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Enumerating Equivalence Classes of Bayesian Networks using EC Graphs

Eunice Yuh-Jie Chen, Arthur Choi, Adnan Darwiche
2016 International Conference on Artificial Intelligence and Statistics  
We consider the problem of learning Bayesian network structures from complete data. In particular, we consider the enumeration of their k-best equivalence classes.  ...  We propose a new search space for A* search, called the EC graph, that facilitates the enumeration of equivalence classes, by representing the space of completed, partially directed acyclic graphs.  ...  Here, we propose to enumerate equivalence classes of Bayesian network structures, also using A* search, but now on the EC graph.  ... 
dblp:conf/aistats/ChenCD16 fatcat:gmt2x24ocfg57kwkxhxvg3hkrm

Finding the k-best Equivalence Classes of Bayesian Network Structures for Model Averaging

Yetian Chen, Jin Tian
In this paper we develop an algorithm to find the k-best equivalence classes of Bayesian networks.  ...  We demonstrate our algorithm in the task of Bayesian model averaging.  ...  Finding the k-best Equivalence Classes of Bayesian Networks The following definitions will be useful in the development of our algorithm.  ... 
doi:10.1609/aaai.v28i1.9064 fatcat:75kch2hzjvhjhlfsnvobok4j64

Learning Bayesian networks with ancestral constraints

Eunice Yuh-Jie Chen, Yujia Shen, Arthur Choi, Adnan Darwiche
2016 Neural Information Processing Systems  
We consider the problem of learning Bayesian networks optimally, when subject to background knowledge in the form of ancestral constraints.  ...  The proposed framework exploits oracles for learning structures using decomposable scores, which cannot accommodate ancestral constraints since they are non-decomposable.  ...  Acknowledgments This work was partially supported by NSF grant #IIS-1514253 and ONR grant #N00014-15-1-2339. 9 When no limits are placed on the sizes of families (as was done here), heuristic-search approaches  ... 
dblp:conf/nips/ChenSCD16 fatcat:heded6nw55g6pnrfqn3prvos3u

Joint Discovery of Skill Prerequisite Graphs and Student Models

Yetian Chen, José P. González-Brenes, Jin Tian
2016 Educational Data Mining  
In the first stage, it uses an algorithm called Structural Expectation Maximization to select a class of equivalent Bayesian networks; in the second stage, it uses curriculum information to select a single  ...  Bayesian network.  ...  Thus, the output from Structural EM is actually an equivalence class (EC) that may contain many Bayesian network structures 3 .  ... 
dblp:conf/edm/ChenGT16 fatcat:2nrcehlycvca7nwrivw2gkpevq

On the Construction of the Inclusion Boundary Neighbourhood for Markov Equivalence Classes of Bayesian Network Structures [article]

Vincent Auvray, Louis Wehenkel
2012 arXiv   pre-print
The problem of learning Markov equivalence classes of Bayesian network structures may be solved by searching for the maximum of a scoring metric in a space of these classes.  ...  We use a theoretically motivated neighbourhood, the inclusion boundary, and represent equivalence classes by essential graphs.  ...  CONCLUSION The topic of this paper is the construction and analysis of a search space of Markov equivalence classes of Bayesian networks represented by essential graphs and with the in clusion boundary  ... 
arXiv:1301.0553v1 fatcat:66alqtljyneg7czywbnzhm7u3q

Strong Completeness and Faithfulness in Bayesian Networks [article]

Christopher Meek
2013 arXiv   pre-print
structure are faithful; i.e. the independence facts true of the distribution are all and only those entailed by the network structure.  ...  A completeness result for d-separation applied to discrete Bayesian networks is presented and it is shown that in a strong measure-theoretic sense almost all discrete distributions for a given network  ...  Research for this paper was supported by the Office of Navel Research grant ONR #N00014-93-1-0568.  ... 
arXiv:1302.4973v1 fatcat:rfqb3kdiurdubapfe6kebdrsa4

The Complexity of Bayesian Networks Specified by Propositional and Relational Languages [article]

Fabio Gagliardi Cozman, Denis Deratani Mauá
2017 arXiv   pre-print
We examine the complexity of inference in Bayesian networks specified by logical languages.  ...  We study the complexity of inferences when network, query and domain are the input (the inferential and the combined complexity), when the network is fixed and query and domain are the input (the query  ...  This class of functions is #EXP-equivalent. Proof. Build a relational Bayesian network specification as in the proof of Theorem 4.  ... 
arXiv:1612.01120v3 fatcat:qfvx7d5kqne77pn2ls3xea6w4u

BALanCe: Deep Bayesian Active Learning via Equivalence Class Annealing [article]

Renyu Zhang, Aly A. Khan, Robert L. Grossman, Yuxin Chen
2022 arXiv   pre-print
Intuitively, each equivalence class consists of instantiations of deep models with similar predictions, and BALanCe adaptively adjusts the size of the equivalence classes as learning progresses.  ...  Concretely, BALanCe employs a novel acquisition function which leverages the structure captured by equivalence hypothesis classes and facilitates differentiation among different equivalence classes.  ...  Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of any funding agencies.  ... 
arXiv:2112.13737v2 fatcat:4y7z3t6uf5gihcdr2svrhgvyk4

Leveraging Experience in Lazy Search [article]

Mohak Bhardwaj, Sanjiban Choudhury, Byron Boots, Siddhartha Srinivasa
2021 arXiv   pre-print
We further provide a novel theoretical analysis of lazy search in a Bayesian framework as well as regret guarantees on our imitation learning based approach to motion planning.  ...  We evaluate our algorithms on a wide range of 2D and 7D problems and show that the learned selector outperforms baseline commonly used heuristics.  ...  [5, 6] where we show that the problem is equivalent to a problem in Bayesian Active Learning.  ... 
arXiv:2110.04669v1 fatcat:rtbjrt3whzdc5eksd3lgbtioji

Efficient Online Learning for Optimizing Value of Information: Theory and Application to Interactive Troubleshooting [article]

Yuxin Chen, Jean-Michel Renders, Morteza Haghir Chehreghani, Andreas Krause
2017 arXiv   pre-print
First, assuming the distribution over hypotheses is known, we propose a dynamic hypothesis enumeration strategy, which allows efficient information gathering with strong theoretical guarantees.  ...  Existing algorithms are either heuristics with no guarantees, or scale poorly (with exponential run time in terms of the number of available tests).  ...  This work was done in part while Andreas Krause was visiting the Simons Institute for the Theory of Computing.  ... 
arXiv:1703.05452v2 fatcat:y6p6pwbwkrc3tmhd2mx2xbwgoy

On the hardness of approximate reasoning

Dan Roth
1996 Artificial Intelligence  
We consider various methods used in approximate reasoning such as computing degree of belief and Bayesian belief networks, as well as reasoning techniques such as constraint satisfaction and knowledge  ...  We also identify some restricted classes of propositional formulae for which efficient algorithms for counting satisfying assignments can be given.  ...  I would also like to thank Karen Daniels, Roni Khardon and Salil Vadhan for their comments on an earlier draft of this paper.  ... 
doi:10.1016/0004-3702(94)00092-1 fatcat:yt4pdkftfvblbnjyenyikcks5e

Bayesian Structure Learning by Recursive Bootstrap [article]

Raanan Y. Rohekar, Yaniv Gurwicz, Shami Nisimov, Guy Koren, Gal Novik
2018 arXiv   pre-print
Moreover, the re-use of stable low order independencies allows greater computational efficiency.  ...  We address the problem of Bayesian structure learning for domains with hundreds of variables by employing non-parametric bootstrap, recursively.  ...  Moreover, it is scalable to large domains, having hundreds of variables, where it provides the highest scoring CPDAGs and most reliable structural features on all the tested benchmarks.  ... 
arXiv:1809.04828v1 fatcat:ix7zigjs2fg5pdtiyu7ktd3efe

On linear potential functions for approximating Bayesian computations

Eugene Santos
1996 Journal of the ACM  
In particular, the amounl of probabilistic information ncccssary [n the computations is often overwhelming, For example, the size of conditional prohahility tables in Bayesian networks has long been a  ...  limiting factor in the general usc of these networks, Wc present a new appr(mch for manipulating the probabilistic information given.  ...  There are two key factors which prevent the general use of Bayesian networks. The first is network topolog.  ... 
doi:10.1145/233551.233552 fatcat:zhi4tkwqbfcgbbobiqh2x6ebai

Correlated equilibria in graphical games

Sham Kakade, Michael Kearns, John Langford, Luis Ortiz
2003 Proceedings of the 4th ACM conference on Electronic commerce - EC '03  
Our first main result establishes that this Markov network succinctly represents all correlated equilibria of the graphical game up to expected payoff equivalence.  ...  the graph degree).  ...  ACKNOWLEDGEMENTS We give warm thanks to Dean Foster for numerous helpful discussions, and to Stuart Geman for his help with the proof of Lemma 3.  ... 
doi:10.1145/779928.779934 dblp:conf/sigecom/KakadeKLO03 fatcat:vaifykxajfdx5cgxwlu7t32cl4

Comparative Genome-Scale Reconstruction of Gapless Metabolic Networks for Present and Ancestral Species

Esa Pitkänen, Paula Jouhten, Jian Hou, Muhammad Fahad Syed, Peter Blomberg, Jana Kludas, Merja Oja, Liisa Holm, Merja Penttilä, Juho Rousu, Mikko Arvas, Jens Nielsen
2014 PLoS Computational Biology  
Moreover, the reconstructed networks are fully carbon mapped, allowing their use in 13C flux analysis.  ...  Our comparative approach is particularly useful in scenarios where the quality of available sequence data is lacking, and when reconstructing evolutionary distant species.  ...  First, reactions are enumerated in an increasing order of estimated cost of adding the reaction to the network.  ... 
doi:10.1371/journal.pcbi.1003465 pmid:24516375 pmcid:PMC3916221 fatcat:p23xv7hrmne6leo2c4k32cehb4
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