Repairing inconsistent answer set programs using rules of thumb: A gene regulatory networks case study

Answer set programming is a form of declarative programming that can be used to elegantly model various systems. When the available knowledge about these systems is imperfect, however, the resulting programs can be inconsistent. In such cases, it is of interest to find plausible repairs, i.e. plausible modifications to the original program that ensure the existence of at least one answer set. Although several approaches to this end have already been proposed, most of them merely find a repair which is in some sense minimal. In many applications, however, expert knowledge is available which could allow us to identify better repairs. In particular, we consider the scenario where this expert knowledge is formulated as rules of thumb, but no training data is available to learn how these rules of thumb interact. The main question we address in this paper is whether we can then still aggregate the rules of thumb in a useful way. In addition to standard aggregation techniques, we present a novel statistical approach that assigns weights to these rules of thumb, by sampling, in a particular way, from a pool of possible repairs. In particular, we evaluate how frequently each given rule of thumb is violated in the sample of repairs, and use the Z-score of this distribution to set the weight of that rule. We analyze the potential of using expert knowledge in this way, by focusing on a specific case study: Gene Regulatory Networks. We describe the rules of thumb that express available expert knowledge from the biological literature and explain how they can be encoded while repairing inconsistencies. Finally, we experimentally compare the proposed repair strategies using rules of thumb against the baseline strategy of identifying minimal repairs. A method to repair inconsistent Answer Set Programs using rules of thumb is proposed.Different aggregation methods for rule costs are implemented in ASP.A case study about repairing gene regulatory networks is presented.The most accurate method of repair is a z-score approach.The z-score approach learns the weights from unsupervised sampled repairs.

[1]  Pedro M. Domingos,et al.  Efficient Weight Learning for Markov Logic Networks , 2007, PKDD.

[2]  Martin Gebser,et al.  clasp : A Conflict-Driven Answer Set Solver , 2007, LPNMR.

[3]  R. Dawes.  Judgment under uncertainty: The robust beauty of improper linear models in decision making , 1979 .

[4]  Thomas Eiter,et al.  Paracoherent Answer Set Programming , 2010, KR.

[5]  Stefan Woltran,et al.  Debugging ASP Programs by Means of ASP , 2007, LPNMR.

[6]  Surya Ganguli,et al.  Function constrains network architecture and dynamics: a case study on the yeast cell cycle Boolean network. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[8]  Jan Chomicki,et al.  Answer sets for consistent query answering in inconsistent databases , 2002, Theory and Practice of Logic Programming.

[9]  Vladimir Lifschitz,et al.  Answer set programming and plan generation , 2002, Artif. Intell..

[10]  S. Bornholdt,et al.  Boolean Network Model Predicts Cell Cycle Sequence of Fission Yeast , 2007, PloS one.

[11]  Jonathan J. Ellis,et al.  Predicting Protein Kinase Specificity: Predikin Update and Performance in the DREAM4 Challenge , 2011, PloS one.

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

[13]  Martine De Cock,et al.  Using Rules of Thumb for Repairing Inconsistent Answer Set Programs , 2015, SUM.

[14]  Kathleen Marchal,et al.  ASP-G: an ASP-based method for finding attractors in genetic regulatory networks , 2014, Bioinform..

[15]  T. Syrjänen.  Debugging Inconsistent Answer Set Programs , 2006 .

[16]  Stuart A. Kauffman,et al.  The origins of order , 1993 .

[17]  Martin Gebser,et al.  Repair and Prediction (under Inconsistency) in Large Biological Networks with Answer Set Programming , 2010, KR.

[18]  Martin Gebser,et al.  The BioASP Library: ASP Solutions for Systems Biology , 2010, 2010 22nd IEEE International Conference on Tools with Artificial Intelligence.

[19]  Thomas Eiter,et al.  Preferred Answer Sets for Extended Logic Programs , 1999, Artif. Intell..

[20]  Raymond J. Mooney,et al.  Relational Learning of Pattern-Match Rules for Information Extraction , 1999, CoNLL.

[21]  Yiannis Kourmpetis,et al.  Gene Regulatory Networks from Multifactorial Perturbations Using Graphical Lasso: Application to the DREAM4 Challenge , 2010, PloS one.

[22]  Ulises Cortés,et al.  Semantics for Possibilistic Disjunctive Programs* , 2011, Theory and Practice of Logic Programming.

[23]  Steven Skiena,et al.  Identifying gene regulatory networks from experimental data , 2001, Parallel Comput..

[24]  Aurélien Naldi,et al.  Dynamical analysis of a generic Boolean model for the control of the mammalian cell cycle , 2006, ISMB.

[25]  Michael Mateas,et al.  Answer Set Programming for Procedural Content Generation: A Design Space Approach , 2011, IEEE Transactions on Computational Intelligence and AI in Games.

[26]  Q. Ouyang,et al.  The yeast cell-cycle network is robustly designed. , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[27]  Chris Cornelis,et al.  Modelling gene and protein regulatory networks with Answer Set Programming , 2011, Int. J. Data Min. Bioinform..

[28]  Maurice Bruynooghe,et al.  Database Repair by Signed Formulae , 2004, FoIKS.

[29]  D. Dubois,et al.  Beyond min aggregation in multicriteria decision: (ordered) weighted min, discri-min, leximin , 1997 .

[30]  H. Stuckenschmidt,et al.  Applying Markov Logic for Debugging Probabilistic Temporal Knowledge Bases , 2014 .

[31]  Igor Stéphan,et al.  A Possibilistic Inconsistency Handling in Answer Set Programming , 2005, ECSQARU.

[32]  F. RICCA,et al.  Team-building with answer set programming in the Gioia-Tauro seaport , 2011, Theory and Practice of Logic Programming.

[33]  Stefan Woltran,et al.  AGM-Style Belief Revision of Logic Programs under Answer Set Semantics , 2008, LPNMR.

[34]  Martine De Cock,et al.  Possible and Necessary Answer Sets of Possibilistic Answer Set Programs , 2012, 2012 IEEE 24th International Conference on Tools with Artificial Intelligence.

[35]  John B. Shoven,et al.  I , Edinburgh Medical and Surgical Journal.

[36]  Lijian Yang,et al.  Robustness and Backbone Motif of a Cancer Network Regulated by miR-17-92 Cluster during the G1/S Transition , 2013, PloS one.

[37]  Nicola J. Rinaldi,et al.  Transcriptional Regulatory Networks in Saccharomyces cerevisiae , 2002, Science.

[38]  Stefania Costantini,et al.  Modeling preferences and conditional preferences on resource consumption and production in ASP , 2009, J. Algorithms.

[39]  Marina De Vos,et al.  Debugging Logic Programs under the Answer Set Semantics , 2005, Answer Set Programming.

[40]  Nikolaos Berntenis,et al.  Detection of attractors of large Boolean networks via exhaustive enumeration of appropriate subspaces of the state space , 2013, BMC Bioinformatics.

[41]  Vladimir Lifschitz,et al.  Action Languages, Answer Sets, and Planning , 1999, The Logic Programming Paradigm.

[42]  Ziv Bar-Joseph,et al.  Analyzing time series gene expression data , 2004, Bioinform..

[43]  Martin Gebser,et al.  Detecting inconsistencies in large biological networks with answer set programming , 2008, Theory and Practice of Logic Programming.

[44]  Wolfgang Faber,et al.  Computing preferred answer sets by meta-interpretation in answer set programming , 2003, Theory Pract. Log. Program..

[45]  Gerhard Brewka,et al.  Complex Preferences for Answer Set Optimization , 2004, KR.

[46]  Joohyung Lee,et al.  Markov Logic Style Weighted Rules under the Stable Model Semantics , 2015, ICLP.

[47]  Oren Etzioni,et al.  Learning First-Order Horn Clauses from Web Text , 2010, EMNLP.

[48]  Vladimir Lifschitz,et al.  Answer Set Programming , 2019 .

[49]  Christine Solnon,et al.  Applications of Preferences using Answer Set Programming , 2005, Answer Set Programming.

[50]  Torsten Schaub,et al.  Modeling Biological Networks by Action Languages via Answer Set Programming , 2008, Constraints.

[51]  Ronaldo Fumio Hashimoto,et al.  Budding yeast cell cycle modeled by context-sensitive probabilistic Boolean network , 2009, 2009 IEEE International Workshop on Genomic Signal Processing and Statistics.

[53]  Gopal Gupta,et al.  Dynamic Consistency Checking in Goal-Directed Answer Set Programming , 2014, Theory and Practice of Logic Programming.

[54]  Joohyung Lee,et al.  A Probabilistic Extension of the Stable Model Semantics , 2015, AAAI Spring Symposia.

[55]  Thomas Eiter,et al.  Data Integration and Answer Set Programming , 2005, LPNMR.

[56]  Natarajan Shankar,et al.  Machine Reading Using Markov Logic Networks for Collective Probabilistic Inference , 2011 .

[57]  Sebastian Wernicke,et al.  FANMOD: a tool for fast network motif detection , 2006, Bioinform..

[58]  Andrew McCallum,et al.  Modeling Relations and Their Mentions without Labeled Text , 2010, ECML/PKDD.

[59]  Stefan Bornholdt,et al.  Boolean network models of cellular regulation: prospects and limitations , 2008, Journal of The Royal Society Interface.

[60]  Alberto de la Fuente,et al.  Inferring Gene Networks: Dream or Nightmare? , 2009, Annals of the New York Academy of Sciences.

[61]  Yuqing Zhai,et al.  A Processing Method for Inconsistent Answer Set Programs Based on Minimal Principle , 2012 .

[62]  Hidde de Jong,et al.  Modeling and Simulation of Genetic Regulatory Systems: A Literature Review , 2002, J. Comput. Biol..

[63]  Laurent Trilling,et al.  Logical Modeling and Analysis of Regulatory Genetic Networks in a Non Monotonic Framework , 2015, IWBBIO.

[64]  Raymond J. Mooney,et al.  Max-Margin Weight Learning for Markov Logic Networks , 2009, ECML/PKDD.

[65]  Jue Wang,et al.  Scalable Learning for Structure in Markov Logic Networks , 2014, AAAI Workshop: Statistical Relational Artificial Intelligence.

[66]  S. Havlin,et al.  Scale-free networks are ultrasmall. , 2002, Physical review letters.

[67]  Zhongying Zhao,et al.  Boolean genetic network model for the control of C. elegans early embryonic cell cycles , 2013, BioMedical Engineering OnLine.

[68]  Igor Stéphan,et al.  Possibilistic uncertainty handling for answer set programming , 2006, Annals of Mathematics and Artificial Intelligence.

[69]  Edward R. Dougherty,et al.  From Boolean to probabilistic Boolean networks as models of genetic regulatory networks , 2002, Proc. IEEE.

[70]  Olivier Bodenreider,et al.  Finding Semantic Inconsistencies in UMLS using Answer Set Programming , 2010, AAAI.