Uncertain and negative evidence in continuous time Bayesian networks

The continuous time Bayesian network (CTBN) enables reasoning about complex systems by representing the system as a factored, finite-state, continuous-time Markov process. Inference over the model incorporates evidence, given as state observations through time. The time dimension introduces several new types of evidence that are not found with static models. In this work, we present a comprehensive look at the types of evidence in CTBNs. Moreover, we define and extend inference to reason under uncertainty in the presence of uncertain evidence, as well as negative evidence, concepts extended to static models but not yet introduced into the CTBN model. Created a taxonomy of discrete-state, continuous-time evidence types.Showed generalization and combination relationships between evidence types.Demonstrated the effects of evidence types on a real-world network.Extended exact and approximate inference for CTBNs to handle new evidence types.Demonstrated convergence and scaling of CTBN approximate inference algorithm.

[1]  Sriraam Natarajan,et al.  Learning When to Reject an Importance Sample , 2013, AAAI.

[2]  Jeff A. Bilmes,et al.  On Virtual Evidence and Soft Evidence in Bayesian Networks , 2004 .

[3]  Henry A. Kautz,et al.  Extending Continuous Time Bayesian Networks , 2005, AAAI.

[4]  Jinyuan You,et al.  Update Rules for Parameter Estimation in Continuous Time Bayesian Network , 2006, PRICAI.

[5]  Yun Peng,et al.  Belief Update in Bayesian Networks Using Uncertain Evidence , 2006, 2006 18th IEEE International Conference on Tools with Artificial Intelligence (ICTAI'06).

[6]  Jeffrey S. Chase,et al.  Proceedings of the 2nd USENIX workshop on Tackling computer systems problems with machine learning techniques , 2007 .

[7]  Daphne Koller,et al.  Expectation Maximization and Complex Duration Distributions for Continuous Time Bayesian Networks , 2005, UAI.

[8]  Jing Xu.  A Continuous Time Bayesian Network Approach for Intrusion Detection , 2010 .

[9]  Luigi Portinale,et al.  A Petri Net-Based Tool for the Analysis of Generalized Continuous Time Bayesian Networks , 2014 .

[10]  Ido Cohn.  Mean Field Variational Approximations in Continuous-Time Markov Processes , 2009 .

[11]  David Page,et al.  Forest-Based Point Process for Event Prediction from Electronic Health Records , 2013, ECML/PKDD.

[12]  Adnan Darwiche,et al.  On the Revision of Probabilistic Beliefs using Uncertain Evidence , 2003, IJCAI.

[13]  Fabio Stella,et al.  Conditional Log-Likelihood for Continuous Time Bayesian Network Classifiers , 2013 .

[14]  Fabio Stella,et al.  Continuous time Bayesian network classifiers , 2012, J. Biomed. Informatics.

[15]  Eric Horvitz,et al.  Continuous Time Bayesian Networks for Inferring Users’ Presence and Activities with Extensions for Modeling and Evaluation , 2003 .

[16]  Christian R. Shelton,et al.  Factored Filtering of Continuous-Time Systems , 2011, UAI.

[17]  John W. Sheppard,et al.  Inference Complexity in Continuous Time Bayesian Networks , 2014, UAI.

[18]  Nir Friedman,et al.  Gibbs Sampling in Factorized Continuous-Time Markov Processes , 2008, UAI.

[19]  Jing Xu,et al.  Continuous Time Bayesian Networks for Host Level Network Intrusion Detection , 2008, ECML/PKDD.

[20]  Cleve B. Moler,et al.  Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later , 1978, SIAM Rev..

[21]  Fabio Stella,et al.  Gene network inference using continuous time Bayesian networks: a comparative study and application to Th17 cell differentiation , 2014, BMC Bioinformatics.

[22]  Nir Friedman,et al.  Probabilistic Graphical Models - Principles and Techniques , 2009 .

[23]  Avi Pfeffer,et al.  Asynchronous Dynamic Bayesian Networks , 2005, UAI.

[24]  Fabio Stella,et al.  Continuous Time Bayesian Networks for Gene Network Reconstruction: A Comparative Study on Time Course Data , 2014, ISBRA.

[25]  Jing Xu,et al.  Importance Sampling for Continuous Time Bayesian Networks , 2010, J. Mach. Learn. Res..

[26]  Huidong Jin,et al.  PutMode: prediction of uncertain trajectories in moving objects databases , 2010, Applied Intelligence.

[27]  Daphne Koller,et al.  Continuous Time Bayesian Networks , 2012, UAI.

[28]  Sriraam Natarajan,et al.  Multiplicative Forests for Continuous-Time Processes , 2012, NIPS.

[29]  Jinyuan You,et al.  An Intelligent System Based On Adaptive CTBN For Uncertainty Reasoning In Sensor Networks , 2010, Intell. Autom. Soft Comput..

[30]  Shaojie Qiao,et al.  Key techniques for predicting the uncertain trajectories of moving objects with dynamic environment awareness , 2011 .

[31]  Christian R. Shelton,et al.  Solving Structured Continuous-Time Markov Decision Processes , 2008, ISAIM.

[32]  Nir Friedman,et al.  Learning Bayesian Networks with Local Structure , 1996, UAI.

[33]  Gianfranco Ciardo,et al.  Tutorial on Structured Continuous-Time Markov Processes , 2014, J. Artif. Intell. Res..

[34]  Nir Friedman,et al.  Mean Field Variational Approximation for Continuous-Time Bayesian Networks , 2009, J. Mach. Learn. Res..

[35]  Logan Perreault,et al.  Using continuous-time Bayesian networks for standards-based diagnostics and prognostics , 2014, 2014 IEEE AUTOTEST.

[36]  Communities.  British Household Panel Survey , 2014 .

[37]  Yu Fan,et al.  Learning Continuous-Time Social Network Dynamics , 2009, UAI.

[38]  Jing Xu,et al.  Intrusion Detection using Continuous Time Bayesian Networks , 2010, J. Artif. Intell. Res..

[39]  Fabio Stella,et al.  A Classification Based Scoring Function for Continuous Time Bayesian Network Classifiers , 2013, NFMCP.

[40]  Nir Friedman,et al.  Continuous-Time Belief Propagation , 2010, ICML.

[41]  Brendan Murphy,et al.  Structure from failure , 2007 .

[42]  Suchi Saria,et al.  Reasoning at the Right Time Granularity , 2007, UAI.

[43]  Luigi Portinale,et al.  Generalized Continuous Time Bayesian Networks and their GSPN Semantics , 2010 .

[44]  Yu Fan.  Continuous Time Bayesian Network Approximate Inference and Social Network Applications , 2009 .

[45]  Yu Fan,et al.  Sampling for Approximate Inference in Continuous Time Bayesian Networks , 2008, ISAIM.

[46]  Fabio Stella,et al.  Classification and clustering with continuous time Bayesian network models , 2015, Journal of Intelligent Information Systems.

[47]  Jing Xu,et al.  Continuous Time Bayesian Network Reasoning and Learning Engine , 2010, J. Mach. Learn. Res..

[48]  Fabio Stella,et al.  A continuous time Bayesian network model for cardiogenic heart failure , 2012 .

[49]  Daphne Koller,et al.  Expectation Propagation for Continuous Time Bayesian Networks , 2005, UAI.

[50]  Fabio Stella,et al.  Learning continuous time Bayesian network classifiers , 2014, Int. J. Approx. Reason..

[51]  Avi Pfeffer,et al.  Continuous Time Particle Filtering , 2005, IJCAI.

[52]  Yee Whye Teh,et al.  Fast MCMC sampling for Markov jump processes and extensions , 2012, J. Mach. Learn. Res..

[53]  C. Loan,et al.  Nineteen Dubious Ways to Compute the Exponential of a Matrix , 1978 .

[54]  Gatti,et al.  Graphical Models for Continuous Time Inference and Decision Making , 2010 .