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Student: Renato Lui Geh
Advisor: Denis Deratani Mauá
Abstract
Sum-product networks (SPNs) are probabilistic graphical models that model a tractable
probability distribution. Proposed in 2011, SPNs compute exact inference in linear time in the
number of edges of its graph if certain criteria are met [1]. SPNs have shown many interesting
properties, such as a higher representability of functions the deeper its architecture whilst
maintaining its efficiency [2]. Other interesting theoretical properties include a
generalization of SPNs to any semiring with disjoint product [3]. With regards to applications,
SPNs have shown impressive results in various tasks, such as protein folding [4], modeling
speech [5], image classification and completion [1,6,7], activity recognition [8] and modeling
natural language [9]. In this undergraduate research project, we implement various
state-of-the-art learning algorithms.
Objectives
The objectives of this undergraduate research project is to study Sum-Product Networks and
implement state-of-the-art SPN learning algorithms. Namely the following:
- Poon-Domingos learning algorithm [1].
- Dennis-Ventura structural learning algorithm [7].
- Gens-Domingos structural learning algorithm [6].
The code is free and open-source, and is available as part of the GoSPN inference and learning framework for
Sum-Product Networks.
Acknowledgements
This undergraduate research project is financed by CNPq grant #800585/2016-0.
References
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Hoifung Poon, Pedro Domingos. "Sum-Product Networks: A New Deep Architecture". 2011.
Uncertainty in Artificial Intelligence (UAI 2011). Ed. 27.
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Olivier Delalleaum, Yoshua Bengio. "Shallow vs. Deep Sum-Product Networks". 2011. Advances in
Neural Information Processing Systems (NIPS 2011). Ed. 24.
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Abram L. Friesen, Pedro Domingos. "The Sum-Product Theorem: A Foundation for Learning Tractable
Models". 2016. International Conference on Machine Learning (ICML 2016). Ed. 33.
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Abram L. Friesen, Pedro Domingos. "Recursive Decomposition for Non-convex Optimization". 2015.
International Conference on Artificial Intelligence (IJCAI 2015). Ed. 24.
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Robert Peharz, Georg Kapeller, Pejman Mowlaee, Franz Pernkopf. "Modeling Speech with
Sum-Product Networks: Application to Bandwidth Extension". IEEE International Conference on
Acoustics, Speech, and Signal Processing (ICAASSP 2014). Ed. 39.
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Robert Gens, Pedro Domingos. "Learning the Structure of Sum-Product Networks". International
Conference on Machine Learning (ICML 2013). Ed. 30.
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Aaron Dennis, Dan Ventura. "Learning the Architecture of Sum-Product Networks Using Clustering
on Variables". Advances in Neural Information Processing Systems (NIPS 2012). Ed. 25.
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Mohamed R. Amer, Sinisa Todorovic. "Sum-Product Networks for Activity Recognition". IEEE
Transactions on Pattern Recognition and Machine Intelligence (TPAMI 2015).
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Wei-Chen Cheng, Stanley Kok, Hoai Vu Pham, Hai Leong Chieu, Kian Ming Chai. "Language Modelling
with Sum-Product Networks". Annual Conference of the Speech Communication Association
(INTERSPEECH 2014). Ed. 15.