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

2020
*
arXiv
*
pre-print

An

arXiv:1912.02765v2
fatcat:qgyjrktx2zc75k2fj62o4a2cki
*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. ...##
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Learning Credal Sum-Product Networks
[article]

2020
*
arXiv
*
pre-print

Tractable learning is

arXiv:1901.05847v2
fatcat:vj4curb5yvgddbvzet4khauug4
*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 ...##
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Modeling speech with sum-product networks: Application to bandwidth extension

2014
*
2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
*

Missing frequency bins are replaced by the

doi:10.1109/icassp.2014.6854292
dblp:conf/icassp/PeharzKMP14
fatcat:zxucy5w7xvcsxckrhm4mrmlhru
*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. ...##
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Modeling spatial layout for scene image understanding via a novel multiscale sum-product network

2016
*
Expert systems with applications
*

Besides, MSPN characterizes scene spatial layouts in

doi:10.1016/j.eswa.2016.07.015
fatcat:nk7ibgsvjbcf5kjnxxsizyj6fy
*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. ...##
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Approximation Complexity of Maximum A Posteriori Inference in Sum-Product Networks
[article]

2017
*
arXiv
*
pre-print

We then show that, in trees of height three, it is NP-hard

arXiv:1703.06045v5
fatcat:kva6qgw7nvfqxevdlmgukzrcxq
*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. ...##
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Sum-product networks: A survey

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 . ...

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Sum-product networks: A new deep architecture

2011
*
2011 IEEE International Conference on Computer Vision Workshops (ICCV Workshops)
*

The answer leads

doi:10.1109/iccvw.2011.6130310
dblp:conf/iccvw/PoonD11
fatcat:guslgclr7bgnvmgpyfyrayovgu
*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. ...##
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Bayesian Learning of Sum-Product Networks
[article]

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. ...

##
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Sum-product networks: A survey
[article]

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 ...

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

2018
*
arXiv
*
pre-print

Sum-product networks (

arXiv:1806.01910v2
fatcat:t5wbokb4crb47mdi7evsnr3s44
*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. ...##
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Projective Latent Dependency Forest Models

2019
*
IEEE Access
*

We then propose sum-product projective dependence networks,

doi:10.1109/access.2019.2891292
fatcat:2yiv6sy6bbgc5iiwj57aglldg4
*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*. ...##
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Image Classification Using Sum-Product Networks for Autonomous Flight of Micro Aerial Vehicles

2016
*
2016 5th Brazilian Conference on Intelligent Systems (BRACIS)
*

We investigate

doi:10.1109/bracis.2016.035
dblp:conf/bracis/SguerraC16
fatcat:tw3fbynq3fds7ikggkkba5hyfi
*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. ...##
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Sum Product Networks for Activity Recognition

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. ...

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

2017
*
arXiv
*
pre-print

We propose

arXiv:1706.03416v2
fatcat:uxv2rimhmjb4hayzthtxdgpmpi
*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*. ...##
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Deep Model Compression and Inference Speedup of Sum-Product Networks on Tensor Trains

2019
*
IEEE Transactions on Neural Networks and Learning Systems
*

For the first time, through mapping an

doi:10.1109/tnnls.2019.2928379
pmid:31403446
fatcat:u6p2q7ebfbfgxblqcqfqvpgloq
*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*. ...
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