahman2016]


_Tahrima Rahman and Vibhav Gogate_


**Merging Strategies for Sum-Product Networks: From Trees to

Graphs**


UAI 2016

* 

[Rashwan2016]


_Rashwan, Abdullah and Zhao, Han and Poupart, Pascal_


**Online and Distributed Bayesian Moment Matching for Parameter Learning in Sum-Product Networks**


Proceedings of the 19th International Conference on Artificial Intelligence and Statistics

* 

[Rashwan2018a]


_Rashwan, Abdullah and Poupart, Pascal and Zhitang, Chen_


**Discriminative Training of Sum-Product Networks by Extended Baum-Welch**


PGM 2018

* 

[Rashwan2018b]


_Rashwan, Abdullah and Kalra, Agastya and  Poupart, Pascal and Doshi, Prashant and Trimponias, George and Hsu, Wei-Shou_


**Online Structure Learning for Feed-Forward and Recurrent Sum-Product Networks**


NIPS 2018

* 

[Ratajczak2014]


_Ratajczak, Martin and Tschiatschek, S and Pernkopf, F_


**Sum-Product Networks for Structured Prediction: Context-Specific Deep Conditional Random Fields**


Workshop on Learning Tractable Probabilistic Models 2014

* 

[Ratajczak2018]


_Ratajczak, Martin and Tschiatschek, S and Pernkopf, F_


**Sum-Product Networks for Sequence Labeling**


preprint

* 

[Rathke2017]


_Rathke, F.; Desana, M. and Schnörr, C._


**Locally Adaptive Probabilistic Models for Global Segmentation of Pathological OCT Scans**


MICCAI 2017

* 

[Rooshenas2014]


_Rooshenas, Amirmohammad and Lowd, Daniel_


**Learning Sum-Product Networks with Direct and Indirect Variable Interactions**


ICML 2014

* 

[Rooshenas2016]


_Rooshenas, Amirmohammad and Lowd, Daniel_


**Discriminative Structure Learning of Arithmetic Circuits**


Proceedings of the 19th International Conference on Artificial Intelligence and Statistics

* 

[Shao2019]


_Shao, Xiaoting and Molina, Alejandro and Vergari, Antonio and Stelzner, Karl and Peharz, Robert and Liebig, Thomas and Kersting, Kristian_


**Conditional Sum-Product Networks: Imposing Structure on Deep Probabilistic Architectures**


arXiv:1905.08550

* 

[Sharir2018]


_Sharir, Or and Shashua, Amnon_


** Sum-Product-Quotient Networks**


AISTATS 2018

* 

[Sguerra2016]


_Sguerra, Bruno Massoni and Cozman, Fabio G._


**Image Classification Using Sum-Product Networks for Autonomous Flight of Micro Aerial Vehicles**


BRACIS 2016 - 5th Brazilian Conference on Intelligent Systems

* 

[Stelzner2019]


_Stelzner, Karl and Peharz, Robert and Kersting, Kristian_


**Faster Attend-Infer-Repeat with Tractable Probabilistic Models**


ICML 2019

* 

[Stuhlmueller2012]


_Stuhlmuller, Andreas and Goodman, Noah D._


**A Dynamic Programming Algorithm for Inference in Recursive Probabilistic Programs**


StaRAI 2012

* 

[Sommer2018]


_Sommer, Lukas and Oppermann, Julian and Molina, Alejandro and Binnig, Carsten and Kersting, Kristian and Koch, Andreas_


**Automatic Mapping of the Sum-Product Network Inference Problem to FPGA-Based Accelerators**


ICCD 2018

* 

[Tan2019]


_Tan, Ping Liang, and Peharz, Robert_


**Hierarchical Decompositional Mixtures of Variational Autoencoders**


ICML 2019

* 

[Trapp2016]


_Trapp, Martin and Peharz, Robert and Skowron, Marcin and Madl, Tamas and Pernkopf, Franz and Trappl, Robert_


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


Workshop on Practical Bayesian Nonparametrics at NIPS 2016

* 

[Trapp2017]


_Trapp, Martin and Madl, Tamas and Peharz, Robert and Pernkopf, Franz and Trappl, Robert_


**Safe Semi-Supervised Learning of Sum-Product Networks**


UAI 2017

* 

[Trapp2018]


_Trapp, Martin and Peharz, Robert and Rasmussen, Carl and Pernkopf, Franz_


**Learning Deep Mixtures of Gaussian Process Experts Using Sum-Product Networks**


Workshop on Tractable Probabilistic Models

* 

[Trapp2019]


_Trapp, Martin and Peharz, Robert and Ge, Hong and Pernkopf, Franz and Ghahramani, Zoubin_


**Bayesian Learning of Sum-Product Networks**


NeurIPS 2019

* 

[Vergari2015]


_Vergari, Antonio and Di Mauro, Nicola and Esposito, Floriana_


**Simplifying, Regularizing and Strengthening Sum-Product Network Structure Learning**


ECML-PKDD 2015

* 

[Vergari2017]


_Vergari, Antonio and Peharz, Robert and Di Mauro, Nicola and Esposito, Floriana_


**Encoding and Decoding Representations with Sum- and Max-Product Networks**


ICLR 2017 - Workshop Track

* 

[Vergari2018a]


_Vergari, Antonio and Peharz, Robert and Di Mauro, Nicola and Molina, Alejandro and Kersting, Kristian and Esposito, Floriana_


**Sum-Product Autoencoding: Encoding and Decoding Representations with Sum-Product Networks**


Proceedings of the 32nd AAAI Conference on Artificial Intelligence (AAAI 2018)

* 

[Vergari2018b]


_Vergari, Antonio and Di Mauro, Nicola and Esposito, Floriana_


**Visualizing and Understanding Sum-Product Networks**


Machine Learning Journal

* 

[Vergari2019]


_Vergari, Antonio and Molina, Alejandro and Peharz, Robert and Ghahramani, Zoubin and Kersting, Kristian and Valera, Isabel_


**Automatic Bayesian Density Analysis**


Proceedings of the 33rd AAAI Conference on Artificial Intelligence (AAAI 2019)

* 

  [Wang2015]


_Wang, Jinghua and Wang, Gang_


**Hierarchical Spatial Sum-Product Networks for action recognition in Still Images**


arXiv:1511.05292

* 

[Wolfshaar2019]


_van de Wolfshaar, Jos and Pronobix, Andrzej_ 


**Deep Convolutional Sum-Product Networks for Probabilistic Image Representations**


arXiv:1902.06155

* 

  [Yuan2016]


_Zehuan Yuan and Hao Wang and Limin Wang and Tong Lu and Shivakumara Palaiahnakote and Chew Lim Tan_


**Modeling Spatial Layout for Scene Image Understanding Via a Novel Multiscale Sum-Product Network**


Expert Systems with Applications

* 

[Zhao2015]


_Zhao, Han and Melibari, Mazen and Poupart, Pascal_


**On the Relationship between Sum-Product Networks and Bayesian Networks**


ICML 2015

* 

[Zhao2016a]


_Zhao, Han and Adel, Tameem and Gordon, Geoff and Amos, Brandon_


**Collapsed Variational Inference for Sum-Product Networks**


ICML 2016

* 

[Zhao2016b]


_Zhao, Han and Poupart, Pascal and Gordon, Geoff_


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


NIPS 2016

* 

[Zhao2017]


_Zhao, Han and Gordon, Geoff and Poupart, Pascal_


**Efficient Computation of Moments in Sum-Product Networks**


NIPS 2017

* 

[Zheng2018]


_Zheng, Kaiyu and Pronobis, Andrzej and Rao, Rajesh P.N._


**Learning Graph-Structured Sum-Product Networks for Probabilistic Semantic Maps**


AAAI 2018