Markov Models
Mixing Time Estimation in Reversible Markov Chains from a Single Sample Path
Daniel J. Hsu, Aryeh Kontorovich, Csaba Szepesvari
The interval is computed from a single finite-length sample path from the Markov chain, and does not require the knowledge of any parameters of the chain. This stands in contrast to previous approaches, which either only provide point estimates, or require a reset mechanism, or additional prior knowledge.
Lifted Symmetry Detection and Breaking for MAP Inference
Timothy Kopp, Parag Singla, Henry Kautz
Symmetry breaking is a technique for speeding up propositional satisfiability testing by adding constraints to the theory that restrict the search space while preserving satisfiability. In this work, we extend symmetry breaking to the problem of model finding in weighted and unweighted relational theories, a class of problems that includes MAP inference in Markov Logic and similar statistical-relational languages. We introduce term symmetries, which are induced by an evidence set and extend to symmetries over a relational theory. We provide the important special case of term equivalent symmetries, showing that such symmetries can be found in low-degree polynomial time. We show how to break an exponential number of these symmetries with added constraints whose number is linear in the size of the domain. We demonstrate the effectiveness of these techniques through experiments in two relational domains. We also discuss the connections between relational symmetry breaking and work on lifted inference in statistical-relational reasoning.
Supplementary Materials for Bayesian Robust Optimization for Imitation Learning Daniel S. Brown
When using the robust performance metric described in Section 4.2, we have We solve the above linear program to obtain the results presented in Section 5.1. Work done while at UT Austin. We use Scipy's linear programming software (v 1.4.1) MDP is solved to obtain the sample's likelihood and determine the transition probabilities within the Markov chain. We used a learning rate of 0.01.