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On the Sample Complexity of Learning Sum-Product Networks [article]

Ishaq Aden-Ali, Hassan Ashtiani
2020 arXiv   pre-print
An SPN is a rooted directed acyclic graph (DAG) consisting of a set of leaves (corresponding to base distributions), a set of sum nodes (which represent mixtures of their children distributions) and a  ...  A similar result holds for tree structured SPNs with discrete leaves. We obtain the upper bounds based on the recently proposed notion of distribution compression schemes.  ...  Note that s ≡ŝ is an equivalence relation, therefore we can talk about the equivalence classes of this relation. We use these equivalence classes to give the following definition.  ... 
arXiv:1912.02765v2 fatcat:qgyjrktx2zc75k2fj62o4a2cki

Learning Credal Sum-Product Networks [article]

Amelie Levray, Vaishak Belle
2020 arXiv   pre-print
Tractable learning is a powerful new paradigm that attempts to learn distributions that support efficient probabilistic querying.  ...  By leveraging local structure, representations such as sum-product networks (SPNs) can capture high tree-width models with many hidden layers, essentially a deep architecture, while still admitting a range  ...  While it is possible to specify SPNs by hand, weight learning is additionally required to obtain a probability distribution, but also the specification of SPNs has to obey conditions of completeness and  ... 
arXiv:1901.05847v2 fatcat:vj4curb5yvgddbvzet4khauug4

Modeling speech with sum-product networks: Application to bandwidth extension

Robert Peharz, Georg Kapeller, Pejman Mowlaee, Franz Pernkopf
2014 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)  
Missing frequency bins are replaced by the SPNs using most-probable-explanation inference, where the state-dependent reconstructions are weighted with the HMM state posterior.  ...  We use SPNs as observation models in hidden Markov models (HMMs), which model the temporal evolution of log short-time spectra.  ...  Motivated by the success of SPNs on the also ill-posed and related problem of image completion, we used SPNs as observation models in HMMs, modeling the temporal evolution of log short-time spectra.  ... 
doi:10.1109/icassp.2014.6854292 dblp:conf/icassp/PeharzKMP14 fatcat:zxucy5w7xvcsxckrhm4mrmlhru

Modeling spatial layout for scene image understanding via a novel multiscale sum-product network

Zehuan Yuan, Hao Wang, Limin Wang, Tong Lu, Shivakumara Palaiahnakote, Chew Lim Tan
2016 Expert systems with applications  
Besides, MSPN characterizes scene spatial layouts in a fine-to-coarse manner to enforce the consistency in labeling.  ...  We conduct experiments on two challenging benchmarks consisting of the MSRC-21 dataset and the SIFT FLOW dataset.  ...  Note that both the short-range relations inside every scene image patch and the long-range relations among patches are modeled by different SPNs, respectively.  ... 
doi:10.1016/j.eswa.2016.07.015 fatcat:nk7ibgsvjbcf5kjnxxsizyj6fy

Approximation Complexity of Maximum A Posteriori Inference in Sum-Product Networks [article]

Diarmaid Conaty, Denis D. Mauá, Cassio P. de Campos
2017 arXiv   pre-print
We then show that, in trees of height three, it is NP-hard to approximate the problem within a factor 2^f(n) for any sublinear function f of the size of the input n.  ...  We show that this is a tight bound, as we can find an approximation within a linear factor in networks of height two.  ...  We thank Jun Mei for spotting a typo in the proof of Theorem 3.  ... 
arXiv:1703.06045v5 fatcat:kva6qgw7nvfqxevdlmgukzrcxq

Sum-product networks: A survey

Raquel Sanchez-Cauce, Iago Paris, Francisco Javier Diez Vegas
2021 IEEE Transactions on Pattern Analysis and Machine Intelligence  
A sum-product network (SPN) is a probabilistic model, based on a rooted acyclic directed graph, in which terminal nodes represent probability distributions and non-terminal nodes represent convex sums  ...  (weighted averages) and products of probability functions.  ...  RSC received a postdoctoral grant and IP a predoctoral grant and from UNED, both co-financed by the Regional Government of Madrid and the Youth Employment Initiative (YEI) of the European Union. 12 .  ... 
doi:10.1109/tpami.2021.3061898 pmid:33630736 fatcat:2nivccgqkrabhaza5nsvvkjs4i

Sum-product networks: A new deep architecture

Hoifung Poon, Pedro Domingos
2011 2011 IEEE International Conference on Computer Vision Workshops (ICCV Workshops)  
The answer leads to a new kind of deep architecture, which we call sumproduct networks (SPNs).  ...  SPNs are directed acyclic graphs with variables as leaves, sums and products as internal nodes, and weighted edges.  ...  Note that a weighted edge must emanate from a sum node and pruning such edges will not violate the validity of the SPN. Therefore, the learned SPN is guaranteed to be valid.  ... 
doi:10.1109/iccvw.2011.6130310 dblp:conf/iccvw/PoonD11 fatcat:guslgclr7bgnvmgpyfyrayovgu

Bayesian Learning of Sum-Product Networks [article]

Martin Trapp, Robert Peharz, Hong Ge, Franz Pernkopf, Zoubin Ghahramani
2019 arXiv   pre-print
on intuition rather than a clear learning principle.  ...  While parameter learning in SPNs is well developed, structure learning leaves something to be desired: Even though there is a plethora of SPN structure learners, most of them are somewhat ad-hoc and based  ...  Note that the relation between y and ψy is similar to the relation between z and T , i.e. each ψy corresponds in general to many y's.  ... 
arXiv:1905.10884v3 fatcat:okjahbmdofb4hhr3bxo2uzuipm

Sum-product networks: A survey [article]

Iago París, Raquel Sánchez-Cauce, Francisco Javier Díez
2020 arXiv   pre-print
A sum-product network (SPN) is a probabilistic model, based on a rooted acyclic directed graph, in which terminal nodes represent univariate probability distributions and non-terminal nodes represent convex  ...  combinations (weighted sums) and products of probability functions.  ...  Acknowledgments We thank Pascal Poupart for convincing us about the advantages of SPNs, and Concha Bielza, Adnan Darwiche, Pedro Larrañaga, Alejandro Molina, Andrzej Pronobis, Martin Trapp, Jos van de  ... 
arXiv:2004.01167v1 fatcat:zmwyvhyqerh67ju5duiuo3uecy

Probabilistic Deep Learning using Random Sum-Product Networks [article]

Robert Peharz, Antonio Vergari, Karl Stelzner, Alejandro Molina, Martin Trapp, Kristian Kersting, Zoubin Ghahramani
2018 arXiv   pre-print
Sum-product networks (SPNs), on the other hand, are an excellent architecture in that regard, as they allow to efficiently evaluate likelihoods, as well as arbitrary marginalization and conditioning tasks  ...  In this paper, we make a drastic simplification and use random SPN structures which are trained in a "classical deep learning manner", i.e. employing automatic differentiation, SGD, and GPU support.  ...  One might suspect, that the result, although not interpretable as log-probability, still yields a decent signal to detect outliers.  ... 
arXiv:1806.01910v2 fatcat:t5wbokb4crb47mdi7evsnr3s44

Projective Latent Dependency Forest Models

Yong Jiang, Yang Zhou, Kewei Tu
2019 IEEE Access  
We then propose sum-product projective dependence networks, a combination of PLDFMs and SPNs that scales up to a large number of random variables.  ...  In this paper, we proposed projective LDFMs (PLDFMs), a variant of LDFM, for which joint and marginal probabilities become tractable (cubic time with respect to the number of random variables) to compute  ...  Both joint and marginal probabilities can be computed in a SPN in linear time with respect to the size of the SPN.  ... 
doi:10.1109/access.2019.2891292 fatcat:2yiv6sy6bbgc5iiwj57aglldg4

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

Bruno Massoni Sguerra, Fabio G. Cozman
2016 2016 5th Brazilian Conference on Intelligent Systems (BRACIS)  
We investigate a strategy where image classification is used to guide a MAV; one of the main requirements then is to have a classifier that can produce results quickly during operation.  ...  The goal here is to explore the performance of Sum-Product Networks and Arithmetic Circuits as image classifiers, because these formalisms lead to deep probabilistic models that are tractable during operation  ...  Also, we would like to thank Guilherme Hatori Pereira Horoi for his help with the Libra toolkit.  ... 
doi:10.1109/bracis.2016.035 dblp:conf/bracis/SguerraC16 fatcat:tw3fbynq3fds7ikggkkba5hyfi

Sum Product Networks for Activity Recognition

Mohamed R. Amer, Sinisa Todorovic
2016 IEEE Transactions on Pattern Analysis and Machine Intelligence  
A product node in SPN represents a particular arrangement of parts, and a sum node represents alternative arrangements.  ...  We focus on activities that may have variable spatiotemporal arrangements of parts, and numbers of actors. Such activities are represented by a Sum-Product Network (SPN).  ...  Then, we relate our work to that on aggregating counts of visual words in the video, and non-linear deep models.  ... 
doi:10.1109/tpami.2015.2465955 pmid:26390445 fatcat:amkzwgoh6zd73dy3tyzjjsyp6y

Learning Large-Scale Topological Maps Using Sum-Product Networks [article]

Kaiyu Zheng
2017 arXiv   pre-print
We propose to use a novel probabilistic deep model, Sum-Product Networks (SPNs), due to their unique properties.  ...  Although much work has been done in topological map extraction, we have found little previous work on the problem of learning the topological map using a probabilistic model.  ...  to correct probability distribution.  ... 
arXiv:1706.03416v2 fatcat:uxv2rimhmjb4hayzthtxdgpmpi

Deep Model Compression and Inference Speedup of Sum-Product Networks on Tensor Trains

Ching-Yun Ko, Cong Chen, Zhuolun He, Yuke Zhang, Kim Batselier, Ngai Wong
2019 IEEE Transactions on Neural Networks and Learning Systems  
For the first time, through mapping an SPN onto a tSPN and employing specially customized optimization techniques, we demonstrate improvements up to a factor of 100 on both model compression and inference  ...  This brief reveals an important connection between SPNs and tensor trains (TTs), leading to a new canonical form which we call tensor SPNs (tSPNs).  ...  One is to scale the edge weights out of each sum node such that they add up to one, i.e., turning it back into a normalized SPN.  ... 
doi:10.1109/tnnls.2019.2928379 pmid:31403446 fatcat:u6p2q7ebfbfgxblqcqfqvpgloq
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