└── README.md /README.md: -------------------------------------------------------------------------------- 1 | # Discontinued 2 | 3 | **awesome-spn** has been **discontinued** as of 01/01/2021! 4 | 5 | Please visit and contribute to the [website](https://arranger1044.github.io/probabilistic-circuits/) and [repo](https://github.com/arranger1044/probabilistic-circuits/) on **probabilistic circuits** 6 | 7 | # Awesome Sum-Product Networks 8 | 9 | **awesome-spn** is a curated and structured list of resources about 10 | *Sum-Product Networks* (SPNs), tractable deep density estimators. 11 | 12 | This includes (even not formally published) research papers sorted by year and topics as well as 13 | links to tutorials and code and other related Tractable Probabilistic 14 | Models (TPMs). It is inspired by the 15 | [SPN page](http://spn.cs.washington.edu/) at the Washington University. 16 | 17 | ## Licence and Contributing 18 | [![CC0](http://i.creativecommons.org/p/zero/1.0/88x31.png)](http://creativecommons.org/publicdomain/zero/1.0/) 19 | 20 | **awesome-spn** is released under Public Domain. Feel free to complete 21 | and/or correct any of these 22 | lists. [Pull requests](https://github.com/arranger1044/awesome-spn/pulls) 23 | are very welcome! 24 | 25 | ## Table of Contents 26 | 27 | * [Papers](#papers) 28 | * [Year](#year) 29 | * [2020](#2020) 30 | * [2019](#2019) 31 | * [2018](#2018) 32 | * [2017](#2017) 33 | * [2016](#2016) 34 | * [2015](#2015) 35 | * [2014](#2014) 36 | * [2013](#2013) 37 | * [2012](#2012) 38 | * [2011](#2011) 39 | * [Topic](#topics) 40 | * [Survey](#survey) 41 | * [Weight Learning](#weight-learning) 42 | * [Structure Learning](#structure-learning) 43 | * [Representation Learning](#representation-learning) 44 | * [Modeling](#modeling) 45 | * [Applications](#applications) 46 | * [Theory](#theory) 47 | * [Hardware](#hardware) 48 | * [Related Works](#related-works) 49 | * [Arithmetic Circuits](#arithmetic-circuits) 50 | * [Other TPMs](#other-tpms) 51 | * [Exploiting Sum-Product Theorem](#Exploiting-Sum-Product-Theorem) 52 | * [Resources](#resources) 53 | * [Dataset](#dataset) 54 | * [Code](#code) 55 | * [Talks and Tutorials](#talks-and-tutorials) 56 | * [Blog posts](#blog-posts) 57 | 58 | * [References](#resources) 59 | 60 | 61 | ## Papers 62 | 63 | Sorted by [year](#year) or [topics](#topics) 64 | 65 | ### Year 66 | 67 | #### 2020 68 | - [[Paris2020](#paris2020)] 69 | [**Sum-product networks: A survey**](https://arxiv.org/abs/2004.01167) *preprint* [`survey`](#survey) 70 | 71 | #### 2019 72 | - [[Trapp2019](#trapp2019)] 73 | [**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) 74 | - [[Tan2019](#tan2019)] 75 | [**Hierarchical Decompositional Mixtures of Variational Autoencoders**](http://proceedings.mlr.press/v97/tan19b/tan19b.pdf) *ICML 2019* [`modeling`](#modeling) 76 | - [[Peharz2019](#peharz2019)] 77 | [**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) 78 | - [[Stelzner2019](#stelzner2019)] [**Faster Attend-Infer-Repeat with Tractable Probabilistic Models**](http://proceedings.mlr.press/v97/stelzner19a/stelzner19a.pdf) *ICML 2019* [`applications`](#applications) 79 | - [[Shao2019](#shao2019)] [**Conditional Sum-Product Networks: Imposing Structure on Deep Probabilistic Architectures**](https://arxiv.org/pdf/1905.08550.pdf) *preprint* [`modeling`](#modeling) 80 | - [[Vergari2019](#vergari2019)] [**Automatic Bayesian Density Analysis**](https://www.researchgate.net/publication/326621815_Automatic_Bayesian_Density_Analysis) *AAAI 2019* [`modeling`](#modeling) 81 | - [[Butz2019](#butz2019)] [**Deep Convolutional Sum-Product Networks**](https://www.aaai.org/Papers/AAAI/2019/AAAI-ButzC.3622.pdf) *AAAI 2019* [`modeling`](#modeling) 82 | - [[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) 83 | - [[Wolfshaar2019](#wolfshaar2019)] [**Deep Convolutional Sum-Product Networks for Probabilistic Image Representations**](https://arxiv.org/pdf/1902.06155.pdf) *preprint* [`modeling`](#modeling) 84 | 85 | #### 2018 86 | 87 | - [[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) 88 | - [[Ko2018](#ko2018)] [**Deep Compression of Sum-Product Networks on Tensor Networks**](https://arxiv.org/abs/1811.03963) *preprint* [`modeling`](#modeling) 89 | - [[Sommer2018](#sommer2018)] [**Automatic Mapping of the Sum-Product Network Inference Problem to FPGA-Based Accelerators**](https://ieeexplore.ieee.org/document/8615710) *ICCD2018* [`hardware`](#hardware) 90 | - [[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) 91 | - [[Vergari2018b](#vergari2018b)] [**Visualizing and Understanding Sum-Product Networks**](https://arxiv.org/abs/1608.08266) *Machine Learning Journal* [`representation learning`](#representation-learning) 92 | - [[Bueff2018](#bueff2018)] 93 | [**Tractable Querying and Learning in Hybrid Domains via Sum-Product Networks**](https://arxiv.org/abs/1807.05464) *preprint* [`structure-learning`](#structure-learning) 94 | - [[Rashwan2018b](#rashwan2018b)] 95 | [**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) 96 | - [[Rashwan2018a](#rashwan2018a)] 97 | [**Discriminative Training of Sum-Product Networks by Extended Baum-Welch**](http://pgm2018.utia.cz/data/proc/rashwan18a.pdf) *PGM 2018* [`weight-learning`](#weight-learning) 98 | - [[Jaini2018a](#jaini2018a)] 99 | [**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) 100 | - [[Conaty2018](#conaty2018)] 101 | [**Cascading Sum-Product Networks using Robustness**](http://pgm2018.utia.cz/data/proc/conaty18a.pdf) *PGM 2018* [`applications`](#applications) 102 | - [[Joshi2018](#joshi2018)] 103 | [**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 104 | - [[Ratajczak2018](#ratajczak2018)] 105 | [**Sum-Product Networks for Sequence Labeling**](https://arxiv.org/abs/1807.02324) *arXiv preprint* [`applications`](#applications) [`modeling`](#modeling) 106 | - [[Butz2018b](#butz2018b)] 107 | [**An Empirical Study of Methods for SPN Learning and Inference**](http://proceedings.mlr.press/v72/butz18a/butz18a.pdf) *PGM 2018* [`structure-learning`](#structure-learning) 108 | - [[Butz2018a](#butz2018a)] 109 | [**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) 110 | - [[Sharir2018](#sharir2018)] 111 | [**Sum-Product-Quotient Networks**](https://arxiv.org/abs/1710.04404) *AISTATS 2018* 112 | [`modeling`](#modeling) 113 | - [[Zheng2018](#zheng2018)] 114 | [**Learning Graph-Structured Sum-Product Networks for Probabilistic Semantic Maps**](https://arxiv.org/abs/1709.08274) *AAAI 2018* 115 | [`modeling`](#modeling) [`applications`](#applications) 116 | - [[Mei2018](#mei2018)] [**Maximum A Posteriori Inference in Sum-Product Networks**](https://arxiv.org/abs/1708.04846) *AAAI 2018* [`theory`](#theory) 117 | - [[Vergari2018a](#vergari2018a)] 118 | [**Sum-Product Autoencoding: Encoding and Decoding Representations with Sum-Product Networks**](http://www.di.uniba.it/~ndm/pubs/vergari18aaai.pdf) *AAAI 2018* 119 | [`representation learning`](#representation-learning) 120 | - [[Molina2018](#molina2018)] 121 | [**Mixed Sum-Product Networks: A Deep Architecture for Hybrid Domains**](http://www.ml.informatik.tu-darmstadt.de/papers/molina2018aaai_mspns.pdf) *AAAI 2018* 122 | [`modeling`](#modeling) 123 | 124 | #### 2017 125 | 126 | - [[Dennis2017b](#dennis2017b)] 127 | [**Autoencoder-Enhanced Sum-Product Networks**](http://ieeexplore.ieee.org/document/8260779/) *ICMLA 2017* [`modeling`](#modeling) 128 | - [[Dennis2017a](#dennis2017a)] 129 | [**Online Structure-Search for Sum-Product Networks**](http://ieeexplore.ieee.org/document/8260628/) *ICMLA 2017* [`structure-learning`](#structure-learning) 130 | - [[DiMauro2017](#dimauro2017)] 131 | [**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* 132 | [`structure-learning`](#structure-learning) 133 | - [[Desana2017](#desana2017)] 134 | [**Sum-Product Graphical Models**](https://arxiv.org/abs/1708.06438) 135 | *arXiv* [`modeling`](#modeling) 136 | - [[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) 137 | - [[Friesen2017](#friesen2017)] [**Unifying Sum-Product Networks and Submodular Fields**](http://padl.ws/papers/Paper%201.pdf) *PADL@ICML 2017* [`applications`](#applications) [`modeling`](#modeling) 138 | - [[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) 139 | - [[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) 140 | - [[Trapp2017](#trapp2017)] [**Safe Semi-Supervised Learning of Sum-Product Networks**](http://auai.org/uai2017/proceedings/papers/108.pdf) *UAI 2017* [`weight learning`](#weight-learning) 141 | - [[Mauà2017](#mauà2017)] [**Credal Sum-Product Networks**](http://pure.qub.ac.uk/portal/files/128951275/maua17.pdf) *ISIPTA 2017* [`modeling`](#modeling) 142 | - [[Conaty2017](#conaty2017)] [**Approximation Complexity of Maximum A Posteriori Inference in Sum-Product Networks**](https://arxiv.org/abs/1703.06045) *UAI 2017* [`theory`](#theory) 143 | - [[Zhao2017](#zhao2017)] [**Efficient Computation of Moments in Sum-Product Networks**](https://arxiv.org/abs/1702.04767) *NIPS 2017* [`weight-learning`](#weight-learning) 144 | - [[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) 145 | - [[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) 146 | - [[Gens2017](#gens2017)] [**Compositional Kernel Machines**](https://openreview.net/pdf?id=S1Bm3T_lg) *ICLR 2017 - Workshop* [`modeling`](#modeling) 147 | - [[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) 148 | 149 | 150 | #### 2016 151 | - [[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) 152 | - [[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) 153 | - [[Melibari2016c](#melibari2016c)] [**Dynamic Sum-Product Networks for Tractable Inference on Sequence Data**](http://arxiv.org/abs/1511.04412) 154 | *PGM2016* [`modeling`](#modeling) [`structure-learning`](#structure-learning) 155 | - [[Jaini2016](#jaini2016)] 156 | [**Online Algorithms for Sum-Product Networks with Continuous Variables**](http://jmlr.org/proceedings/papers/v52/jaini16.pdf) 157 | *PGM2016* [`weight-learning`](#weight-learning) 158 | - [[Desana2016](#desana2016)] 159 | [**Learning Arbitrary Sum-Product Network Leaves with Expectation-Maximization**](http://arxiv.org/abs/1604.07243) 160 | *arXiv* [`weight-learning`](#weight-learning) 161 | - [[Peharz2016](#peharz2016)] 162 | [**On the Latent Variable Interpretation in Sum-Product Networks**](http://arxiv.org/abs/1601.06180) 163 | *arXiv* [`theory`](#theory) [`weight-learning`](#weight-learning) 164 | - [[Zhao2016b](#zhao2016b)] 165 | [**A unified approach for learning the parameters of sum-product networks**](http://arxiv.org/abs/1601.00318) *NIPS 2016* [`weight-learning`](#weight-learning) 166 | - [[Yuan2016](#yuan2016)] 167 | [**Modeling Spatial Layout for Scene Image Understanding Via a Novel Multiscale Sum-Product Network**](http://www.sciencedirect.com/science/article/pii/S0957417416303591) 168 | *Expert Systems and Applications* [`applications`](#applications) 169 | - [[Rahman2016](#rahman2016)] 170 | [**Merging Strategies for Sum-Product Networks: From Trees to Graphs**](http://www.hlt.utdallas.edu/~vgogate/papers/uai16.pdf) 171 | *UAI2016* [`structure-learning`](#structure-learning) 172 | - [[Friesen2016](#friesen2016)] 173 | [**The Sum-Product Theorem: A Foundation for Learning Tractable Models**](http://homes.cs.washington.edu/~pedrod/papers/mlc16.pdf) 174 | *ICML2016* [`theory`](#theory) 175 | - [[Zhao2016a](#zhao2016a)] 176 | [**Collapsed Variational Inference for Sum-Product Networks**](http://jmlr.org/proceedings/papers/v48/zhaoa16.pdf) 177 | *ICML2016* [`weight-learning`](#weight-learning) 178 | - [[Rashwan2016](#rashwan2016)] 179 | [**Online and Distributed Bayesian Moment Matching for Parameter Learning in Sum-Product Networks**](http://www.jmlr.org/proceedings/papers/v51/rashwan16.pdf) 180 | *AISTATS2016* [`weight-learning`](#weight-learning) 181 | - [[Krakovna2016](#krakovna2016)] 182 | [**A Minimalistic Approach to Sum-Product Network Learning for Real Applications**](http://arxiv.org/abs/1602.04259) 183 | *ICLR2016* [`structure-learning`](#structure-learning) 184 | - [[Melibari2016b](#melibari2016b)] 185 | [**Sum-Product-Max Networks for Tractable Decision Making**](http://trust.sce.ntu.edu.sg/aamas16/pdfs/p1419.pdf) 186 | *AAMAS2016* [`modeling`](#modeling) 187 | - [[Melibari2016a](#melibari2016a)] [**Decision Sum-Product-Max Networks**](https://cs.uwaterloo.ca/~mmelibar/publications/melibari-aaai2016.pdf) 188 | *AAAI2016* [`modeling`](#modeling) [`structure-learning`](#structure-learning) 189 | - [[Nath2016](#nath2016)] 190 | [**Learning Tractable Probabilistic Models for Fault Localization**](http://homes.cs.washington.edu/~pedrod/papers/aaai16.pdf) 191 | *AAAI2016* [`applications`](#applications) 192 | 193 | 194 | #### 2015 195 | - [[Peharz2015b](#peharz2015b)] 196 | [**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) 197 | *Thesis* [`theory`](#theory) 198 | - [[Wang2015](#wang2015)] 199 | [**Hierarchical Spatial Sum-Product Networks for action recognition in Still Images**](http://arxiv.org/abs/1511.05292) 200 | *arXiv* [`applications`](#applications) 201 | - [[Amer2015](#amer2015)] 202 | [**Sum Product Networks for Activity Recognition**](http://web.engr.oregonstate.edu/~sinisa/research/publications/PAMI_SPN.pdf) 203 | *TPAMI2015* [`applications`](#applications) 204 | - [[Li2015](#li2015)] 205 | [**Combining Sum-Product Network and Noisy-OrModel for Ontology Matching**](http://disi.unitn.it/~pavel/om2015/papers/om2015_TSpaper1.pdf) 206 | *OM2015* [`applications`](#applications) 207 | - [[Vergari2015](#vergari2015)] 208 | [**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) 209 | *ECML-PKDD2015* [`structure-learning`](#structure-learning) 210 | - [[Dennis2015](#dennis2015)] 211 | [**Greedy Structure Search for Sum-Product Networks**](http://www.ijcai.org/Proceedings/15/Papers/136.pdf) *IJCAI2015* [`structure-learning`](#structure-learning) 212 | - [[Friesen2015](#friesen2015)] 213 | [**Recursive Decomposition for Nonconvex Optimization**](https://www.cs.washington.edu/node/11282) 214 | *IJCAI2015* [`theory`](#theory) 215 | - [[Niepert2015](#niepert2015)] 216 | [**Learning and Inference in Tractable Probabilistic Knowledge Bases**](http://homes.cs.washington.edu/~pedrod/papers/uai15.pdf) 217 | *UAI2015* [`modeling`](#modeling) 218 | - [[Adel2015](#adel2015)] 219 | [**Learning the Structure of Sum-Product Networks via an SVD-based Algorithm**](http://auai.org/uai2015/proceedings/papers/83.pdf) 220 | *UAI2015* [`structure-learning`](#structure-learning) 221 | - [[Zhao2015](#zhao2015)] 222 | [**On the Relationship between Sum-Product Networks and Bayesian Networks**](http://jmlr.org/proceedings/papers/v37/zhaoc15.pdf) 223 | *ICML2015* [`theory`](#theory) 224 | - [[Peharz2015a](#peharz2015a)] 225 | [**On Theoretical Properties of Sum-Product Networks**](http://www.jmlr.org/proceedings/papers/v38/peharz15.pdf) 226 | *AISTATS2015* [`theory`](#theory) 227 | - [[Nath2015](#nath2015)] 228 | [**Learning Relational Sum-Product Networks**](http://homes.cs.washington.edu/~pedrod/papers/aaai15.pdf) 229 | *AAAI2015* [`modeling`](#modeling) 230 | 231 | #### 2014 232 | - [[Martens2014](#martens2014)] 233 | [**On the Expressive Efficiency of Sum Product Networks**](http://arxiv.org/abs/1411.7717) 234 | *arXiv* [`theory`](#theory) 235 | - [[Cheng2014](#cheng2014)] 236 | [**Language Modeling with Sum-Product Networks**](http://spn.cs.washington.edu/papers/is14.pdf) 237 | *INTERSPEECH2014* [`modeling`](#modeling) [`applications`](#applications) 238 | - [[Peharz2014a](#peharz2014a)] 239 | [**Modeling Speech with Sum-Product Networks: Application to Bandwidth Extension**](http://spn.cs.washington.edu/papers/icassp14.pdf) 240 | *ICASSP2014* [`applications`](#applications) 241 | - [[Lee2014](#lee2014)] 242 | [**Non-Parametric Bayesian Sum-Product Networks**](http://spn.cs.washington.edu/papers/ltpm2014_paper_6.pdf) 243 | *LTPM2014* [`structure-learning`](#structure-learning) 244 | - [[Ratajczak2014](#ratajczak2014)] 245 | [**Sum-Product Networks for Structured Prediction: Context-Specific Deep Conditional Random Fields**](https://www.spsc.tugraz.at/biblio/ratajczak20143046) 246 | *LTPM2014* [`applications`](#applications) 247 | - [[Nath2014](#nath2014)] 248 | [**Learning Tractable Statistical Relational Models**](http://spn.cs.washington.edu/papers/ltpm2014_paper_4.pdf) 249 | *LTPM2014* [`modeling`](#modeling) 250 | - [[Peharz2014b](#peharz2014b)] 251 | [**Learning Selective Sum-Product Networks**](http://spn.cs.washington.edu/papers/ltpm2014_paper_9.pdf) 252 | *LTPM2014* [`weight-learning`](#weight-learning) [`modeling`](#modeling) 253 | - [[Rooshenas2014](#rooshenas2014)] 254 | [**Learning Sum-Product Networks with Direct and Indirect Interactions**](http://ix.cs.uoregon.edu/~lowd/icml14rooshenas.pdf) 255 | *ICML2014* [`structure-learning`](#structure-learning) 256 | 257 | 258 | #### 2013 259 | 260 | - [[Lee2013](#lee2013)] 261 | [**Online Incremental Structure Learning of Sum-Product Networks**](https://bi.snu.ac.kr/Publications/Conferences/International/ICONIP2013_SWLee.pdf) 262 | *ICONIP2013* [`structure-learning`](#structure-learning) 263 | - [[Peharz2013](#peharz2013)] 264 | [**Greedy Part-Wise Learning of Sum-Product Networks**](https://www.spsc.tugraz.at/sites/default/files/MergeSPN.pdf) 265 | *ECML-PKDD2013* [`structure-learning`](#structure-learning) 266 | - [[Gens2013](#gens2013)] 267 | [**Learning the Structure of Sum-Product Networks**](http://jmlr.org/proceedings/papers/v28/gens13.pdf) 268 | *ICML2013* [`structure-learning`](#structure-learning) 269 | 270 | 271 | 272 | #### 2012 273 | - [[Gens2012](#gens2012)] 274 | [**Discriminative Learning of Sum-Product Networks**](http://spn.cs.washington.edu/papers/dspn.pdf) 275 | *NIPS2012* [`weight-learning`](#weight-learning) 276 | - [[Dennis2012](#dennis2012)] 277 | [**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) 278 | *NIPS2012* [`structure-learning`](#structure-learning) 279 | - [[Stuhlmueller2012](#stuhlmueller2012)] 280 | [**Dynamic Programming Algorithm for Inference in Recursive Probabilistic Programs**](http://arxiv.org/abs/1206.3555) 281 | *StaRAI2012* [`modeling`](#modeling) 282 | - [[Amer2012](#amer2012)] 283 | [**Sum-product Networks for Modeling Activities with Stochastic Structure**](http://web.engr.oregonstate.edu/~sinisa/research/publications/cvpr12_SPN.pdf) 284 | *CVPR2012* [`applications`](#applications) 285 | 286 | 287 | #### 2011 288 | 289 | 290 | - [[Delalleau2011](#dellaleau2011)] 291 | [**Shallow vs. Deep Sum-Product Networks**](http://papers.nips.cc/paper/4350-shallow-vs-deep-sum-product-networks.pdf) 292 | *NIPS2011* [`theory`](#theory) 293 | - [[Poon2011](#poon2011)] 294 | [**Sum-Product Networks: A New Deep Architecture**](http://spn.cs.washington.edu/papers/spn.pdf) 295 | *UAI2011* [`modeling`](#modeling) [`weight-learning`](#weight-learning) 296 | 297 | 298 | 299 | 300 | 301 | ### Topics 302 | 303 | 304 | #### Survey 305 | - [[Paris2020](#paris2020)] 306 | [**Sum-product networks: A survey**](https://arxiv.org/abs/2004.01167) `survey` 307 | 308 | #### Weight Learning 309 | 310 | - [[Peharz2019](#peharz2019)] 311 | [**Random Sum-Product Networks: A Simple and Effective Approach to Probabilistic Deep Learning**](https://arxiv.org/abs/1806.01910) `RAT-SPNs` 312 | - [[Rashwan2018a](#rashwan2018a)] 313 | [**Discriminative Training of Sum-Product Networks by Extended Baum-Welch**](http://pgm2018.utia.cz/data/proc/rashwan18a.pdf) `EBW SPN` 314 | - [[Trapp2017](#trapp2017)] 315 | [**Safe Semi-Supervised Learning of Sum-Product Networks**]() `semi supervised` 316 | - [[Zhao2017](#zhao2017)] 317 | [**Efficient Computation of Moments in Sum-Product Networks**](https://arxiv.org/abs/1702.04767) `ADF` 318 | - [[Jaini2016](#jaini2016)] 319 | [**Online Algorithms for Sum-Product Networks with Continuous Variables**](http://jmlr.org/proceedings/papers/v52/jaini16.pdf) `OBMM` 320 | - [[Desana2016](#desana2016)] 321 | [**Learning Arbitrary Sum-Product Network Leaves with Expectation-Maximization**](http://arxiv.org/abs/1604.07243) `EM` 322 | - [[Zhao2016b](#zhao2016b)] 323 | [**A unified approach for learning the parameters of sum-product networks**](http://arxiv.org/abs/1601.00318) `CCCP` 324 | - [[Zhao2016a](#zhao2016a)] 325 | [**Collapsed Variational Inference for Sum-Product Networks**](http://jmlr.org/proceedings/papers/v48/zhaoa16.pdf) `variational method` 326 | - [[Rashwan2016](#rashwan2016)] 327 | [**Online and Distributed Bayesian Moment Matching for Parameter Learning in Sum-Product Networks**](http://www.jmlr.org/proceedings/papers/v51/rashwan16.pdf) 328 | `OBMM` `EGD` 329 | - [[Peharz2014b](#peharz2014b)] 330 | [**Learning Selective Sum-Product Networks**](http://spn.cs.washington.edu/papers/ltpm2014_paper_9.pdf) 331 | `ML` `SSPN` 332 | - [[Poon2011](#poon2011)] 333 | [**Sum-Product Networks: A New Deep Architecture**](http://spn.cs.washington.edu/papers/spn.pdf) `EM` `Hard EM` `SGD` 334 | - [[Gens2012](#gens2012)] 335 | [**Discriminative Learning of Sum-Product Networks**](http://spn.cs.washington.edu/papers/dspn.pdf) 336 | `disc Hard EM` `disc Hard SGD` 337 | 338 | 339 | #### Structure Learning 340 | 341 | - [[Trapp2019](#trapp2019)] 342 | [**Bayesian Learning of Sum-Product Networks**](https://papers.nips.cc/paper/8864-bayesian-learning-of-sum-product-networks.pdf) `bayesian structure learning` 343 | - [[Bueff2018](#bueff2018)] 344 | [**Tractable Querying and Learning in Hybrid Domains via Sum-Product Networks**](https://arxiv.org/abs/1807.05464) `WMI-SPN` 345 | - [[Rashwan2018b](#rashwan2018b)] 346 | [**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` 347 | - [[Jaini2018a](#jaini2018a)] 348 | [**Prometheus: Directly Learning Acyclic Directed Graph Structures for Sum-Product Networks**](http://pgm2018.utia.cz/data/proc/jaini18a.pdf) `Prometheus` 349 | - [[Butz2018b](#butz2018b)] 350 | [**An Empirical Study of Methods for SPN Learning and Inference**](http://proceedings.mlr.press/v72/butz18a/butz18a.pdf) `PP` 351 | - [[Dennis2017a](#dennis2017a)] 352 | [**Online Structure-Search for Sum-Product Networks**](http://ieeexplore.ieee.org/document/8260628/) 353 | - [[DiMauro2017](#dimauro2017)] `online SEARCHSPN` 354 | [**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` 355 | - [[Hsu2017](#hsu2017)] [**Online Structure Learning for Sum-Product Networks with Gaussian Leaves**](https://openreview.net/pdf?id=S1QefL5ge) `online structure learning` 356 | - [[Trapp2016](#trapp2016)] [**Structure Inference in Sum-Product Networks using Infinite Sum-Product Trees**](https://drive.google.com/file/d/0B3WHb3BabixAVWFVaDEzdThSbk0/view) `infiniteSPT` `Bayesian nonparametrics` 357 | - [[Melibari2016c](#melibari2016c)] 358 | [**Dynamic Sum-Product Networks for Tractable Inference on Sequence Data**](http://arxiv.org/abs/1511.04412) `hill-climbing` 359 | - [[Rahman2016](#rahman2016)] 360 | [**Merging Strategies for Sum-Product Networks: From Trees to Graphs**](http://www.hlt.utdallas.edu/~vgogate/papers/uai16.pdf) 361 | `pruning` `dagSPN` 362 | - [[Vergari2015](#vergari2015)] 363 | [**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) 364 | `LearnSPN-b` `LearnSPN-bt` `LearnSPN-btb` 365 | - [[Dennis2015](#dennis2015)] 366 | [**Greedy Structure Search for Sum-Product Networks**](http://www.ijcai.org/Proceedings/15/Papers/136.pdf) `dagSPN` 367 | - [[Adel2015](#adel2015)] 368 | [**Learning the Structure of Sum-Product Networks via an SVD-based Algorithm**](http://auai.org/uai2015/proceedings/papers/83.pdf) 369 | `SPN-SVD` `DSPN-SVD` 370 | - [[Nath2015](#nath2015)] 371 | [**Learning Relational Sum-Product Networks**](http://homes.cs.washington.edu/~pedrod/papers/aaai15.pdf) `relational` 372 | - [[Lee2014](#lee2014)] 373 | [**Non-Parametric Bayesian Sum-Product Networks**](http://spn.cs.washington.edu/papers/ltpm2014_paper_6.pdf) `non-parametrics` 374 | - [[Peharz2014b](#peharz2014b)] [**Learning Selective Sum-Product Networks**](http://spn.cs.washington.edu/papers/ltpm2014_paper_9.pdf) `SSPN` 375 | - [[Rooshenas2014](#rooshenas2014)] [**Learning Sum-Product Networks with Direct and Indirect Interactions**](http://ix.cs.uoregon.edu/~lowd/icml14rooshenas.pdf) `ID-SPN` 376 | - [[Lee2013](#lee2013)] 377 | [**Online Incremental Structure Learning of Sum-Product Networks**](https://bi.snu.ac.kr/Publications/Conferences/International/ICONIP2013_SWLee.pdf) 378 | - [[Peharz2013](#peharz2013)] 379 | [**Greedy Part-Wise Learning of Sum-Product Networks**](https://www.spsc.tugraz.at/sites/default/files/MergeSPN.pdf) `bottom-up` 380 | - [[Gens2013](#gens2013)] 381 | [**Learning the Structure of Sum-Product Networks**](http://jmlr.org/proceedings/papers/v28/gens13.pdf) `top-down` `LearnSPN` 382 | - [[Dennis2012](#dennis2012)] 383 | [**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) 384 | `top-down``k-means` 385 | 386 | 387 | #### Representation Learning 388 | 389 | - [[Vergari2018a](#vergari2018a)] 390 | [**Sum-Product Autoencoding: Encoding and Decoding Representations with Sum-Product Networks**](http://www.di.uniba.it/~ndm/pubs/vergari18aaai.pdf) `SPAE` 391 | - [[Vergari2017](#vergari2017)] [**Encoding and Decoding Representations with Sum- and Max-Product Networks**](https://openreview.net/forum?id=rkndY2VYx) `decoding` 392 | - [[Vergari2018b](#vergari2018b)] [**Visualizing and Understanding Sum-Product Networks**](https://arxiv.org/abs/1608.08266) `embeddings` 393 | 394 | 395 | #### Modeling 396 | 397 | - [[Tan2019](#tan2019)] 398 | [**Hierarchical Decompositional Mixtures of Variational Autoencoders**](http://proceedings.mlr.press/v97/tan19b/tan19b.pdf) `SPVAE` 399 | - [[Peharz2019](#peharz2019)] 400 | [**Random Sum-Product Networks: A Simple and Effective Approach to Probabilistic Deep Learning**](https://arxiv.org/abs/1806.01910) `RAT-SPNs` 401 | - [[Vergari2019](#vergari2019)] [**Automatic Bayesian Density Analysis**](https://www.researchgate.net/publication/326621815_Automatic_Bayesian_Density_Analysis) `ABDA` 402 | - [[Shao2019](#shao2019)] [**Conditional Sum-Product Networks: Imposing Structure on Deep Probabilistic Architectures**](https://arxiv.org/pdf/1905.08550.pdf) `CSPN` 403 | - [[Wolfshaar2019](#wolfshaar2019)] [**Deep Convolutional Sum-Product Networks for Probabilistic Image Representations**](https://arxiv.org/pdf/1902.06155.pdf) `WickerSPN` 404 | - [[Butz2019](#butz2019)] [**Deep Convolutional Sum-Product Networks**](https://www.aaai.org/Papers/AAAI/2019/AAAI-ButzC.3622.pdf) `DCSPN` 405 | - [[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` 406 | - [[Ko2018](#ko2018)] [**Deep Compression of Sum-Product Networks on Tensor Networks**](https://arxiv.org/abs/1811.03963) `tSPN` 407 | - [[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` 408 | - [[Ratajczak2018](#ratajczak2018)] 409 | [**Sum-Product Networks for Sequence Labeling**](https://arxiv.org/abs/1807.02324) `SPN-HO-LC-CRF` `SPN-HO-MEMM` 410 | - [[Zheng2018](#zheng2018)] 411 | [**Learning Graph-Structured Sum-Product Networks for Probabilistic Semantic Maps**](https://arxiv.org/abs/1709.08274) 412 | `GraphSPN` 413 | - [[Molina2018](#molina2018)] 414 | [**Mixed Sum-Product Networks: A Deep Architecture for Hybrid Domains**](http://www.ml.informatik.tu-darmstadt.de/papers/molina2018aaai_mspns.pdf) `MSPN` 415 | - [[Sharir2018](#sharir2018)] 416 | [**Sum-Product-Quotient Networks**](https://arxiv.org/abs/1710.04404) `SPQN` 417 | - [[Dennis2017b](#dennis2017b)] 418 | [**Autoencoder-Enhanced Sum-Product Networks**](http://ieeexplore.ieee.org/document/8260779/) `AESPN` 419 | - [[Desana2017](#desana2017)] 420 | [**Sum-Product Graphical Models**](https://arxiv.org/abs/1708.06438) 421 | `SPGM` 422 | - [[Mauà2017](#mauà2017)] [**Credal Sum-Product Networks**](http://pure.qub.ac.uk/portal/files/128951275/maua17.pdf) `CSPN` 423 | - [[Gens2017](#gens2017)] [**Compositional Kernel Machines**](https://openreview.net/pdf?id=S1Bm3T_lg) `CKM` 424 | - [[Friesen2017](#friesen2017)] [**Unifying Sum-Product Networks and Submodular Fields**](http://padl.ws/papers/Paper%201.pdf) `SSPN` 425 | - [[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` 426 | - [[Melibari2016c](#melibari2016c)] [**Dynamic Sum-Product Networks for Tractable Inference on Sequence Data**](http://arxiv.org/abs/1511.04412) `dynamic-SPN` 427 | - [[Melibari2016b](#melibari2016b)] 428 | [**Sum-Product-Max Networks for Tractable Decision Making**](http://trust.sce.ntu.edu.sg/aamas16/pdfs/p1419.pdf) `decision-diagram` 429 | - [[Melibari2016a](#melibari2016a)] 430 | [**Decision Sum-Product-Max Networks**](https://cs.uwaterloo.ca/~mmelibar/publications/melibari-aaai2016.pdf) `decision-diagram` 431 | - [[Friesen2015](#friesen2015)] 432 | [**Recursive Decomposition for Nonconvex Optimization**](https://www.cs.washington.edu/node/11282) `opt` 433 | - [[Niepert2015](#niepert2015)] 434 | [**Learning and Inference in Tractable Probabilistic Knowledge Bases**](http://homes.cs.washington.edu/~pedrod/papers/uai15.pdf) `relational` 435 | - [[Nath2015](#nath2015)] 436 | [**Learning Relational Sum-Product Networks**](http://homes.cs.washington.edu/~pedrod/papers/aaai15.pdf) `relational` 437 | - [[Nath2014](#nath2014)] 438 | [**Learning Tractable Statistical Relational Models**](http://spn.cs.washington.edu/papers/ltpm2014_paper_4.pdf) 439 | `relational` 440 | - [[Peharz2014b](#peharz2014b)] [**Learning Selective Sum-Product Networks**](http://spn.cs.washington.edu/papers/ltpm2014_paper_9.pdf) `SSPN` 441 | - [[Stuhlmueller2012](#stuhlmueller2012)] 442 | [**Dynamic Programming Algorithm for Inference in Recursive Probabilistic Programs**](http://arxiv.org/abs/1206.3555) 443 | `FSPN` 444 | - [[Poon2011](#poon2011)] 445 | [**Sum-Product Networks: A New Deep Architecture**](http://spn.cs.washington.edu/papers/spn.pdf) `SPN` 446 | 447 | 448 | #### Applications 449 | 450 | - [[Stelzner2019](#stelzner2019)] [**Faster Attend-Infer-Repeat with Tractable Probabilistic Models**](http://proceedings.mlr.press/v97/stelzner19a/stelzner19a.pdf) `SuPAIR` 451 | - [[Conaty2018](#conaty2018)] 452 | [**Cascading Sum-Product Networks using Robustness**](http://pgm2018.utia.cz/data/proc/conaty18a.pdf) `Cascaded CSPN` 453 | - [[Joshi2018](#joshi2018)] 454 | [**Exact, Tractable Inference in the Sigma Cognitive Architecture via Sum-Product Networks**](http://www.cogsys.org/papers/ACSvol6/article08.pdf) `cognitive architectures` 455 | - [[Ratajczak2018](#ratajczak2018)] 456 | [**Sum-Product Networks for Sequence Labeling**](https://arxiv.org/abs/1807.02324) 457 | `speech` 458 | - [[Butz2018a](#butz2018a)] 459 | [**Efficient Examination of Soil Bacteria Using Probabilistic Graphical Models**](https://link.springer.com/chapter/10.1007/978-3-319-92058-0_30) 460 | - [[Zheng2018](#zheng2018)] 461 | [**Learning Graph-Structured Sum-Product Networks for Probabilistic Semantic Maps**](https://arxiv.org/abs/1709.08274) 462 | `semantic mapping in robotics` 463 | - [[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` 464 | - [[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` 465 | - [[Friesen2017](#friesen2017)] [**Submodular Sum-Product Networks for Scene Understanding**](https://openreview.net/pdf?id=ryEGFD9gl) *OpenReview@ICLR 2017* `segmentation` 466 | - [[Sguerra2016](#sguerra2016)] 467 | [**Image Classification Using Sum-Product Networks for Autonomous Flight of Micro Aerial Vehicles**](http://ieeexplore.ieee.org/abstract/document/7839576/) `image-classification` `ID-Spn` 468 | - [[Yuan2016](#yuan2016)] 469 | [**Modeling Spatial Layout for Scene Image Understanding Via a Novel Multiscale Sum-Product Network**](http://www.sciencedirect.com/science/article/pii/S0957417416303591) 470 | `cv` `segmentation` 471 | - [[Nath2016](#nath2016)] 472 | [**Learning Tractable Probabilistic Models for Fault Localization**](http://homes.cs.washington.edu/~pedrod/papers/aaai16.pdf) 473 | - [[Wang2015](#wang2015)] 474 | [**Hierarchical Spatial Sum-Product Networks for action recognition in Still Images**](http://arxiv.org/abs/1511.05292) `cv` `activity-recognition` 475 | - [[Amer2015](#amer2015)] 476 | [**Sum Product Networks for Activity Recognition**](http://web.engr.oregonstate.edu/~sinisa/research/publications/PAMI_SPN.pdf) 477 | `cv` `activity-recognition` 478 | - [[Li2015](#li2015)] [**Combining Sum-Product Network and Noisy-OrModel for Ontology Matching**](http://disi.unitn.it/~pavel/om2015/papers/om2015_TSpaper1.pdf) `sem-web` 479 | - [[Cheng2014](#cheng2014)] 480 | [**Language Modeling with Sum-Product Networks**](http://spn.cs.washington.edu/papers/is14.pdf) 481 | `sequence` 482 | - [[Ratajczak2014](#ratajczak2014)] 483 | [**Sum-Product Networks for Structured Prediction: Context-Specific Deep Conditional Random Fields**](https://www.spsc.tugraz.at/biblio/ratajczak20143046) 484 | `speech` 485 | - [[Peharz2014a](#peharz2014a)] 486 | [**Modeling Speech with Sum-Product Networks: Application to Bandwidth Extension**](http://spn.cs.washington.edu/papers/icassp14.pdf) `speech` 487 | - [[Amer2012](#amer2012)] 488 | [**Sum-product Networks for Modeling Activities with Stochastic Structure**](http://web.engr.oregonstate.edu/~sinisa/research/publications/cvpr12_SPN.pdf) 489 | `cv``activity-recognition` 490 | 491 | 492 | #### Theory 493 | 494 | - [[Mei2018](#mei2018)] [**Maximum A Posteriori Inference in Sum-Product Networks**](https://arxiv.org/abs/1708.04846) `MAP inference` 495 | - [[Conaty2017](#conaty2017)] [**Approximation Complexity of Maximum A Posteriori Inference in Sum-Product Networks**](https://arxiv.org/abs/1703.06045) `MAP inference` 496 | - [[Zhao2016b](#zhao2016b)] 497 | [**A Unified Approach for Learning the Parameters of Sum-Product Networks**](https://arxiv.org/abs/1601.00318) `CCCP` 498 | - [[Peharz2016](#peharz2016)] 499 | [**On the Latent Variable Interpretation in Sum-Product Networks**](http://arxiv.org/abs/1601.06180) `EM` 500 | - [[Friesen2016](#friesen2016)] 501 | [**The Sum-Product Theorem: A Foundation for Learning Tractable Models**](http://homes.cs.washington.edu/~pedrod/papers/mlc16.pdf) 502 | `opt` `sum-prod-theorem` 503 | - [[Peharz2015b](#peharz2015b)] 504 | [**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) 505 | - [[Friesen2015](#friesen2015)] 506 | [**Recursive Decomposition for Nonconvex Optimization**](https://www.cs.washington.edu/node/11282) 507 | `opt` `sum-prod-theorem` 508 | - [[Zhao2015](#zhao2015)] 509 | [**On the Relationship between Sum-Product Networks and Bayesian Networks**](http://jmlr.org/proceedings/papers/v37/zhaoc15.pdf) 510 | - [[Peharz2015a](#peharz2015a)] [**On Theoretical Properties of Sum-Product Networks**](http://www.jmlr.org/proceedings/papers/v38/peharz15.pdf) 511 | - [[Martens2014](#martens2014)] 512 | [**On the Expressive Efficiency of Sum Product Networks**](http://arxiv.org/abs/1411.7717) `depth` 513 | - [[Delalleau2011](#dellaleau2011)] 514 | [**Shallow vs. Deep Sum-Product Networks**](http://papers.nips.cc/paper/4350-shallow-vs-deep-sum-product-networks.pdf) `depth` 515 | 516 | #### Hardware 517 | 518 | - [[Sommer2018](#sommer2018)] [**Automatic Mapping of the Sum-Product Network Inference Problem to FPGA-Based Accelerators**](https://ieeexplore.ieee.org/document/8615710) `FPGA` 519 | 520 | 521 | ## Related Works 522 | 523 | ### Arithmetic Circuits 524 | 525 | - [[Darwiche2003](#darwiche2003)] 526 | [**A Differential Approach to Inference in Bayesian Networks**](Advances 527 | in Neural Information Processing Systems 2011) *J. ACM 2003* 528 | - [[Lowd2013](#lowd2013)] 529 | [**Learning Markov Networks With Arithmetic Circuits**](http://ix.cs.uoregon.edu/~lowd/aistats13lowd.pdf) 530 | *AISTATS 2013* 531 | - [[Rooshenas2016](#rooshenas2016)] 532 | [**Discriminative Structure Learning of Arithmetic Circuits**](http://www.jmlr.org/proceedings/papers/v51/rooshenas16.pdf) 533 | *AISTATS 2016* 534 | - [[Choi2017](#Choi2017)] 535 | [**On Relaxing Determinism in Arithmetic Circuits**](http://proceedings.mlr.press/v70/choi17a/choi17a.pdf) 536 | *ICML 2017* 537 | 538 | 539 | ### Other TPMs 540 | 541 | - [[Livni2013](#livni2013)] 542 | [**A Provably Efficient Algorithm for Training Deep Networks**](http://arxiv.org/abs/1304.7045) 543 | *arXiv 2013* 544 | 545 | ### Exploiting Sum-Product Theorem 546 | 547 | - [[Gens2017](#gens2017)] 548 | [**Compositional Kernel Machines**](https://openreview.net/pdf?id=S1Bm3T_lg) 549 | *ICLR 2017 - Workshop* 550 | 551 | ## Resources 552 | 553 | ### Dataset 554 | - 20 commonly used 555 | [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)] 556 | 557 | ### Code 558 | 559 | - [[Trapp2019](#trapp2019)] [**BayesianSumProductNetworks.jl**](https://github.com/trappmartin/BayesianSumProductNetworks) Julia implementation of Bayesian structure and parameter learning. 560 | - [[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` 561 | - [[Mai2018](#mei2018)] [**MAP inference**](https://github.com/shtechair/maxspn) routines and experiments in `Go` 562 | - [[Vergari2018](#vergari2018)] [**SPAE**](https://github.com/arranger1044/spae) encoding and decoding embeddings from SPNs in `python3` 563 | - [[Molina2018](#molina2018)] [**MSPN**](https://github.com/alejandromolinaml/MSPN) learning SPNs in hybrid domains in `python3` 564 | - [[Zheng2018](#zheng2018)] [**GraphSPN**](https://github.com/zkytony/graphspn) a general framework for probabilistic structured prediction. `python3` 565 | - [[DiMauro2017](#dimauro2017)] [**alt-vs-spyn**](https://github.com/fabriziov/alt-vs-spyn) `dockerized` `python3` implementation of structure learning variants 566 | - [[Desana2017](#desana2017)] [**SPGM**](https://github.com/ocarinamat/SumProductGraphMod) implementation in `C++` 567 | - [[Pronobis2017b](#pronobis2017b)] [**LibSPN**](http://www.libspn.org/) tensorflow implementation with bindings in `python3` 568 | - [**SumProductNetworks.jl**](https://github.com/trappmartin/SumProductNetworks.jl) Software package for SPNs. `julia` 569 | - [[Hsu2017](#hsu2017)] [**Tachyon**](https://github.com/KalraA/Tachyon) structure and parameter learning in `python3` 570 | - [[Hsu2017](#hsu2017)] Online structure learning for [**continuous leaf**](https://github.com/whsu/spn) SPNs `python3` 571 | - [[Peharz2016](#peharz2016)] Weight learning by the correct [**EM algorithm**](https://github.com/smatmo/LatentSPN) in `C++` 572 | - [[Zhao2016a, Zhao2016b](#zhao2016b)] Parameter optimization using MLE and Bayesian approach 573 | [**spn-opt**](http://www.cs.cmu.edu/~hzhao1/papers/ICML2016/spn_release.zip) `C++` 574 | - [[Vergari2018b](#vergari2018b)] 575 | [**spyn-repr**](https://github.com/arranger1044/spyn-repr) 576 | extracting embeddings from SPNs `python3` 577 | - [[Vergari2015](#vergari2015)] [**spyn**](https://github.com/arranger1044/spyn) LearnSPN-B/T/B and SPN 578 | inference routines in Python `python3` 579 | - [[Rooshenas2014](#rooshenas2014)] ID-SPN and inference routines 580 | on ACs implemented in the 581 | [**Libra Toolkit**](http://libra.cs.uoregon.edu/) `Ocaml` 582 | - [[Peharz2014a](#peharz2014a)] 583 | [**ABE-SPN**](https://www.spsc.tugraz.at/tools/artificial-bandwidth-extension-sum-product-networks) 584 | Artificial Bandwidth-Extension with Sum-Product Networks `MATLAB` `C++` 585 | - [**GoSPN**](https://github.com/RenatoGeh/gospn) implementing 586 | LearnSPN in Go `Go` 587 | - [[Cheng2014](#cheng2014)] 588 | [**lmspn**](https://github.com/stakok/lmspn) Language modeling 589 | with SPNs `C++` `CUDA` 590 | - [**C++/Cuda porting**](https://github.com/vseledkin/SumProductNetwork) 591 | of Poon's architecture `C++` `CUDA` 592 | - [**Python porting**](https://github.com/vseledkin/Sum-Product-Networks) 593 | of Poon's architecture `python2` 594 | - [[Gens2013](#gens2013)] 595 | [**LearnSPN**](http://spn.cs.washington.edu/learnspn/) `Java` 596 | - [[Poon2011](#poon2011)] Code to **train** [**Poon's architecture 597 | weigths by EM**](http://spn.cs.washington.edu/spn/) `Java` `MPI` 598 | 599 | ### Talks and Tutorials 600 | 601 | - Di Mauro and Vergari [**Learning Sum-Product Networks**](http://people.idsia.ch/~alessandro/pgm/DiMauroVergari.pdf) 602 | tutorial at PGM'16 _2016_ 603 | - Poupart P. **Deep Learning, Sum-Product Networks** [**Part I**](https://www.youtube.com/watch?v=eF0APeEIJNw) 604 | [**Part II**](https://www.youtube.com/watch?v=9-1YE_N-lnw) _2015_ 605 | - Hernàndez-Lobato, J. M. [**An Introduction to Sum-Product Networks**](https://jmhldotorg.files.wordpress.com/2013/11/slidescambridgesumproductnetworks2013.pdf) _2013_ 606 | - Gens, R. [**Learning the Structure of Sum-Product Networks**](http://spn.cs.washington.edu/talks/Gens_SLSPN_ICML2013.pdf) 607 | [[Gens2013](#gens2013)] _2013_ 608 | - Gens, R. [**Discriminative Learning of Sum-Product Networks**](http://videolectures.net/nips2012_gens_discriminative_learning/) [[Gens2012]](#gens2012) _2012_ 609 | - Poon, 610 | H. [**Sum-Product Networks: A New Deep Architecture**](http://spn.cs.washington.edu/talks/spn11.pdf) 611 | [[Poon2011](#poon2011)] _2011_ 612 | 613 | ### Blog Posts 614 | - [**Tensor-Based Sum-Product Networks: Part I**](http://jostosh.github.io/spn01/), _Jos van de Wolfshaar_, June 11, 2019. 615 | - [**Tensor-Based Sum-Product Networks: Part II**](http://jostosh.github.io/spn02/), _Jos van de Wolfshaar_, July 10, 2019. 616 | 617 | ## References 618 | 619 | *

620 | [Adel2015]
621 | _Adel, Tameem and Balduzzi, David and Ghodsi, Ali_
622 | **Learning the Structure of Sum-Product Networks via an SVD-based Algorithm**
623 | Uncertainty in Artificial Intelligence 2015

624 | *

625 | [Amer2012]
626 | _Amer, Mohamed and Todorovic, Sinisa_
627 | **Sum-Product Networks for Modeling Activities with Stochastic Structure**
628 | 2012 IEEE Conference on CVPR

629 | *

630 | [Amer2015]
631 | _Amer, Mohamed and Todorovic, Sinisa_
632 | **Sum Product Networks for Activity Recognition**
633 | IEEE Transactions on Pattern Analysis and Machine Intelligence

634 | *

635 | [Bueff2018]
636 | _Bueff, Andreas and Spelchert, Stefanie and Belle, Vaishak_
637 | **Tractable Querying and Learning in Hybrid Domains via Sum-Product Networks**
638 | preprint

639 | *

640 | [Butz2018a]
641 | _Butz, Cory J. and dos Santos André E. and Oliveira Jhonatan S. and Stavrinides John_
642 | **Efficient Examination of Soil Bacteria Using Probabilistic Graphical Models**
643 | International Conference on Industrial, Engineering and Other Applications of Applied Intelligent Systems 2018

644 | *

645 | [Butz2018b]
646 | _Butz, Cory J. and Oliveira Jhonatan S. and dos Santos André E., Teixeira, A. L. and Poupart, P. and Kalra, A._
647 | **An Empirical Study of Methods for SPN Learning and Inference**
648 | PGM 2018

649 | *

650 | [Butz2019]
651 | _Butz, Cory J and Oliveira, Jhonatan S. and dos Santos, André E. and Teixeira, André L._
652 | **Deep Convolutional Sum-Product Networks**
653 | AAAI 2019

654 | *

655 | [Cheng2014]
656 | _Cheng, Wei-Chen and Kok, Stanley and Pham, Hoai Vu and Chieu, Hai Leong and Chai, Kian Ming Adam_
657 | **Language modeling with Sum-Product Networks**
658 | INTERSPEECH 2014

659 | *

660 | [Choi2017]
661 | _Cheng, Arthur and Darwiche, Adnan_
662 | **On Relaxing Determinism in Arithmetic Circuits**
663 | ICML 2017

664 | *

665 | [Conaty2017]
666 | _Conaty, Diarmaid and Deratani Mauá, Denis and de Campos, Cassio P._
667 | **Approximation Complexity of Maximum A Posteriori Inference in Sum-Product Networks**
668 | UAI 2017

669 | *

670 | [Conaty2018]
671 | _Conaty, Diarmaid and Del Rincon, Jesus Martinez and de Campos, Cassio P._
672 | **Cascading Sum-Product Networks using Robustness**
673 | PGM 2018

674 | *

675 | [Darwiche2003]
676 | _Darwiche, Adnan_
677 | **A Differential Approach to Inference in Bayesian Networks**
678 | Journal of the ACM 2003

679 | *

680 | [Dellaleau2011]
681 | _Delalleau, Olivier and Bengio, Yoshua_
682 | **Shallow vs. Deep Sum-Product Networks**
683 | Advances in Neural Information Processing Systems 2011

684 | *

685 | [Dennis2012]
686 | _Dennis, Aaron and Ventura, Dan_
687 | **Learning the Architecture of Sum-Product Networks Using Clustering on Varibles**
688 | Advances in Neural Information Processing Systems 25

689 | *

690 | [Dennis2015]
691 | _Dennis, Aaron and Ventura, Dan_
692 | **Greedy Structure Search for Sum-product Networks**
693 | International Joint Conference on Artificial Intelligence 2015

694 | *

695 | [Dennis2017a]
696 | _Dennis, Aaron and Ventura, Dan_
697 | **Online Structure-Search for Sum-Product Networks**
698 | 16th IEEE International Conference on Machine Learning and Applications (ICMLA) 2017

699 | *

700 | [Dennis2017b]
701 | _Dennis, Aaron and Ventura, Dan_
702 | **Autoencoder-Enhanced Sum-Product Networks**
703 | 16th IEEE International Conference on Machine Learning and Applications (ICMLA) 2017

704 | *

705 | [Desana2016]
706 | _Desana, Mattia and Schn{\"{o}}rr Christoph_
707 | **Learning Arbitrary Sum-Product Network Leaves with Expectation-Maximization**
708 | arxiv.org/abs/1604.07243

709 | *

[Desana2017]
710 | _Desana, Mattia and Schn{\"{o}}rr Christoph_
711 | **Sum-Product Graphical Models**
712 | arxiv.org/abs/1708.06438

713 | *

[DiMauro2017]
714 | _Di Mauro, Nicola and Esposito, Floriana and Ventola, Fabrizio Giuseppe and Vergari, Antonio_
715 | **Alternative variable splitting methods to learn Sum-Product Networks**
716 | Proceedings of the 16th International Conference of the Italian Association for Artificial Intelligence (AI*IA 2017)

717 | *

[Friesen2015]
718 | _Friesen, Abram L. and Domingos, Pedro_
719 | **Recursive Decomposition for Nonconvex Optimization**
720 | Proceedings of the 24th International Joint Conference on Artificial Intelligence

721 | *

[Friesen2016]
722 | _Friesen, Abram L. and Domingos, Pedro_
723 | **The Sum-Product Theorem: A Foundation for Learning Tractable Models**
724 | ICML 2016

725 | *

[Friesen2017]
726 | _Friesen, Abram L. and Domingos, Pedro_
727 | **Unifying Sum-Product Networks and Submodular Fields**
728 | Principled Approaches to Deep Learning Workshop at ICML 2017

729 | *

[Gens2012]
730 | _Gens, Robert and Domingos, Pedro_
731 | **Discriminative Learning of Sum-Product Networks**
732 | NIPS 2012

733 | *

734 | [Gens2013]
735 | _Gens, Robert and Domingos, Pedro_
736 | **Learning the Structure of Sum-Product Networks**
737 | ICML 2013

738 | *

739 | [Gens2017]
740 | _Gens, Robert and Domingos, Pedro_
741 | **Compositional Kernel Machines**
742 | ICLR 2017 - Workshop Track

743 | *

744 | [Hsu2017]
745 | _Hsu, Wilson and Kalra, Agastya and Poupart, Pascal_
746 | **Online Structure Learning for Sum-Product Networks with Gaussian Leaves**
747 | ICLR 2017 - Workshop Track

748 | *

749 | [Jaini2016]
750 | _Jaini, Priyank and Rashwan, Abdullah and Zhao, Han and Liu, Yue and 751 | Banijamali, Ershad and Chen, Zhitang and Poupart, Pascal_
752 | **Online Algorithms for Sum-Product Networks with Continuous Variables**
753 | International Conference on Probabilistic Graphical Models 2016

754 | *

755 | [Jaini2018a]
756 | _Jaini, Priyank and Ghose Amur and Poupart, Pascal_
757 | **Prometheus: Directly Learning Acyclic Directed Graph Structures for Sum-Product Networks**
758 | PGM 2018

759 | [Jaini2018b]
760 | _Jaini, Priyank and Poupart, Pascal and Yu, Yaoliang_
761 | **Deep Homogeneous Mixture Models: Representation, Separation, and Approximation**
762 | NIPS 2018

763 | *

764 | [Joshi2018]
765 | _Joshi, Himanshu, Paul S. Rosenbloom, and Volkan Ustun_
766 | **Exact, Tractable Inference in the Sigma Cognitive Architecture via Sum-Product Networks**
767 | Advances in Cognitive Systems 6 (2018)

768 | *

769 | [Ko2018]
770 | _Ko, Ching-Yun and Chen, Cong and Zhang, Yuke and Batselier, Kim and Wong, Ngai_
771 | **Deep Compression of Sum-Product Networks on Tensor Networks**
772 | arXiv 2018

773 | *

774 | [Krakovna2016]
775 | _Krakovna, Viktoriya and Looks, Moshe_
776 | **A Minimalistic Approach to Sum-Product Network Learning for Real Applications**
777 | ICLR 2016

778 | *

779 | [Lee2013]
780 | _Lee, Sang-Woo and Heo, Min-Oh and Zhang, Byoung-Tak_
781 | **Online Incremental Structure Learning of Sum-Product Networks**
782 | ICONIP 2013

783 | *

784 | [Lee2014]
785 | _Lee, Sang-Woo and Watkins, Christopher and Zhang, Byoung-Tak_
786 | **Non-Parametric Bayesian Sum-Product Networks**
787 | Workshop on Learning Tractable Probabilistic Models 2014

788 | *

789 | [Li2015]
790 | _Weizhuo Li_
791 | **Combining sum-product network and noisy-or model for ontology matching**
792 | Proceedings of the 10th International Workshop on Ontology Matching

793 | *

794 | [Livni2013]
795 | _Livni, Roi and Shalev-Shwartz, Shai and Shamir, Ohad_
796 | **A Provably Efficient Algorithm for Training Deep Networks**
797 | arXiv 2013

798 | *

799 | [Lowd2013]
800 | _Lowd, Daniel and Rooshenas, Amirmohammad_
801 | **Learning Markov Networks With Arithmetic Circuits**
802 | Proceedings of the 16th International Conference on Artificial Intelligence and Statistics 2013

803 | *

804 | [Martens2014]
805 | _Martens, James and Medabalimi, Venkatesh_
806 | **On the Expressive Efficiency of Sum Product Networks**
807 | arXiv/1411.7717

808 | *

809 | [Mauà2017]
810 | _Mauá, Deratani Denis and Cozman Fabio Gagliardi and Conaty, Diarmaid and de Campos, Cassio P._
811 | **Credal Sum-Product Networks**
812 | ISIPTA 2017

813 | *

814 | [Mei2018]
815 | _Mei, Jun and Jiang, Yong and Tu, Kewei_
816 | **Maximum A Posteriori Inference in Sum-Product Networks**
817 | AAAI 2018

818 | *

819 | [Melibari2016a]
820 | _Melibari, Mazen and Poupart, Pascal and Doshi, Prashant_
821 | **Decision Sum-Product-Max Networks**
822 | Proceedings of the 30th AAAI Conference on Artificial Intelligence (AAAI 2016)

823 | *

824 | [Melibari2016b]
825 | _Melibari, Mazen and Poupart, Pascal and Doshi, Prashant_
826 | **Sum-Product-Max Networks for Tractable Decision Making**
827 | Proceedings of the 2016 International Conference on Autonomous Agents & Multiagent Systems

828 | *

829 | [Melibari2016c]
830 | _Melibari, Mazen and Poupart, Pascal and Doshi, Prashant and 831 | Trimponias, George_
832 | **Dynamic Sum-Product Networks for Tractable Inference on Sequence Data**
833 | International Conference on Probabilistic Graphical Models 2016

834 | *

835 | [Molina2017]
836 | _Molina, Alejandro and Natarajan, Sriraam and Kersting, Kristian_
837 | **Poisson Sum-Product Networks: A Deep Architecture for Tractable Multivariate Poisson Distributions**
838 | Proceedings of the 31st AAAI Conference on Artificial Intelligence (AAAI 2017)

839 | *

840 | [Molina2018]
841 | _Molina, Alejandro and Vergari, Antonio and Di Mauro, Nicola and Natarajan, Sriraam and Esposito, Floriana and Kersting, Kristian_
842 | **Mixed Sum-Product Networks: A Deep Architecture for Hybrid Domains**
843 | Proceedings of the 32nd AAAI Conference on Artificial Intelligence (AAAI 2018)

844 | *

845 | [Molina2019]
846 | _Molina, Alejandro and Vergari, Antonio and Stelzner, Karl and Peharz, Robert and Subramani, Pranav and Di Mauro, Nicola and Poupart, Pascal and Kersting, Kristian_
847 | **SPFlow: An Easy and Extensible Library for Deep Probabilistic Learning using Sum-Product Networks**
848 | arXiv:1901.03704

849 | *

850 | [Nath2014]
851 | _Nath, Aniruddh and Domingos, Pedro_
852 | **Learning Tractable Statistical Relational Models**
853 | Workshop on Learning Tractable Probabilistic Models

854 | *

855 | [Nath2015]
856 | _Nath, Aniruddh and Domingos, Pedro_
857 | **Learning Relational Sum-Product Networks**
858 | Proceedings of the 29th AAAI Conference on Artificial Intelligence (AAAI 2015)

859 | *

860 | [Nath2016]
861 | _Nath, Aniruddh and Domingos, Pedro_
862 | **Learning Tractable Probabilistic Models for Fault Localization**
863 | Proceedings of the 30th AAAI Conference on Artificial Intelligence (AAAI 2016)

864 | *

865 | [Niepert2015]
866 | _Niepert, Mathias and Domingos, Pedro_
867 | **Learning and Inference in Tractable Probabilistic Knowledge Bases**
868 | UAI 2015

869 | *

870 | [Paris2020]
871 | _París, Iago and Sánchez-Cauce, Raquel and Díez, Francisco Javier_
872 | **Sum-product networks: A survey**
873 | arXiv:2004.01167

874 | *

875 | [Peharz2013]
876 | _Peharz, Robert and Geiger, Bernhard and Pernkopf, Franz_
877 | **Greedy Part-Wise Learning of Sum-Product Networks**
878 | ECML-PKDD 2013

879 | *

880 | [Peharz2014a]
881 | _Peharz, Robert and Kapeller, Georg and Mowlaee, Pejman and Pernkopf, Franz_
882 | **Modeling Speech with Sum-Product Networks: Application to Bandwidth Extension**
883 | ICASSP2014

884 | *

885 | [Peharz2014b]
886 | _Robert Peharz and Gens, Robert and Domingos, Pedro_
887 | **Learning Selective Sum-Product Networks**
888 | Workshop on Learning Tractable Probabilistic Models 2014

889 | *

890 | [Peharz2015a]
891 | _Robert Peharz and Tschiatschek, Sebastian and Pernkopf, Franz and Domingos, Pedro_
892 | **On Theoretical Properties of Sum-Product Networks**
893 | Proceedings of the 18th International Conference on Artificial Intelligence and Statistics

894 | *

895 | [Peharz2015b]
896 | _Peharz, Robert_
897 | **Foundations of Sum-Product Networks for Probabilistic Modeling**
898 | PhD Thesis

899 | *

900 | [Peharz2016]
901 | _Robert Peharz and Robert Gens and Franz Pernkopf and Pedro Domingos_
902 | **On the Latent Variable Interpretation in Sum-Product Networks**
903 | arxiv.org/abs/1601.06180

904 | *

905 | [Peharz2019]
906 | _Robert Peharz and Antonio Vergari and Karl Stelzner and Alejandro Molina and Martin Trapp and Xiaoting Shao and Kristian Kersting and Zoubin Ghahramani_
907 | **Random Sum-Product Networks: A Simple and Effective Approach to Probabilistic Deep Learning**
908 | UAI 2019

909 | *

910 | [Poon2011]
911 | _Poon, Hoifung and Domingos, Pedro_
912 | **Sum-Product Network: a New Deep Architecture**
913 | UAI 2011

914 | *

915 | [Pronobis2017a]
916 | _Pronobis, A. and Riccio, F. and Rao, R.~P.~N._
917 | **Deep Spatial Affordance Hierarchy: Spatial Knowledge Representation for Planning in Large-scale Environments**
918 | SSRR 2017

919 | *

920 | [Pronobis2017b]
921 | _Pronobis, A. and Ranganath, A. and Rao, R.~P.~N._
922 | **LibSPN: A Library for Learning and Inference with Sum-Product Networks and TensorFlow**
923 | Principled Approaches to Deep Learning Workshop at ICML 2017

924 | *

925 | [Rahman2016]
926 | _Tahrima Rahman and Vibhav Gogate_
927 | **Merging Strategies for Sum-Product Networks: From Trees to 928 | Graphs**
929 | UAI 2016

930 | *

931 | [Rashwan2016]
932 | _Rashwan, Abdullah and Zhao, Han and Poupart, Pascal_
933 | **Online and Distributed Bayesian Moment Matching for Parameter Learning in Sum-Product Networks**
934 | Proceedings of the 19th International Conference on Artificial Intelligence and Statistics

935 | *

936 | [Rashwan2018a]
937 | _Rashwan, Abdullah and Poupart, Pascal and Zhitang, Chen_
938 | **Discriminative Training of Sum-Product Networks by Extended Baum-Welch**
939 | PGM 2018

940 | *

941 | [Rashwan2018b]
942 | _Rashwan, Abdullah and Kalra, Agastya and Poupart, Pascal and Doshi, Prashant and Trimponias, George and Hsu, Wei-Shou_
943 | **Online Structure Learning for Feed-Forward and Recurrent Sum-Product Networks**
944 | NIPS 2018

945 | *

946 | [Ratajczak2014]
947 | _Ratajczak, Martin and Tschiatschek, S and Pernkopf, F_
948 | **Sum-Product Networks for Structured Prediction: Context-Specific Deep Conditional Random Fields**
949 | Workshop on Learning Tractable Probabilistic Models 2014

950 | *

951 | [Ratajczak2018]
952 | _Ratajczak, Martin and Tschiatschek, S and Pernkopf, F_
953 | **Sum-Product Networks for Sequence Labeling**
954 | preprint

955 | *

956 | [Rathke2017]
957 | _Rathke, F.; Desana, M. and Schnörr, C._
958 | **Locally Adaptive Probabilistic Models for Global Segmentation of Pathological OCT Scans**
959 | MICCAI 2017

960 | *

961 | [Rooshenas2014]
962 | _Rooshenas, Amirmohammad and Lowd, Daniel_
963 | **Learning Sum-Product Networks with Direct and Indirect Variable Interactions**
964 | ICML 2014

965 | *

966 | [Rooshenas2016]
967 | _Rooshenas, Amirmohammad and Lowd, Daniel_
968 | **Discriminative Structure Learning of Arithmetic Circuits**
969 | Proceedings of the 19th International Conference on Artificial Intelligence and Statistics

970 | *

971 | [Shao2019]
972 | _Shao, Xiaoting and Molina, Alejandro and Vergari, Antonio and Stelzner, Karl and Peharz, Robert and Liebig, Thomas and Kersting, Kristian_
973 | **Conditional Sum-Product Networks: Imposing Structure on Deep Probabilistic Architectures**
974 | arXiv:1905.08550

975 | *

976 | [Sharir2018]
977 | _Sharir, Or and Shashua, Amnon_
978 | ** Sum-Product-Quotient Networks**
979 | AISTATS 2018

980 | *

981 | [Sguerra2016]
982 | _Sguerra, Bruno Massoni and Cozman, Fabio G._
983 | **Image Classification Using Sum-Product Networks for Autonomous Flight of Micro Aerial Vehicles**
984 | BRACIS 2016 - 5th Brazilian Conference on Intelligent Systems

985 | *

986 | [Stelzner2019]
987 | _Stelzner, Karl and Peharz, Robert and Kersting, Kristian_
988 | **Faster Attend-Infer-Repeat with Tractable Probabilistic Models**
989 | ICML 2019

990 | *

991 | [Stuhlmueller2012]
992 | _Stuhlmuller, Andreas and Goodman, Noah D._
993 | **A Dynamic Programming Algorithm for Inference in Recursive Probabilistic Programs**
994 | StaRAI 2012

995 | *

996 | [Sommer2018]
997 | _Sommer, Lukas and Oppermann, Julian and Molina, Alejandro and Binnig, Carsten and Kersting, Kristian and Koch, Andreas_
998 | **Automatic Mapping of the Sum-Product Network Inference Problem to FPGA-Based Accelerators**
999 | ICCD 2018

1000 | *

1001 | [Tan2019]
1002 | _Tan, Ping Liang, and Peharz, Robert_
1003 | **Hierarchical Decompositional Mixtures of Variational Autoencoders**
1004 | ICML 2019

1005 | *

1006 | [Trapp2016]
1007 | _Trapp, Martin and Peharz, Robert and Skowron, Marcin and Madl, Tamas and Pernkopf, Franz and Trappl, Robert_
1008 | **Structure Inference in Sum-Product Networks using Infinite Sum-Product Trees**
1009 | Workshop on Practical Bayesian Nonparametrics at NIPS 2016

1010 | *

1011 | [Trapp2017]
1012 | _Trapp, Martin and Madl, Tamas and Peharz, Robert and Pernkopf, Franz and Trappl, Robert_
1013 | **Safe Semi-Supervised Learning of Sum-Product Networks**
1014 | UAI 2017

1015 | *

1016 | [Trapp2018]
1017 | _Trapp, Martin and Peharz, Robert and Rasmussen, Carl and Pernkopf, Franz_
1018 | **Learning Deep Mixtures of Gaussian Process Experts Using Sum-Product Networks**
1019 | Workshop on Tractable Probabilistic Models

1020 | *

1021 | [Trapp2019]
1022 | _Trapp, Martin and Peharz, Robert and Ge, Hong and Pernkopf, Franz and Ghahramani, Zoubin_
1023 | **Bayesian Learning of Sum-Product Networks**
1024 | NeurIPS 2019

1025 | *

1026 | [Vergari2015]
1027 | _Vergari, Antonio and Di Mauro, Nicola and Esposito, Floriana_
1028 | **Simplifying, Regularizing and Strengthening Sum-Product Network Structure Learning**
1029 | ECML-PKDD 2015

1030 | *

1031 | [Vergari2017]
1032 | _Vergari, Antonio and Peharz, Robert and Di Mauro, Nicola and Esposito, Floriana_
1033 | **Encoding and Decoding Representations with Sum- and Max-Product Networks**
1034 | ICLR 2017 - Workshop Track

1035 | *

1036 | [Vergari2018a]
1037 | _Vergari, Antonio and Peharz, Robert and Di Mauro, Nicola and Molina, Alejandro and Kersting, Kristian and Esposito, Floriana_
1038 | **Sum-Product Autoencoding: Encoding and Decoding Representations with Sum-Product Networks**
1039 | Proceedings of the 32nd AAAI Conference on Artificial Intelligence (AAAI 2018)

1040 | *

1041 | [Vergari2018b]
1042 | _Vergari, Antonio and Di Mauro, Nicola and Esposito, Floriana_
1043 | **Visualizing and Understanding Sum-Product Networks**
1044 | Machine Learning Journal

1045 | *

1046 | [Vergari2019]
1047 | _Vergari, Antonio and Molina, Alejandro and Peharz, Robert and Ghahramani, Zoubin and Kersting, Kristian and Valera, Isabel_
1048 | **Automatic Bayesian Density Analysis**
1049 | Proceedings of the 33rd AAAI Conference on Artificial Intelligence (AAAI 2019)

1050 | *

1051 | [Wang2015]
1052 | _Wang, Jinghua and Wang, Gang_
1053 | **Hierarchical Spatial Sum-Product Networks for action recognition in Still Images**
1054 | arXiv:1511.05292

1055 | *

1056 | [Wolfshaar2019]
1057 | _van de Wolfshaar, Jos and Pronobix, Andrzej_
1058 | **Deep Convolutional Sum-Product Networks for Probabilistic Image Representations**
1059 | arXiv:1902.06155

1060 | *

1061 | [Yuan2016]
1062 | _Zehuan Yuan and Hao Wang and Limin Wang and Tong Lu and Shivakumara Palaiahnakote and Chew Lim Tan_
1063 | **Modeling Spatial Layout for Scene Image Understanding Via a Novel Multiscale Sum-Product Network**
1064 | Expert Systems with Applications

1065 | *

1066 | [Zhao2015]
1067 | _Zhao, Han and Melibari, Mazen and Poupart, Pascal_
1068 | **On the Relationship between Sum-Product Networks and Bayesian Networks**
1069 | ICML 2015

1070 | *

1071 | [Zhao2016a]
1072 | _Zhao, Han and Adel, Tameem and Gordon, Geoff and Amos, Brandon_
1073 | **Collapsed Variational Inference for Sum-Product Networks**
1074 | ICML 2016

1075 | *

1076 | [Zhao2016b]
1077 | _Zhao, Han and Poupart, Pascal and Gordon, Geoff_
1078 | **A Unified Approach for Learning the Parameters of Sum-Product Networks**
1079 | NIPS 2016

1080 | *

1081 | [Zhao2017]
1082 | _Zhao, Han and Gordon, Geoff and Poupart, Pascal_
1083 | **Efficient Computation of Moments in Sum-Product Networks**
1084 | NIPS 2017

1085 | *

1086 | [Zheng2018]
1087 | _Zheng, Kaiyu and Pronobis, Andrzej and Rao, Rajesh P.N._
1088 | **Learning Graph-Structured Sum-Product Networks for Probabilistic Semantic Maps**
1089 | AAAI 2018

1090 | 1091 | --------------------------------------------------------------------------------