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Sum-Product Networks

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 PADL@ICML 2017 code
• [Friesen2017] Unifying Sum-Product Networks and Submodular Fields PADL@ICML 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-downk-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 OpenReview@ICLR 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 cvactivity-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 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</p>

• [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_
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  AAAI 2018

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

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

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  International Conference on Probabilistic Graphical Models 2016

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

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

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  **Foundations of Sum-Product Networks for Probabilistic Modeling**
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  NeurIPS 2019

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  Machine Learning Journal

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  ICML 2015

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  NIPS 2016

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