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Random Generation of Relational Bayesian Networks

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University of Nantes
University of Nantes

Only the title page (génération aléatoire de réseaux Bayésiens relationnels) is in French Presentation during JFRB’14 25-27 juin, IHP, Paris, France

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PRMs Random generation Population Conclusion & ongoing work Génération aléatoire de réseaux Bayésiens relationnels Mouna Ben Ishak1;2, Philippe Leray2 and Nahla Ben Amor1 1 Laboratoire de Recherche Opérationnelle de Décision et de Contrôle de Processus (LARODEC), ISG Tunis, Tunisie 2 Laboratoire d’Informatique de Nantes Atlantique (LINA), UMR CNRS 6241, Université de Nantes, France Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 1/27
PRMs Random generation Population Conclusion & ongoing work Motivation (1/3) f1 f2 f3 … fm x1 v1 v3 v2 … v1 x2 v2 v1 V3 … v1 x3 v1 v2 v3 … v2 … … … … … … xn v1 v3 v2 … v1 Learned model Features Observations Training set Learning algorithm Flat data representation Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 2/27
PRMs Random generation Population Conclusion & ongoing work Motivation (2/3) Presentation Presentation Business logic DDDaaatttaaa Business logic DDDaaatttaaa Relational representation!!! Relational representation!!! How to use relational data with classical machine learning algorithms? How to use this data with classical machine learning algorithms? Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 3/27
PRMs Random generation Population Conclusion & ongoing work Motivation (3/3) Propositionalization It has been shown that propositionalization is not always appropriate to perform learning in relational domains (Maier et al., 10) Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 4/27
PRMs Random generation Population Conclusion & ongoing work Motivation (3/3) Propositionalization It has been shown that propositionalization is not always appropriate to perform learning in relational domains (Maier et al., 10) Relational transition Extend classical machine learning techniques in the context of relational data representation Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 4/27
PRMs Random generation Population Conclusion & ongoing work Outline ... 1. PRMs 2. Random generation 2.1. Relational schema random generation 2.2. PRM random generation 3. Population 4. Conclusion & ongoing work Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 5/27
PRMs Random generation Population Conclusion & ongoing work Bayesian networks (BN) (Pearl, 85) Definition G qualitative description of conditional dependences / independences between variables directed acyclic graph (DAG) quantitative description of these dependences conditional probability distributions (CPDs) Gender Occupation Age Low Middle High Age Occupation Oc1 Oc2 Oc3 Low,F 0.5 0.1 0.4 Low,M 0.3 0.5 0.2 Middle,F 0.2 0.4 0.4 Middle,M 0.9 0.1 0 High,F 0.3 0.5 0.2 High,M 0.2 0.3 0.5 Gender M F Gender 0.4 0.3 0.3 Age 0.4 0.6 Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 6/27
PRMs Random generation Population Conclusion ongoing work BN structure learning Constraint-based methods BN = independence model ) find cond. indep. (CI) in data in order to build the DAG ex : IC (Pearl Verma, 91), PC (Spirtes et al., 93) problem : reliability of CI statistical tests (ok for n 100) Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 7/27
PRMs Random generation Population Conclusion ongoing work BN structure learning Constraint-based methods BN = independence model problem : reliability of CI statistical tests (ok for n 100) Score-based methods BN = probabilistic model that must fit data as well as possible ) search the DAG space in order to maximize a scoring function ex : Maximum Weighted Spanning Tree (Chow Liu, 68), Greedy Search (Chickering, 95), evolutionary approaches (Larranaga et al., 96) (Wang Yang, 10) problem : size of search space (ok for n 1000) Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 7/27
PRMs Random generation Population Conclusion ongoing work BN structure learning Constraint-based methods BN = independence model problem : reliability of CI statistical tests (ok for n 100) Score-based methods BN = probabilistic model that must fit data as well as possible problem : size of search space (ok for n 1000) Hybrid/ local search methods local search / neighbor identification (statistical tests) global (score) optimization usually for scalability reasons (ok for high n) Génératioenxalé:atoMireMdeHrésCeauax Blgayoésrieitnhs rmelatio(nTneslsamardJFinRBo’1s4 et a25l-.2,70jui6n,)IHP, Paris, France 7/27
PRMs Random generation Population Conclusion ongoing work Evaluating structure learning algorithms Standard practice generating data from a reference model applying a structure learning algorithm with this data comparing the learned and reference models Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 8/27
PRMs Random generation Population Conclusion ongoing work Evaluating structure learning algorithms Standard practice generating data from a reference model applying a structure learning algorithm with this data comparing the learned and reference models Which reference model ? existence of reference benchmarks (e.g., Asia, Alarm, ...). randomly generated models (Ide et al., 04) arbitrarily large BN by tiling (Tsamardinos et al., 06) Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 8/27
PRMs Random generation Population Conclusion ongoing work Which kind of data ? BN learning from data... but which kind of data ? Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 9/27
PRMs Random generation Population Conclusion ongoing work Which kind of data ? BN learning from data... but which kind of data ? how to deal with structured data ? Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 9/27
PRMs Random generation Population Conclusion ongoing work Relational schema Movie User Vote Movie User Rating Gender Age Occupation RealiseDate Genre A relational schema R classes + relational variables Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 10/27
PRMs Random generation Population Conclusion ongoing work Relational schema Movie User Vote Movie User Rating Gender Age Occupation RealiseDate Genre A relational schema R classes + relational variables reference slots (e.g., Vote:Movie;Vote:User) Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 10/27
PRMs Random generation Population Conclusion ongoing work Relational schema Movie User Vote Movie User Rating Gender Age Occupation RealiseDate Genre A relational schema R classes + relational variables reference slots (e.g., Vote:Movie;Vote:User) slot chain = a sequence of reference slots allow to walk in the relational schema to create new variables Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 10/27
PRMs Random generation Population Conclusion ongoing work Relational schema Movie User Vote Movie User Rating Gender Age Occupation RealiseDate Genre A relational schema R classes + relational variables reference slots (e.g., Vote:Movie;Vote:User) slot chain = a sequence of reference slots allow to walk in the relational schema to create new variables ex : Vote:User:User1:Movie : all the movies voted by a particular user Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 10/27
PRMs Random generation Population Conclusion ongoing work Probabilistic Relational Models (Koller Pfeffer, 98) Definition A PRM associated to R : a qualitative dependency structure S (with possible long slot chains and aggregation functions) a set of parameters S Vote User.Gender M F 0.4 0.6 Rating Movie User RealiseDate Genre Gender Age Occupation Movie.Genre Votes.Rating Low High Drama, M 0.5 0.5 Drama, F 0.3 0.7 Horror, M 0.2 0.8 Horror, F 0.9 0.1 Comedy, M 0.5 0.5 Comedy, F 0.6 0.4 User.Gender Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 11/27
PRMs Random generation Population Conclusion ongoing work Probabilistic Relational Models Definition Vote User.Gender M F 0.4 0.6 Rating Movie User RealiseDate Genre Gender Age Occupation Movie.Genre Votes.Rating Low High Drama, M 0.5 0.5 Drama, F 0.3 0.7 Horror, M 0.2 0.8 Horror, F 0.9 0.1 Comedy, M 0.5 0.5 Comedy, F 0.6 0.4 User.Gender Aggregators Vote:User:User1:Movie:genre ! Vote:rating movie rating from one user can be dependent with the genre of all the movies voted by this user how to describe the dependency with an unknown number of parents ? solution : using an aggregated value, e.g. = MODE Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 11/27
PRMs Random generation Population Conclusion ongoing work Ground Bayesian Network GBN BN created from one PRM and an instantiated database = relational skeleton Age Rating Age Gender Occupation Age Gender Occupation Gender Occupation Genre RealiseDate Genre Genre Genre Genre U1 U2 U3 M1 M2 M3 M4 M5 #U1, #M1 Rating #U1, #M2 Rating #U2, #M1 Rating #U2, #M3 Rating #U2, #M4 Rating #U3, #M1 Rating #U3, #M2 Rating #U3, #M3 Rating #U3, #M5 RealiseDate RealiseDate RealiseDate RealiseDate Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 12/27
PRMs Random generation Population Conclusion ongoing work Ground Bayesian Network GBN BN created from one PRM and an instantiated database = relational skeleton + probabilistic dependencies used for probabilistic inference Age Rating Age Gender Occupation Age Gender Occupation Gender Occupation Genre RealiseDate Genre Genre Genre Genre U1 U2 U3 M1 M2 M3 M4 M5 #U1, #M1 Rating #U1, #M2 Rating #U2, #M1 Rating #U2, #M3 Rating #U2, #M4 Rating #U3, #M1 Rating #U3, #M2 Rating #U3, #M3 Rating #U3, #M5 RealiseDate RealiseDate RealiseDate RealiseDate Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 12/27
PRMs Random generation Population Conclusion ongoing work PRM structure learning Constraint-based methods relational PC (Maier et al., 10) relational CD (Maier et al., 13) don’t deal with aggregation functions Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 13/27
PRMs Random generation Population Conclusion ongoing work PRM structure learning Constraint-based methods Score-based methods greedy search (Getoor et al., 07) Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 13/27
PRMs Random generation Population Conclusion ongoing work PRM structure learning Constraint-based methods Score-based methods Hybrid methods relational MMHC (Ben Ishak et al., in progress) Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 13/27
PRMs Random generation Population Conclusion ongoing work PRM structure learning Constraint-based methods Score-based methods Hybrid methods Critics - previous works lack of evaluation process, in a common framework absence of relational benchmarks for evaluation algorithms absence of relational data generation process Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 13/27
PRMs Random generation Population Conclusion ongoing work PRM structure learning Constraint-based methods Score-based methods Hybrid methods Critics - previous works Proposition a synthetic approach to randomly generate and populate PRMs and databases Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 13/27
PRMs Random generation Population Conclusion ongoing work PRMs random generation Related work (Maier et al., 10, 13) relational schemas are generated as tree structure ... too simple (Wuillemin et al., 12) object-oriented paradigm rather than relational one no population nor interaction with a relational database Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 14/27
PRMs Random generation Population Conclusion ongoing work The overall process PPRRMM DDBB iinnssttaannccee Instantiate Sample Model generation RReellaattiioonnaall SScchheemmaa PPrroobbaabbiilliissttiiccddeeppeennddeenncciieess Instance generation RReellaattiioonnaall SSkkeelleettoonn PPrroobbaabbiilliissttiiccddeeppeennddeenncciieess GGrroouunnddBBNN Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 15/27
PRMs Random generation Population Conclusion ongoing work The overall platform RDB Visualization Inference Learning PRM PRM API Parameters learning Structure learning + score-based + constraint-based + Hybrid Statistical learning + Bayesian learning Benchmarking + Evaluation FIGURE: PRM API under the PILGRIM platform Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 16/27
PRMs Random generation Population Conclusion ongoing work Outline ... 1. PRMs 2. Random generation 2.1. Relational schema random generation 2.2. PRM random generation 3. Population 4. Conclusion ongoing work Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 17/27
PRMs Random generation Population Conclusion ongoing work Generating the relational schema Hypotheses with respect to the relational model definition (Date, 08) : avoid referential cycles when generating constraints 8Xi ;Xi 2 X there exist a referential path from Xi to Xj : searching for DAG structures with a single connected component Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 18/27
PRMs Random generation Population Conclusion ongoing work Example Clazz0 Clazz1 Clazz2 Clazz3 n1 n0 n2 n3 Clazz0 Clazz1 Clazz2 Clazz3 att0 att1 att0 att1 att2 att0 att1 att2 att3 att0 Clazz0 Clazz1 Clazz2 Clazz3 clazz0id clazz1id clazz3id clazz2id clazz1id clazz0id clazz3id clazz2id Clazz0 Clazz1 #clazz1fkatt10 Clazz2 Clazz3 att0 att1 att0 att1 att2 att0 att1 att2 att3 att0 clazz1id clazz0id clazz3id clazz2id #clazz0fkatt03 #claszz1fkatt13 #clazz2fkatt23 #clazz1fkatt12 G generate primary keys generate attributes generate foreign keys generate foreign keys 1 2 3 3 Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 19/27
PRMs Random generation Population Conclusion ongoing work Generating the PRM Goal randomly generating probabilistic dependencies S between the attributes of the classes structure sampling CPDs like for usual BNs Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 20/27
PRMs Random generation Population Conclusion ongoing work Generating the PRM Goal Hypothesis the dependency structure S should be a DAG one descriptive attribute is dependent with another one, but with which slot chain ? we need a user-defined maximum slot chain length Kmax Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 20/27
PRMs Random generation Population Conclusion ongoing work Generating the PRM Goal Hypothesis Principle step I : add dependencies while keeping a DAG structure, first into classes, then intra classes step II : random choice of a legal slot chain weighted by its length Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 20/27
PRMs Random generation Population Conclusion ongoing work Example Clazz0 Clazz1 claszz1fkatt13. clazz1fkatt10-1] Clazz2 Clazz3 att0 att1 att0 att0 att0 clazz1fkatt10 clazz0fkatt03 claszz1fkatt13 clazz2fkatt23 clazz1fkatt12 att2 att1 att3 att1 att2 [Clazz0.clazz1fkatt10] [Clazz2.clazz1fkatt12] -1] clazz2fkatt23Calzz2.MODE [-1] MODE clazz1fkatt12clazz1fkatt12. [Clazz2.[Calzz2.clazz2fkatt23-1. MODE Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 21/27
PRMs Random generation Population Conclusion ongoing work Outline ... 1. PRMs 2. Random generation 2.1. Relational schema random generation 2.2. PRM random generation 3. Population 4. Conclusion ongoing work Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 22/27
PRMs Random generation Population Conclusion ongoing work GBN creation and sampling Generating the relational skeleton by generating a random number of objects per class adding links between objects : all referencing classes have their generated objects related to objects from referenced classes Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 23/27
PRMs Random generation Population Conclusion ongoing work GBN creation and sampling Generating the relational skeleton Creating the GBN the GBN is constructed by using the CPDs already defined by the PRM Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 23/27
PRMs Random generation Population Conclusion ongoing work GBN creation and sampling Generating the relational skeleton Creating the GBN Populating the database sampling from the GBN Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 23/27
PRMs Random generation Population Conclusion ongoing work Example Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 24/27
PRMs Random generation Population Conclusion ongoing work Outline ... 1. PRMs 2. Random generation 2.1. Relational schema random generation 2.2. PRM random generation 3. Population 4. Conclusion ongoing work Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 25/27
PRMs Random generation Population Conclusion ongoing work Conclusion - Perspectives Conclusion we proposed one process to randomly generate PRMs and instantiate them to populate a relational database Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 26/27
PRMs Random generation Population Conclusion ongoing work Conclusion - Perspectives Conclusion we proposed one process to randomly generate PRMs and instantiate them to populate a relational database Ongoing work propose a new approach to learn PRM structure from relational data comparing it with existing state-of-the-art approaches, with databases using our random generation process extend our generation approach to address other relational probabilistic graphical models (e.g., DAPER) Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 26/27
A suivre :-) Jeudi 9h30 - Ghada Trabelsi - Evaluation des algos d’apprentissage de structure des RB dynamiques Jeudi 10h - Anthony Coutant - Apprentissage d’une extension des PRM Vendredi 10h30 - Maroua Haddad - Apprentissage des réseaux possibilistes D Données Data U Connaissances Utilisateurs User Ke Knowledge
A suivre :-) Jeudi 9h30 - Ghada Trabelsi - Evaluation des algos d’apprentissage de structure des RB dynamiques Jeudi 10h - Anthony Coutant - Apprentissage d’une extension des PRM Vendredi 10h30 - Maroua Haddad - Apprentissage des réseaux possibilistes Any question ?

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Random Generation of Relational Bayesian Networks

  • 1. PRMs Random generation Population Conclusion & ongoing work Génération aléatoire de réseaux Bayésiens relationnels Mouna Ben Ishak1;2, Philippe Leray2 and Nahla Ben Amor1 1 Laboratoire de Recherche Opérationnelle de Décision et de Contrôle de Processus (LARODEC), ISG Tunis, Tunisie 2 Laboratoire d’Informatique de Nantes Atlantique (LINA), UMR CNRS 6241, Université de Nantes, France Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 1/27
  • 2. PRMs Random generation Population Conclusion & ongoing work Motivation (1/3) f1 f2 f3 … fm x1 v1 v3 v2 … v1 x2 v2 v1 V3 … v1 x3 v1 v2 v3 … v2 … … … … … … xn v1 v3 v2 … v1 Learned model Features Observations Training set Learning algorithm Flat data representation Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 2/27
  • 3. PRMs Random generation Population Conclusion & ongoing work Motivation (2/3) Presentation Presentation Business logic DDDaaatttaaa Business logic DDDaaatttaaa Relational representation!!! Relational representation!!! How to use relational data with classical machine learning algorithms? How to use this data with classical machine learning algorithms? Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 3/27
  • 4. PRMs Random generation Population Conclusion & ongoing work Motivation (3/3) Propositionalization It has been shown that propositionalization is not always appropriate to perform learning in relational domains (Maier et al., 10) Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 4/27
  • 5. PRMs Random generation Population Conclusion & ongoing work Motivation (3/3) Propositionalization It has been shown that propositionalization is not always appropriate to perform learning in relational domains (Maier et al., 10) Relational transition Extend classical machine learning techniques in the context of relational data representation Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 4/27
  • 6. PRMs Random generation Population Conclusion & ongoing work Outline ... 1. PRMs 2. Random generation 2.1. Relational schema random generation 2.2. PRM random generation 3. Population 4. Conclusion & ongoing work Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 5/27
  • 7. PRMs Random generation Population Conclusion & ongoing work Bayesian networks (BN) (Pearl, 85) Definition G qualitative description of conditional dependences / independences between variables directed acyclic graph (DAG) quantitative description of these dependences conditional probability distributions (CPDs) Gender Occupation Age Low Middle High Age Occupation Oc1 Oc2 Oc3 Low,F 0.5 0.1 0.4 Low,M 0.3 0.5 0.2 Middle,F 0.2 0.4 0.4 Middle,M 0.9 0.1 0 High,F 0.3 0.5 0.2 High,M 0.2 0.3 0.5 Gender M F Gender 0.4 0.3 0.3 Age 0.4 0.6 Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 6/27
  • 8. PRMs Random generation Population Conclusion ongoing work BN structure learning Constraint-based methods BN = independence model ) find cond. indep. (CI) in data in order to build the DAG ex : IC (Pearl Verma, 91), PC (Spirtes et al., 93) problem : reliability of CI statistical tests (ok for n 100) Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 7/27
  • 9. PRMs Random generation Population Conclusion ongoing work BN structure learning Constraint-based methods BN = independence model problem : reliability of CI statistical tests (ok for n 100) Score-based methods BN = probabilistic model that must fit data as well as possible ) search the DAG space in order to maximize a scoring function ex : Maximum Weighted Spanning Tree (Chow Liu, 68), Greedy Search (Chickering, 95), evolutionary approaches (Larranaga et al., 96) (Wang Yang, 10) problem : size of search space (ok for n 1000) Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 7/27
  • 10. PRMs Random generation Population Conclusion ongoing work BN structure learning Constraint-based methods BN = independence model problem : reliability of CI statistical tests (ok for n 100) Score-based methods BN = probabilistic model that must fit data as well as possible problem : size of search space (ok for n 1000) Hybrid/ local search methods local search / neighbor identification (statistical tests) global (score) optimization usually for scalability reasons (ok for high n) Génératioenxalé:atoMireMdeHrésCeauax Blgayoésrieitnhs rmelatio(nTneslsamardJFinRBo’1s4 et a25l-.2,70jui6n,)IHP, Paris, France 7/27
  • 11. PRMs Random generation Population Conclusion ongoing work Evaluating structure learning algorithms Standard practice generating data from a reference model applying a structure learning algorithm with this data comparing the learned and reference models Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 8/27
  • 12. PRMs Random generation Population Conclusion ongoing work Evaluating structure learning algorithms Standard practice generating data from a reference model applying a structure learning algorithm with this data comparing the learned and reference models Which reference model ? existence of reference benchmarks (e.g., Asia, Alarm, ...). randomly generated models (Ide et al., 04) arbitrarily large BN by tiling (Tsamardinos et al., 06) Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 8/27
  • 13. PRMs Random generation Population Conclusion ongoing work Which kind of data ? BN learning from data... but which kind of data ? Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 9/27
  • 14. PRMs Random generation Population Conclusion ongoing work Which kind of data ? BN learning from data... but which kind of data ? how to deal with structured data ? Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 9/27
  • 15. PRMs Random generation Population Conclusion ongoing work Relational schema Movie User Vote Movie User Rating Gender Age Occupation RealiseDate Genre A relational schema R classes + relational variables Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 10/27
  • 16. PRMs Random generation Population Conclusion ongoing work Relational schema Movie User Vote Movie User Rating Gender Age Occupation RealiseDate Genre A relational schema R classes + relational variables reference slots (e.g., Vote:Movie;Vote:User) Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 10/27
  • 17. PRMs Random generation Population Conclusion ongoing work Relational schema Movie User Vote Movie User Rating Gender Age Occupation RealiseDate Genre A relational schema R classes + relational variables reference slots (e.g., Vote:Movie;Vote:User) slot chain = a sequence of reference slots allow to walk in the relational schema to create new variables Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 10/27
  • 18. PRMs Random generation Population Conclusion ongoing work Relational schema Movie User Vote Movie User Rating Gender Age Occupation RealiseDate Genre A relational schema R classes + relational variables reference slots (e.g., Vote:Movie;Vote:User) slot chain = a sequence of reference slots allow to walk in the relational schema to create new variables ex : Vote:User:User1:Movie : all the movies voted by a particular user Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 10/27
  • 19. PRMs Random generation Population Conclusion ongoing work Probabilistic Relational Models (Koller Pfeffer, 98) Definition A PRM associated to R : a qualitative dependency structure S (with possible long slot chains and aggregation functions) a set of parameters S Vote User.Gender M F 0.4 0.6 Rating Movie User RealiseDate Genre Gender Age Occupation Movie.Genre Votes.Rating Low High Drama, M 0.5 0.5 Drama, F 0.3 0.7 Horror, M 0.2 0.8 Horror, F 0.9 0.1 Comedy, M 0.5 0.5 Comedy, F 0.6 0.4 User.Gender Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 11/27
  • 20. PRMs Random generation Population Conclusion ongoing work Probabilistic Relational Models Definition Vote User.Gender M F 0.4 0.6 Rating Movie User RealiseDate Genre Gender Age Occupation Movie.Genre Votes.Rating Low High Drama, M 0.5 0.5 Drama, F 0.3 0.7 Horror, M 0.2 0.8 Horror, F 0.9 0.1 Comedy, M 0.5 0.5 Comedy, F 0.6 0.4 User.Gender Aggregators Vote:User:User1:Movie:genre ! Vote:rating movie rating from one user can be dependent with the genre of all the movies voted by this user how to describe the dependency with an unknown number of parents ? solution : using an aggregated value, e.g. = MODE Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 11/27
  • 21. PRMs Random generation Population Conclusion ongoing work Ground Bayesian Network GBN BN created from one PRM and an instantiated database = relational skeleton Age Rating Age Gender Occupation Age Gender Occupation Gender Occupation Genre RealiseDate Genre Genre Genre Genre U1 U2 U3 M1 M2 M3 M4 M5 #U1, #M1 Rating #U1, #M2 Rating #U2, #M1 Rating #U2, #M3 Rating #U2, #M4 Rating #U3, #M1 Rating #U3, #M2 Rating #U3, #M3 Rating #U3, #M5 RealiseDate RealiseDate RealiseDate RealiseDate Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 12/27
  • 22. PRMs Random generation Population Conclusion ongoing work Ground Bayesian Network GBN BN created from one PRM and an instantiated database = relational skeleton + probabilistic dependencies used for probabilistic inference Age Rating Age Gender Occupation Age Gender Occupation Gender Occupation Genre RealiseDate Genre Genre Genre Genre U1 U2 U3 M1 M2 M3 M4 M5 #U1, #M1 Rating #U1, #M2 Rating #U2, #M1 Rating #U2, #M3 Rating #U2, #M4 Rating #U3, #M1 Rating #U3, #M2 Rating #U3, #M3 Rating #U3, #M5 RealiseDate RealiseDate RealiseDate RealiseDate Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 12/27
  • 23. PRMs Random generation Population Conclusion ongoing work PRM structure learning Constraint-based methods relational PC (Maier et al., 10) relational CD (Maier et al., 13) don’t deal with aggregation functions Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 13/27
  • 24. PRMs Random generation Population Conclusion ongoing work PRM structure learning Constraint-based methods Score-based methods greedy search (Getoor et al., 07) Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 13/27
  • 25. PRMs Random generation Population Conclusion ongoing work PRM structure learning Constraint-based methods Score-based methods Hybrid methods relational MMHC (Ben Ishak et al., in progress) Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 13/27
  • 26. PRMs Random generation Population Conclusion ongoing work PRM structure learning Constraint-based methods Score-based methods Hybrid methods Critics - previous works lack of evaluation process, in a common framework absence of relational benchmarks for evaluation algorithms absence of relational data generation process Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 13/27
  • 27. PRMs Random generation Population Conclusion ongoing work PRM structure learning Constraint-based methods Score-based methods Hybrid methods Critics - previous works Proposition a synthetic approach to randomly generate and populate PRMs and databases Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 13/27
  • 28. PRMs Random generation Population Conclusion ongoing work PRMs random generation Related work (Maier et al., 10, 13) relational schemas are generated as tree structure ... too simple (Wuillemin et al., 12) object-oriented paradigm rather than relational one no population nor interaction with a relational database Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 14/27
  • 29. PRMs Random generation Population Conclusion ongoing work The overall process PPRRMM DDBB iinnssttaannccee Instantiate Sample Model generation RReellaattiioonnaall SScchheemmaa PPrroobbaabbiilliissttiiccddeeppeennddeenncciieess Instance generation RReellaattiioonnaall SSkkeelleettoonn PPrroobbaabbiilliissttiiccddeeppeennddeenncciieess GGrroouunnddBBNN Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 15/27
  • 30. PRMs Random generation Population Conclusion ongoing work The overall platform RDB Visualization Inference Learning PRM PRM API Parameters learning Structure learning + score-based + constraint-based + Hybrid Statistical learning + Bayesian learning Benchmarking + Evaluation FIGURE: PRM API under the PILGRIM platform Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 16/27
  • 31. PRMs Random generation Population Conclusion ongoing work Outline ... 1. PRMs 2. Random generation 2.1. Relational schema random generation 2.2. PRM random generation 3. Population 4. Conclusion ongoing work Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 17/27
  • 32. PRMs Random generation Population Conclusion ongoing work Generating the relational schema Hypotheses with respect to the relational model definition (Date, 08) : avoid referential cycles when generating constraints 8Xi ;Xi 2 X there exist a referential path from Xi to Xj : searching for DAG structures with a single connected component Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 18/27
  • 33. PRMs Random generation Population Conclusion ongoing work Example Clazz0 Clazz1 Clazz2 Clazz3 n1 n0 n2 n3 Clazz0 Clazz1 Clazz2 Clazz3 att0 att1 att0 att1 att2 att0 att1 att2 att3 att0 Clazz0 Clazz1 Clazz2 Clazz3 clazz0id clazz1id clazz3id clazz2id clazz1id clazz0id clazz3id clazz2id Clazz0 Clazz1 #clazz1fkatt10 Clazz2 Clazz3 att0 att1 att0 att1 att2 att0 att1 att2 att3 att0 clazz1id clazz0id clazz3id clazz2id #clazz0fkatt03 #claszz1fkatt13 #clazz2fkatt23 #clazz1fkatt12 G generate primary keys generate attributes generate foreign keys generate foreign keys 1 2 3 3 Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 19/27
  • 34. PRMs Random generation Population Conclusion ongoing work Generating the PRM Goal randomly generating probabilistic dependencies S between the attributes of the classes structure sampling CPDs like for usual BNs Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 20/27
  • 35. PRMs Random generation Population Conclusion ongoing work Generating the PRM Goal Hypothesis the dependency structure S should be a DAG one descriptive attribute is dependent with another one, but with which slot chain ? we need a user-defined maximum slot chain length Kmax Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 20/27
  • 36. PRMs Random generation Population Conclusion ongoing work Generating the PRM Goal Hypothesis Principle step I : add dependencies while keeping a DAG structure, first into classes, then intra classes step II : random choice of a legal slot chain weighted by its length Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 20/27
  • 37. PRMs Random generation Population Conclusion ongoing work Example Clazz0 Clazz1 claszz1fkatt13. clazz1fkatt10-1] Clazz2 Clazz3 att0 att1 att0 att0 att0 clazz1fkatt10 clazz0fkatt03 claszz1fkatt13 clazz2fkatt23 clazz1fkatt12 att2 att1 att3 att1 att2 [Clazz0.clazz1fkatt10] [Clazz2.clazz1fkatt12] -1] clazz2fkatt23Calzz2.MODE [-1] MODE clazz1fkatt12clazz1fkatt12. [Clazz2.[Calzz2.clazz2fkatt23-1. MODE Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 21/27
  • 38. PRMs Random generation Population Conclusion ongoing work Outline ... 1. PRMs 2. Random generation 2.1. Relational schema random generation 2.2. PRM random generation 3. Population 4. Conclusion ongoing work Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 22/27
  • 39. PRMs Random generation Population Conclusion ongoing work GBN creation and sampling Generating the relational skeleton by generating a random number of objects per class adding links between objects : all referencing classes have their generated objects related to objects from referenced classes Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 23/27
  • 40. PRMs Random generation Population Conclusion ongoing work GBN creation and sampling Generating the relational skeleton Creating the GBN the GBN is constructed by using the CPDs already defined by the PRM Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 23/27
  • 41. PRMs Random generation Population Conclusion ongoing work GBN creation and sampling Generating the relational skeleton Creating the GBN Populating the database sampling from the GBN Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 23/27
  • 42. PRMs Random generation Population Conclusion ongoing work Example Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 24/27
  • 43. PRMs Random generation Population Conclusion ongoing work Outline ... 1. PRMs 2. Random generation 2.1. Relational schema random generation 2.2. PRM random generation 3. Population 4. Conclusion ongoing work Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 25/27
  • 44. PRMs Random generation Population Conclusion ongoing work Conclusion - Perspectives Conclusion we proposed one process to randomly generate PRMs and instantiate them to populate a relational database Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 26/27
  • 45. PRMs Random generation Population Conclusion ongoing work Conclusion - Perspectives Conclusion we proposed one process to randomly generate PRMs and instantiate them to populate a relational database Ongoing work propose a new approach to learn PRM structure from relational data comparing it with existing state-of-the-art approaches, with databases using our random generation process extend our generation approach to address other relational probabilistic graphical models (e.g., DAPER) Génération aléatoire de réseaux Bayésiens relationnels JFRB’14 25-27 juin, IHP, Paris, France 26/27
  • 46. A suivre :-) Jeudi 9h30 - Ghada Trabelsi - Evaluation des algos d’apprentissage de structure des RB dynamiques Jeudi 10h - Anthony Coutant - Apprentissage d’une extension des PRM Vendredi 10h30 - Maroua Haddad - Apprentissage des réseaux possibilistes D Données Data U Connaissances Utilisateurs User Ke Knowledge
  • 47. A suivre :-) Jeudi 9h30 - Ghada Trabelsi - Evaluation des algos d’apprentissage de structure des RB dynamiques Jeudi 10h - Anthony Coutant - Apprentissage d’une extension des PRM Vendredi 10h30 - Maroua Haddad - Apprentissage des réseaux possibilistes Any question ?