I am a Ph.D. candidate at the University of Rochester working with Prof. Henry Kautz. My research interests include topics related to Markov logic, random fields, probabilistic graphical models, exponential families of probability distributions and machine learning in general.
Hard constraints (given as first order logic formulas in Markov logic) together with the observations can force truth values on a large set of ground atoms. This results in a pruned state space, moreover we may no longer need to instantiate many groundings of the soft constraints in the network. We used a hyper-arc consistency algorithm to derive new ground literals as a preprocessing step. As a result we ended up saving a lot both on the space and time complexity of the whole inference algorithm. (Project with Prof. Henry Kautz and Prof. Parag Singla, IIT, Delhi.)
Tivadar Papai, Parag Singla, & Henry Kautz (2011). Constraint Propagation for Efficient Inference in Markov Logic. J. Lee (Ed.): Proceedings of the 17th International Conference on Principles and Practice of Constraint Programming (CP 2011), LNCS 6876, pp. 691705. Springer, Heidelberg.
Incorporating the knowledge of a domain expert into Markov logic networks is not straightforward, because the natural parameterization, i.e., the weights of formulas in the knowledge base are hard to relate to the (conditional) probabilities of formulas. We show that with the proper reparameterization the expert's (possibly inconsistent) knowledge can be combined with the data within the framework of Bayesian statistics. (Joint work with Dr. Shalini Ghosh, SRI International and Prof. Henry Kautz.)
Tivadar Papai, Shalini Ghosh, and Henry Kautz (2012). Combining Subjective Probabilities and Data in Training Markov Logic Networks. In Proceedings of the European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases (ECML-PKDD 2012), Bristol, UK, Septemeber 2012.
The marginal probabilities of ground atoms when Markov logic networks are unrolled into conditional or Markov random fields depend on the size of the domain. We restrict our research to sequential (temporal) data. We propose a different discriminative graphical model that we can unroll our Markov logic theory into which does not have certain undesired theoretical weaknesses of MRFs/CRFs, and naturally gives way for implementing of efficient particle filtering. (Work with Prof. Henry Kautz and Prof. Daniel Stefankovic.)
Tivadar Papai, Henry Kautz, Daniel Stefankovic. Slice Normalized Dynamic Markov logic Networks. In Proceedings of Advances in Neural Information Processing Systems 25 (NIPS 2012}), Lake Tahoe, NV, USA, November 2012.
We propose Modal Markov Logic as a framework to reason under the principle of maximum entropy for modal logics K45, KD45 and S5. We choose the state space to contain all the non-equivalent pointed Kripke structures (epistemic situations) over a fixed set of propositions. Although the size of the state space grows doubly exponentially with the number of propositions in the domain, we propose an exact inference algorithm which has only exponential cost in the size of the knowledge base.
Tivadar Papai, Henry Kautz, Daniel Stefankovic. Reasoning Under the Principle of Maximum Entropy for Modal Logics K45, KD45, and S5. In Proceedings of the 14th Conference on Theoretical Aspects of Rationality and Knowledge (TARK 2013), Chennai, India, January 2013.
Tivadar Papai, Henry Kautz. Modal Markov Logic for Multiple Agents. (Under review.)