Discontinued

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

Please visit and contribute to the website and repo 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 at the Washington University.

Licence and Contributing

awesome-spn is released under Public Domain. Feel free to complete and/or correct any of these lists. Pull requests are very welcome!

Table of Contents

• Papers

  • Year
    • 2020
    • 2019
    • 2018
    • 2017
    • 2016
    • 2015
    • 2014
    • 2013
    • 2012
    • 2011
  • Topic
    • Survey
    • Weight Learning
    • Structure Learning
    • Representation Learning
    • Modeling
    • Applications
    • Theory
    • Hardware

• Related Works

  • Arithmetic Circuits
  • Other TPMs
  • Exploiting Sum-Product Theorem

• Resources

  • Dataset
  • Code
  • Talks and Tutorials
  • Blog posts

• References

Papers

Sorted by year or topics

Year

2020

• [Paris2020] Sum-product networks: A survey preprint survey

2019

• [Trapp2019] Bayesian Learning of Sum-Product Networks NeurIPS 2019 structure-learning
• [Tan2019] Hierarchical Decompositional Mixtures of Variational Autoencoders ICML 2019 modeling
• [Peharz2019] Random Sum-Product Networks: A Simple and Effective Approach to Probabilistic Deep Learning UAI 2019 modeling weight learning
• [Stelzner2019] Faster Attend-Infer-Repeat with Tractable Probabilistic Models ICML 2019 applications
• [Shao2019] Conditional Sum-Product Networks: Imposing Structure on Deep Probabilistic Architectures preprint modeling
• [Vergari2019] Automatic Bayesian Density Analysis AAAI 2019 modeling
• [Butz2019] Deep Convolutional Sum-Product Networks AAAI 2019 modeling
• [Molina2019] SPFlow: An Easy and Extensible Library for Deep Probabilistic Learning using Sum-Product Networks preprint applications
• [Wolfshaar2019] Deep Convolutional Sum-Product Networks for Probabilistic Image Representations preprint modeling

2018

• [Jaini2018b] Deep Homogeneous Mixture Models: Representation, Separation, and Approximation NeurIPS 2018 modeling
• [Ko2018] Deep Compression of Sum-Product Networks on Tensor Networks preprint modeling
• [Sommer2018] Automatic Mapping of the Sum-Product Network Inference Problem to FPGA-Based Accelerators ICCD2018 hardware
• [Trapp2018] Learning Deep Mixtures of Gaussian Process Experts Using Sum-Product Networks Workshop on Tractable Probabilistic Models modeling
• [Vergari2018b] Visualizing and Understanding Sum-Product Networks Machine Learning Journal representation learning
• [Bueff2018] Tractable Querying and Learning in Hybrid Domains via Sum-Product Networks preprint structure-learning
• [Rashwan2018b] Online Structure Learning for Feed-Forward and Recurrent Sum-Product Networks NIPS 2018 structure-learning
• [Rashwan2018a] Discriminative Training of Sum-Product Networks by Extended Baum-Welch PGM 2018 weight-learning
• [Jaini2018a] Prometheus: Directly Learning Acyclic Directed Graph Structures for Sum-Product Networks PGM 2018 structure-learning
• [Conaty2018] Cascading Sum-Product Networks using Robustness PGM 2018 applications
• [Joshi2018] Exact, Tractable Inference in the Sigma Cognitive Architecture via Sum-Product Networks Advances in Cognitive Systems 2018 [applications](#applications
• [Ratajczak2018] Sum-Product Networks for Sequence Labeling arXiv preprint applications modeling
• [Butz2018b] An Empirical Study of Methods for SPN Learning and Inference PGM 2018 structure-learning
• [Butz2018a] Efficient Examination of Soil Bacteria Using Probabilistic Graphical Models IEA-AIE 2018 applications
• [Sharir2018] Sum-Product-Quotient Networks AISTATS 2018 modeling
• [Zheng2018] Learning Graph-Structured Sum-Product Networks for Probabilistic Semantic Maps AAAI 2018 modeling applications
• [Mei2018] Maximum A Posteriori Inference in Sum-Product Networks AAAI 2018 theory
• [Vergari2018a] Sum-Product Autoencoding: Encoding and Decoding Representations with Sum-Product Networks AAAI 2018 representation learning
• [Molina2018] Mixed Sum-Product Networks: A Deep Architecture for Hybrid Domains AAAI 2018 modeling

2017

• [Dennis2017b] Autoencoder-Enhanced Sum-Product Networks ICMLA 2017 modeling
• [Dennis2017a] Online Structure-Search for Sum-Product Networks ICMLA 2017 structure-learning
• [DiMauro2017] Alternative Variable Splitting Methods to Learn Sum-Product Networks AIxIA 2017 structure-learning
• [Desana2017] Sum-Product Graphical Models arXiv modeling
• [Pronobis2017b] LibSPN: A Library for Learning and Inference with Sum-Product Networks and TensorFlow [email protected] 2017 code
• [Friesen2017] Unifying Sum-Product Networks and Submodular Fields [email protected] 2017 applications modeling
• [Pronobis2017a] Deep Spatial Affordance Hierarchy: Spatial Knowledge Representation for Planning in Large-scale Environments SSRR 2017 applications
• [Rathke2017] Locally Adaptive Probabilistic Models for Global Segmentation of Pathological OCT Scans MICCAI 2017 applications
• [Trapp2017] Safe Semi-Supervised Learning of Sum-Product Networks UAI 2017 weight learning
• [Mauà2017] Credal Sum-Product Networks ISIPTA 2017 modeling
• [Conaty2017] Approximation Complexity of Maximum A Posteriori Inference in Sum-Product Networks UAI 2017 theory
• [Zhao2017] Efficient Computation of Moments in Sum-Product Networks NIPS 2017 weight-learning
• [Vergari2017] Encoding and Decoding Representations with Sum- and Max-Product Networks ICLR 2017 - Workshop representation learning
• [Hsu2017] Online Structure Learning for Sum-Product Networks with Gaussian Leaves ICLR 2017 - Workshop structure-learning
• [Gens2017] Compositional Kernel Machines ICLR 2017 - Workshop modeling
• [Molina2017] Poisson Sum-Product Networks: A Deep Architecture for Tractable Multivariate Poisson Distributions AAAI2017 modeling

2016

• [Sguerra2016] Image Classification Using Sum-Product Networks for Autonomous Flight of Micro Aerial Vehicles BRACIS 2016 applications
• [Trapp2016] Structure Inference in Sum-Product Networks using Infinite Sum-Product Trees Practical Bayesian Nonparametrics structure-learning
• [Melibari2016c] Dynamic Sum-Product Networks for Tractable Inference on Sequence Data PGM2016 modeling structure-learning
• [Jaini2016] Online Algorithms for Sum-Product Networks with Continuous Variables PGM2016 weight-learning
• [Desana2016] Learning Arbitrary Sum-Product Network Leaves with Expectation-Maximization arXiv weight-learning
• [Peharz2016] On the Latent Variable Interpretation in Sum-Product Networks arXiv theory weight-learning
• [Zhao2016b] A unified approach for learning the parameters of sum-product networks NIPS 2016 weight-learning
• [Yuan2016] Modeling Spatial Layout for Scene Image Understanding Via a Novel Multiscale Sum-Product Network Expert Systems and Applications applications
• [Rahman2016] Merging Strategies for Sum-Product Networks: From Trees to Graphs UAI2016 structure-learning
• [Friesen2016] The Sum-Product Theorem: A Foundation for Learning Tractable Models ICML2016 theory
• [Zhao2016a] Collapsed Variational Inference for Sum-Product Networks ICML2016 weight-learning
• [Rashwan2016] Online and Distributed Bayesian Moment Matching for Parameter Learning in Sum-Product Networks AISTATS2016 weight-learning
• [Krakovna2016] A Minimalistic Approach to Sum-Product Network Learning for Real Applications ICLR2016 structure-learning
• [Melibari2016b] Sum-Product-Max Networks for Tractable Decision Making AAMAS2016 modeling
• [Melibari2016a] Decision Sum-Product-Max Networks AAAI2016 modeling structure-learning
• [Nath2016] Learning Tractable Probabilistic Models for Fault Localization AAAI2016 applications

2015

• [Peharz2015b] Foundations of Sum-Product Networks for Probabilistic Modeling Thesis theory
• [Wang2015] Hierarchical Spatial Sum-Product Networks for action recognition in Still Images arXiv applications
• [Amer2015] Sum Product Networks for Activity Recognition TPAMI2015 applications
• [Li2015] Combining Sum-Product Network and Noisy-OrModel for Ontology Matching OM2015 applications
• [Vergari2015] Simplifying, Regularizing and Strengthening Sum-Product Network Structure Learning ECML-PKDD2015 structure-learning
• [Dennis2015] Greedy Structure Search for Sum-Product Networks IJCAI2015 structure-learning
• [Friesen2015] Recursive Decomposition for Nonconvex Optimization IJCAI2015 theory
• [Niepert2015] Learning and Inference in Tractable Probabilistic Knowledge Bases UAI2015 modeling
• [Adel2015] Learning the Structure of Sum-Product Networks via an SVD-based Algorithm UAI2015 structure-learning
• [Zhao2015] On the Relationship between Sum-Product Networks and Bayesian Networks ICML2015 theory
• [Peharz2015a] On Theoretical Properties of Sum-Product Networks AISTATS2015 theory
• [Nath2015] Learning Relational Sum-Product Networks AAAI2015 modeling

2014

• [Martens2014] On the Expressive Efficiency of Sum Product Networks arXiv theory
• [Cheng2014] Language Modeling with Sum-Product Networks INTERSPEECH2014 modeling applications
• [Peharz2014a] Modeling Speech with Sum-Product Networks: Application to Bandwidth Extension ICASSP2014 applications
• [Lee2014] Non-Parametric Bayesian Sum-Product Networks LTPM2014 structure-learning
• [Ratajczak2014] Sum-Product Networks for Structured Prediction: Context-Specific Deep Conditional Random Fields LTPM2014 applications
• [Nath2014] Learning Tractable Statistical Relational Models LTPM2014 modeling
• [Peharz2014b] Learning Selective Sum-Product Networks LTPM2014 weight-learning modeling
• [Rooshenas2014] Learning Sum-Product Networks with Direct and Indirect Interactions ICML2014 structure-learning

2013

• [Lee2013] Online Incremental Structure Learning of Sum-Product Networks ICONIP2013 structure-learning
• [Peharz2013] Greedy Part-Wise Learning of Sum-Product Networks ECML-PKDD2013 structure-learning
• [Gens2013] Learning the Structure of Sum-Product Networks ICML2013 structure-learning

2012

• [Gens2012] Discriminative Learning of Sum-Product Networks NIPS2012 weight-learning
• [Dennis2012] Learning the Architecture of Sum-Product Networks Using Clustering on Variables NIPS2012 structure-learning
• [Stuhlmueller2012] Dynamic Programming Algorithm for Inference in Recursive Probabilistic Programs StaRAI2012 modeling
• [Amer2012] Sum-product Networks for Modeling Activities with Stochastic Structure CVPR2012 applications

2011

• [Delalleau2011] Shallow vs. Deep Sum-Product Networks NIPS2011 theory
• [Poon2011] Sum-Product Networks: A New Deep Architecture UAI2011 modeling weight-learning

Topics

Survey

• [Paris2020] Sum-product networks: A survey survey

Weight Learning

• [Peharz2019] Random Sum-Product Networks: A Simple and Effective Approach to Probabilistic Deep Learning RAT-SPNs
• [Rashwan2018a] Discriminative Training of Sum-Product Networks by Extended Baum-Welch EBW SPN
• [Trapp2017] Safe Semi-Supervised Learning of Sum-Product Networks semi supervised
• [Zhao2017] Efficient Computation of Moments in Sum-Product Networks ADF
• [Jaini2016] Online Algorithms for Sum-Product Networks with Continuous Variables OBMM
• [Desana2016] Learning Arbitrary Sum-Product Network Leaves with Expectation-Maximization EM
• [Zhao2016b] A unified approach for learning the parameters of sum-product networks CCCP
• [Zhao2016a] Collapsed Variational Inference for Sum-Product Networks variational method
• [Rashwan2016] Online and Distributed Bayesian Moment Matching for Parameter Learning in Sum-Product Networks OBMM EGD
• [Peharz2014b] Learning Selective Sum-Product Networks ML SSPN
• [Poon2011] Sum-Product Networks: A New Deep Architecture EM Hard EM SGD
• [Gens2012] Discriminative Learning of Sum-Product Networks disc Hard EM disc Hard SGD

Structure Learning

• [Trapp2019] Bayesian Learning of Sum-Product Networks bayesian structure learning
• [Bueff2018] Tractable Querying and Learning in Hybrid Domains via Sum-Product Networks WMI-SPN
• [Rashwan2018b] Online Structure Learning for Feed-Forward and Recurrent Sum-Product Networks RSPN
• [Jaini2018a] Prometheus: Directly Learning Acyclic Directed Graph Structures for Sum-Product Networks Prometheus
• [Butz2018b] An Empirical Study of Methods for SPN Learning and Inference PP
• [Dennis2017a] Online Structure-Search for Sum-Product Networks
• [DiMauro2017] online SEARCHSPN Alternative Variable Splitting Methods to Learn Sum-Product Networks RGVS EBVS
• [Hsu2017] Online Structure Learning for Sum-Product Networks with Gaussian Leaves online structure learning
• [Trapp2016] Structure Inference in Sum-Product Networks using Infinite Sum-Product Trees infiniteSPT Bayesian nonparametrics
• [Melibari2016c] Dynamic Sum-Product Networks for Tractable Inference on Sequence Data hill-climbing
• [Rahman2016] Merging Strategies for Sum-Product Networks: From Trees to Graphs pruning dagSPN
• [Vergari2015] Simplifying, Regularizing and Strengthening Sum-Product Network Structure Learning LearnSPN-b LearnSPN-bt LearnSPN-btb
• [Dennis2015] Greedy Structure Search for Sum-Product Networks dagSPN
• [Adel2015] Learning the Structure of Sum-Product Networks via an SVD-based Algorithm SPN-SVD DSPN-SVD
• [Nath2015] Learning Relational Sum-Product Networks relational
• [Lee2014] Non-Parametric Bayesian Sum-Product Networks non-parametrics
• [Peharz2014b] Learning Selective Sum-Product Networks SSPN
• [Rooshenas2014] Learning Sum-Product Networks with Direct and Indirect Interactions ID-SPN
• [Lee2013] Online Incremental Structure Learning of Sum-Product Networks
• [Peharz2013] Greedy Part-Wise Learning of Sum-Product Networks bottom-up
• [Gens2013] Learning the Structure of Sum-Product Networks top-down LearnSPN
• [Dennis2012] Learning the Architecture of Sum-Product Networks Using Clustering on Variables top-down``k-means

Representation Learning

• [Vergari2018a] Sum-Product Autoencoding: Encoding and Decoding Representations with Sum-Product Networks SPAE
• [Vergari2017] Encoding and Decoding Representations with Sum- and Max-Product Networks decoding
• [Vergari2018b] Visualizing and Understanding Sum-Product Networks embeddings

Modeling

• [Tan2019] Hierarchical Decompositional Mixtures of Variational Autoencoders SPVAE
• [Peharz2019] Random Sum-Product Networks: A Simple and Effective Approach to Probabilistic Deep Learning RAT-SPNs
• [Vergari2019] Automatic Bayesian Density Analysis ABDA
• [Shao2019] Conditional Sum-Product Networks: Imposing Structure on Deep Probabilistic Architectures CSPN
• [Wolfshaar2019] Deep Convolutional Sum-Product Networks for Probabilistic Image Representations WickerSPN
• [Butz2019] Deep Convolutional Sum-Product Networks DCSPN
• [Jaini2018b] Deep Homogeneous Mixture Models: Representation, Separation, and Approximation SPN-CG
• [Ko2018] Deep Compression of Sum-Product Networks on Tensor Networks tSPN
• [Trapp2018] Learning Deep Mixtures of Gaussian Process Experts Using Sum-Product Networks SPN-GP
• [Ratajczak2018] Sum-Product Networks for Sequence Labeling SPN-HO-LC-CRF SPN-HO-MEMM
• [Zheng2018] Learning Graph-Structured Sum-Product Networks for Probabilistic Semantic Maps GraphSPN
• [Molina2018] Mixed Sum-Product Networks: A Deep Architecture for Hybrid Domains MSPN
• [Sharir2018] Sum-Product-Quotient Networks SPQN
• [Dennis2017b] Autoencoder-Enhanced Sum-Product Networks AESPN
• [Desana2017] Sum-Product Graphical Models SPGM
• [Mauà2017] Credal Sum-Product Networks CSPN
• [Gens2017] Compositional Kernel Machines CKM
• [Friesen2017] Unifying Sum-Product Networks and Submodular Fields SSPN
• [Molina2017] Poisson Sum-Product Networks: A Deep Architecture for Tractable Multivariate Poisson Distributions Poisson SPNs
• [Melibari2016c] Dynamic Sum-Product Networks for Tractable Inference on Sequence Data dynamic-SPN
• [Melibari2016b] Sum-Product-Max Networks for Tractable Decision Making decision-diagram
• [Melibari2016a] Decision Sum-Product-Max Networks decision-diagram
• [Friesen2015] Recursive Decomposition for Nonconvex Optimization opt
• [Niepert2015] Learning and Inference in Tractable Probabilistic Knowledge Bases relational
• [Nath2015] Learning Relational Sum-Product Networks relational
• [Nath2014] Learning Tractable Statistical Relational Models relational
• [Peharz2014b] Learning Selective Sum-Product Networks SSPN
• [Stuhlmueller2012] Dynamic Programming Algorithm for Inference in Recursive Probabilistic Programs FSPN
• [Poon2011] Sum-Product Networks: A New Deep Architecture SPN

Applications

• [Stelzner2019] Faster Attend-Infer-Repeat with Tractable Probabilistic Models SuPAIR
• [Conaty2018] Cascading Sum-Product Networks using Robustness Cascaded CSPN
• [Joshi2018] Exact, Tractable Inference in the Sigma Cognitive Architecture via Sum-Product Networks cognitive architectures
• [Ratajczak2018] Sum-Product Networks for Sequence Labeling speech
• [Butz2018a] Efficient Examination of Soil Bacteria Using Probabilistic Graphical Models
• [Zheng2018] Learning Graph-Structured Sum-Product Networks for Probabilistic Semantic Maps semantic mapping in robotics
• [Pronobis2017a] Deep Spatial Affordance Hierarchy: Spatial Knowledge Representation for Planning in Large-scale Environments SSRR 2017 robot control
• [Rathke2017] Locally Adaptive Probabilistic Models for Global Segmentation of Pathological OCT Scans MICCAI 2017 segmentation
• [Friesen2017] Submodular Sum-Product Networks for Scene Understanding [email protected] 2017 segmentation
• [Sguerra2016] Image Classification Using Sum-Product Networks for Autonomous Flight of Micro Aerial Vehicles image-classification ID-Spn
• [Yuan2016] Modeling Spatial Layout for Scene Image Understanding Via a Novel Multiscale Sum-Product Network cv segmentation
• [Nath2016] Learning Tractable Probabilistic Models for Fault Localization
• [Wang2015] Hierarchical Spatial Sum-Product Networks for action recognition in Still Images cv activity-recognition
• [Amer2015] Sum Product Networks for Activity Recognition cv activity-recognition
• [Li2015] Combining Sum-Product Network and Noisy-OrModel for Ontology Matching sem-web
• [Cheng2014] Language Modeling with Sum-Product Networks sequence
• [Ratajczak2014] Sum-Product Networks for Structured Prediction: Context-Specific Deep Conditional Random Fields speech
• [Peharz2014a] Modeling Speech with Sum-Product Networks: Application to Bandwidth Extension speech
• [Amer2012] Sum-product Networks for Modeling Activities with Stochastic Structure cv``activity-recognition

Theory

• [Mei2018] Maximum A Posteriori Inference in Sum-Product Networks MAP inference
• [Conaty2017] Approximation Complexity of Maximum A Posteriori Inference in Sum-Product Networks MAP inference
• [Zhao2016b] A Unified Approach for Learning the Parameters of Sum-Product Networks CCCP
• [Peharz2016] On the Latent Variable Interpretation in Sum-Product Networks EM
• [Friesen2016] The Sum-Product Theorem: A Foundation for Learning Tractable Models opt sum-prod-theorem
• [Peharz2015b] Foundations of Sum-Product Networks for Probabilistic Modeling
• [Friesen2015] Recursive Decomposition for Nonconvex Optimization opt sum-prod-theorem
• [Zhao2015] On the Relationship between Sum-Product Networks and Bayesian Networks
• [Peharz2015a] On Theoretical Properties of Sum-Product Networks
• [Martens2014] On the Expressive Efficiency of Sum Product Networks depth
• [Delalleau2011] Shallow vs. Deep Sum-Product Networks depth

Hardware

• [Sommer2018] Automatic Mapping of the Sum-Product Network Inference Problem to FPGA-Based Accelerators FPGA

Related Works

Arithmetic Circuits

• [Darwiche2003] [A Differential Approach to Inference in Bayesian Networks](Advances in Neural Information Processing Systems 2011) J. ACM 2003
• [Lowd2013] Learning Markov Networks With Arithmetic Circuits AISTATS 2013
• [Rooshenas2016] Discriminative Structure Learning of Arithmetic Circuits AISTATS 2016
• [Choi2017] On Relaxing Determinism in Arithmetic Circuits ICML 2017

Other TPMs

• [Livni2013] A Provably Efficient Algorithm for Training Deep Networks arXiv 2013

Exploiting Sum-Product Theorem

• [Gens2017] Compositional Kernel Machines ICLR 2017 - Workshop

Resources

Dataset

• 20 commonly used datasets for density estimation as in [Lowd2013][Gens2013][Rooshenas2014][Vergari2015][Adel2015][Zhao2016a][Rooshenas2016]

Code

• [Trapp2019] BayesianSumProductNetworks.jl Julia implementation of Bayesian structure and parameter learning.
• [Molina2019] SPFlow an open-source Python library providing a simple interface to inference, learning, and manipulation routines for SPNs python3
• [Mai2018] MAP inference routines and experiments in Go
• [Vergari2018] SPAE encoding and decoding embeddings from SPNs in python3
• [Molina2018] MSPN learning SPNs in hybrid domains in python3
• [Zheng2018] GraphSPN a general framework for probabilistic structured prediction. python3
• [DiMauro2017] alt-vs-spyn dockerized python3 implementation of structure learning variants
• [Desana2017] SPGM implementation in C++
• [Pronobis2017b] LibSPN tensorflow implementation with bindings in python3
• SumProductNetworks.jl Software package for SPNs. julia
• [Hsu2017] Tachyon structure and parameter learning in python3
• [Hsu2017] Online structure learning for continuous leaf SPNs python3
• [Peharz2016] Weight learning by the correct EM algorithm in C++
• [Zhao2016a, Zhao2016b] Parameter optimization using MLE and Bayesian approach spn-opt C++
• [Vergari2018b] spyn-repr extracting embeddings from SPNs python3
• [Vergari2015] spyn LearnSPN-B/T/B and SPN inference routines in Python python3
• [Rooshenas2014] ID-SPN and inference routines on ACs implemented in the Libra Toolkit Ocaml
• [Peharz2014a] ABE-SPN Artificial Bandwidth-Extension with Sum-Product Networks MATLAB C++
• GoSPN implementing LearnSPN in Go Go
• [Cheng2014] lmspn Language modeling with SPNs C++ CUDA
• C++/Cuda porting of Poon's architecture C++ CUDA
• Python porting of Poon's architecture python2
• [Gens2013] LearnSPN Java
• [Poon2011] Code to train Poon's architecture weigths by EM Java MPI

Talks and Tutorials

• Di Mauro and Vergari Learning Sum-Product Networks tutorial at PGM'16 2016
• Poupart P. Deep Learning, Sum-Product Networks Part I Part II 2015
• Hernàndez-Lobato, J. M. An Introduction to Sum-Product Networks 2013
• Gens, R. Learning the Structure of Sum-Product Networks [Gens2013] 2013
• Gens, R. Discriminative Learning of Sum-Product Networks [Gens2012] 2012
• Poon, H. Sum-Product Networks: A New Deep Architecture [Poon2011] 2011

Blog Posts

• Tensor-Based Sum-Product Networks: Part I, Jos van de Wolfshaar, June 11, 2019.
• Tensor-Based Sum-Product Networks: Part II, 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