Most Probable Explanation for MetaProbLog and Its Application in Heart Sound Segmentation

This paper, presents ongoing work that extends MetaProbLog with Most Probable Explanation (MPE) inference method. The MPE inference method is widely used in Hidden Markov Models in order to derive the most likely states of a model. Recently, we started developing an application that uses MetaProbLog to models phonocardiograms. We target to use this application in order to diagnose heart diseases by using phonocardiogram classification. Motivated by the importance of phonocardiogram classification, we started the implementation of the MPE inference method and an improvement of representation for annotated disjunctions.

[1]  Alessandra Mileo,et al.  Probabilistic Inductive Logic Programming Based on Answer Set Programming , 2014, ArXiv.

[2]  Luc De Raedt,et al.  Probabilistic Explanation Based Learning , 2007, ECML.

[3]  Luc De Raedt,et al.  Anytime Inference in Probabilistic Logic Programs with Tp-Compilation , 2015, IJCAI.

[4]  Leslie Pack Kaelbling,et al.  Lifted Probabilistic Inference with Counting Formulas , 2008, AAAI.

[5]  Stephen Muggleton,et al.  Learning Stochastic Logic Programs , 2000, Electron. Trans. Artif. Intell..

[6]  Fabrizio Riguzzi,et al.  Terminating Evaluation of Logic Programs with Finite Three-Valued Models , 2014, TOCL.

[7]  Joshua B. Tenenbaum,et al.  Exact and Approximate Sampling by Systematic Stochastic Search , 2009, AISTATS.

[8]  Joshua B. Tenenbaum,et al.  Church: a language for generative models , 2008, UAI.

[9]  Kenneth A. Ross,et al.  The well-founded semantics for general logic programs , 1991, JACM.

[10]  Luc De Raedt,et al.  Constraints for probabilistic logic programming , 2012, NIPS 2012.

[11]  Luc De Raedt,et al.  ProbLog: A Probabilistic Prolog and its Application in Link Discovery , 2007, IJCAI.

[12]  J. Pearl.  Causality: Models, Reasoning and Inference , 2000 .

[13]  Gerda Janssens,et al.  Nesting Probabilistic Inference , 2011, ArXiv.

[14]  David Poole,et al.  The Independent Choice Logic for Modelling Multiple Agents Under Uncertainty , 1997, Artif. Intell..

[15]  Craig Boutilier,et al.  Effective sampling and learning for mallows models with pairwise-preference data , 2014, J. Mach. Learn. Res..

[16]  Gabriele Kern-Isberner,et al.  On probabilistic inference in relational conditional logics , 2012, Log. J. IGPL.

[17]  Ned Hall.  Structural equations and causation , 2007 .

[18]  V. S. Subrahmanian,et al.  Stable Semantics for Probabilistic Deductive Databases , 1994, Inf. Comput..

[19]  Taisuke Sato,et al.  PRISM: A Language for Symbolic-Statistical Modeling , 1997, IJCAI.

[20]  Alessandra Mileo,et al.  A System for Probabilistic Inductive Answer Set Programming , 2015, SUM.

[21]  James Cussens,et al.  Stochastic Logic Programs: Sampling, Inference and Applications , 2000, UAI.

[22]  Tamer Ölmez,et al.  Classification of heart sounds using an artificial neural network , 2003, Pattern Recognit. Lett..

[23]  Joost Vennekens,et al.  Towards a General Framework for Actual Causation Using CP-logic , 2014, PLP@ICLP.

[24]  A. N. Kolmogorov,et al.  Foundations of the theory of probability , 1960 .

[25]  J. C. Burkill.  A First Course in Mathematical Analysis , 1962 .

[26]  James Cussens,et al.  CLP(BN): Constraint Logic Programming for Probabilistic Knowledge , 2002, Probabilistic Inductive Logic Programming.

[27]  Christian Brandt,et al.  A robust heart sounds segmentation module based on S-transform , 2013, Biomed. Signal Process. Control..

[28]  Joost Vennekens,et al.  Counterfactual dependency and actual causation in CP-logic and structural models: a comparison , 2012, STAIRS.

[29]  A. Pfeffer,et al.  Figaro : An Object-Oriented Probabilistic Programming Language , 2009 .

[30]  Enrico Pontelli,et al.  Hybrid Probabilistic Logic Programs with Non-monotonic Negation , 2005, ICLP.

[31]  Luc De Raedt,et al.  MCMC Estimation of Conditional Probabilities in Probabilistic Programming Languages , 2013, ECSQARU.

[32]  Bert Van Nuffelen,et al.  A-System: Problem Solving through Abduction , 2001, IJCAI.

[33]  Taisuke Sato,et al.  A Statistical Learning Method for Logic Programs with Distribution Semantics , 1995, ICLP.

[34]  David Poole,et al.  First-order probabilistic inference , 2003, IJCAI.

[35]  Glenn Shafer,et al.  The art of causal conjecture , 1996 .

[36]  Joost Vennekens,et al.  Actual causation in CP-logic , 2011, Theory and Practice of Logic Programming.

[37]  Teodor C. Przymusinski.  Every logic program has a natural stratification and an iterated least fixed point model , 1989, PODS.

[38]  Joseph Y. Halpern,et al.  Causes and Explanations: A Structural-Model Approach. Part II: Explanations , 2001, The British Journal for the Philosophy of Science.

[39]  Nils J. Nilsson,et al.  Probabilistic Logic * , 2022 .

[40]  Krysia Broda,et al.  On Minimality and Integrity Constraints in Probabilistic Abduction , 2013, LPAR.

[41]  Peter J. F. Lucas,et al.  Inference for a New Probabilistic Constraint Logic , 2013, IJCAI.

[42]  Taisuke Sato,et al.  Bayesian inference for statistical abduction using Markov chain Monte Carlo , 2011, ACML.

[43]  Stuart J. Russell,et al.  BLOG: Relational Modeling with Unknown Objects , 2004 .

[44]  Roland H. C. Yap,et al.  Constrained Decision Diagrams , 2005, AAAI.

[45]  David Poole,et al.  Probabilistic Horn Abduction and Bayesian Networks , 1993, Artif. Intell..

[46]  Katsumi Inoue,et al.  Probabilistic Rule Learning in Nonmonotonic Domains , 2011, CLIMA.

[47]  Matthew Richardson,et al.  Markov logic networks , 2006, Machine Learning.

[48]  Fabrizio Riguzzi.  The Distribution Semantics is Well-Defined for All Normal Programs , 2015, PLP@ICLP.

[49]  Frank D. Wood,et al.  A Compilation Target for Probabilistic Programming Languages , 2014, ICML.

[50]  Maurice Bruynooghe,et al.  Logic programs with annotated disjunctions , 2004, NMR.

[51]  Yoshitaka Kameya,et al.  Parameter Learning of Logic Programs for Symbolic-Statistical Modeling , 2001, J. Artif. Intell. Res..

[52]  Lise Getoor,et al.  Learning Probabilistic Relational Models , 1999, IJCAI.

[53]  Paolo Mancarella,et al.  Abductive Logic Programming , 1992, LPNMR.

[54]  Shotaro Akaho,et al.  Supervised ordering - an empirical survey , 2005, Fifth IEEE International Conference on Data Mining (ICDM'05).

[55]  Wilhelm Rödder,et al.  Coherent Knowledge Processing at Maximum Entropy by SPIRIT , 1996, UAI.

[56]  Mark Steyvers,et al.  Finding scientific topics , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[57]  Saburo Muroga,et al.  Binary Decision Diagrams , 2000, The VLSI Handbook.

[58]  Joseph Y. Halpern,et al.  Causes and Explanations: A Structural-Model Approach. Part I: Causes , 2000, The British Journal for the Philosophy of Science.

[59]  Luc De Raedt,et al.  Bayesian Logic Programs , 2001, ILP Work-in-progress reports.

[60]  Wray L. Buntine.  Operations for Learning with Graphical Models , 1994, J. Artif. Intell. Res..

[61]  Andrew J. Viterbi,et al.  Error bounds for convolutional codes and an asymptotically optimum decoding algorithm , 1967, IEEE Trans. Inf. Theory.

[62]  Andrew Thomas,et al.  The BUGS project: Evolution, critique and future directions , 2009, Statistics in medicine.

[63]  Donald Geman,et al.  Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[64]  Joohyung Lee,et al.  System f2lp - Computing Answer Sets of First-Order Formulas , 2009, LPNMR.

[65]  V. S. Costa,et al.  The YAP Prolog system , 2011, Theory and Practice of Logic Programming.

[66]  Christopher R. Hitchcock.  Prevention, Preemption, and the Principle of Sufficient Reason , 2007 .

[67]  James Cussens,et al.  Parameter Estimation in Stochastic Logic Programs , 2001, Machine Learning.

[68]  Joseph Y. Halpern,et al.  Graded Causation and Defaults , 2013, The British Journal for the Philosophy of Science.

[69]  Miguel Tavares Coimbra,et al.  Heart sound segmentation of pediatric auscultations using wavelet analysis , 2013, 2013 35th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC).

[70]  W. K. Hastings,et al.  Monte Carlo Sampling Methods Using Markov Chains and Their Applications , 1970 .

[71]  Luc De Raedt,et al.  On the implementation of the probabilistic logic programming language ProbLog , 2010, Theory and Practice of Logic Programming.

[72]  Taisuke Sato,et al.  New Advances in Logic-Based Probabilistic Modeling by PRISM , 2008, Probabilistic Inductive Logic Programming.

[73]  Shadnaz Asgari,et al.  Pediatric heart sound segmentation using Hidden Markov Model , 2014, 2014 36th Annual International Conference of the IEEE Engineering in Medicine and Biology Society.

[74]  Christopher Hitchcock,et al.  Structural equations and causation: six counterexamples , 2009 .

[75]  C. R. Ramakrishnan,et al.  Constraint-Based Inference in Probabilistic Logic Programs , 2018, Theory and Practice of Logic Programming.

[76]  Gerda Janssens,et al.  Dedicated Tabling for a Probabilistic Setting , 2010, ICLP.

[77]  Kuo-Chu Chang,et al.  Weighing and Integrating Evidence for Stochastic Simulation in Bayesian Networks , 2013, UAI.

[78]  Wannes Meert,et al.  The Most Probable Explanation for Probabilistic Logic Programs with Annotated Disjunctions , 2014, ILP.

[79]  Randal E. Bryant,et al.  Symbolic Boolean manipulation with ordered binary-decision diagrams , 1992, CSUR.

[80]  Maurice Bruynooghe,et al.  Embracing Events in Causal Modelling: Interventions and Counterfactuals in CP-Logic , 2010, JELIA.

[81]  David Poole,et al.  Abducing through negation as failure: stable models within the independent choice logic , 2000, J. Log. Program..

[82]  Luc De Raedt,et al.  Inference and learning in probabilistic logic programs using weighted Boolean formulas , 2013, Theory and Practice of Logic Programming.

[83]  E BryantRandal.  Graph-Based Algorithms for Boolean Function Manipulation , 1986 .

[84]  Pedro M. Domingos,et al.  Unifying Logical and Statistical AI , 2006, 2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS).

[85]  Ned Hall.  Two Concepts of Causation , 2001 .

[86]  Michael I. Jordan,et al.  Latent Dirichlet Allocation , 2001, J. Mach. Learn. Res..

[87]  Pekka Orponen,et al.  Witness of unsatisfiability for a random 3-satisfiability formula , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[88]  Dan Roth,et al.  Lifted First-Order Probabilistic Inference , 2005, IJCAI.

[89]  A. Pekec,et al.  The repeated insertion model for rankings: Missing link between two subset choice models , 2004 .