Markov logic networks (MLNs) combine the power of first-order logic and probabilistic graphical models and as a result are ideally suited for solving large, complex problems in application domains that have both rich relational structure and large amount of uncertainty. However, inference in these rich, relational representations is quite challenging. The aim of this thesis is to advance the state-of-the-art in MLN inference, enabling it to solve much harder and more complex tasks than is possible today. To this end, I will develop techniques that exploit logical structures and symmetries that are either explicitly or implicitly encoded in the MLN representation and demonstrate their usefulness by using them to solve hard real-world problems in the field of natural language understanding.

My dissertation research focuses on the application of hierarchical learning and heuristics based on social signals to solve challenges inherent to enabling human-robot collaboration. I approach this problem through advancing the state of the art in building hierarchical task representations, multi-agent task-level planning, and learning assistive behaviors from demonstration.

We present a probabilistic extension of logic programs under the stable model semantics, inspired by the concept of Markov Logic Networks. The proposed language takes advantage of both formalisms in a single framework, allowing us to represent commonsense reasoning problems that require both logical and probabilistic reasoning in an intuitive and elaboration tolerant way.

We provide a novel, flexible, iterative refinement algorithm to automatically construct an approximate statespace representation for Markov Decision Processes (MDPs). Our approach leverages bisimulation metrics, which have been used in prior work to generate features to represent the state space of MDPs.We address a drawback of this approach, which is the expensive computation of the bisimulation metrics. We propose an algorithm to generate an iteratively improving sequence of state space partitions. Partial metric computations guide the representation search and provide much lower space and computational complexity, while maintaining strong convergence properties. We provide theoretical results guaranteeing convergence as well as experimental illustrations of the accuracy and savings (in time and memory usage) of the new algorithm, compared to traditional bisimulation metric computation.

Individual mood is important for physical and emotional well-being, creativity and working memory. However, due to the lack of long-term real tracking daily data in individual level, most current works focus their efforts on population level and short-term small group. An ignored yet important task is to find the sentiment spreading mechanism in individual level from their daily behavior data. This paper studies this task by raising the following fundamental and summarization question, being not sufficiently answered by the literature so far:Given a social network, how the sentiment spread? The current individual-level network spreading models always assume one can infect others only when he/she has been infected. Considering the negative emotion spreading characters in individual level, we loose this assumption, and give an individual negative emotion spreading model. In this paper, we propose a Graph-Coupled Hidden Markov Sentiment Model for modeling the propagation of infectious negative sentiment locally within a social network. Taking the MIT Social Evolution dataset as an example, the experimental results verify the efficacy of our techniques on real-world data.

This paper proposes a new approach to multi-object tracking by semantic topic discovery. We dynamically cluster frame-by-frame detections and treat objects as topics, allowing the application of the Dirichlet Process Mixture Model (DPMM). The tracking problem is cast as a topic-discovery task where the video sequence is treated analogously to a document. This formulation addresses tracking issues such as object exclusivity constraints as well as cannot-link constraints which are integrated without the need for heuristic thresholds. The video is temporally segmented into epochs to model the dynamics of word (superpixel) co-occurrences and to model the temporal damping effect. In experiments on public data sets we demonstrate the effectiveness of the proposed algorithm.

Most Relevant Explanation (MRE) is a new inference task in Bayesian networks that finds the most relevant partial instantiation of target variables as an explanation for given evidence by maximizing the Generalized Bayes Factor (GBF). No exact algorithm has been developed for solving MRE previously. This paper fills the void and introduces a breadth-first branch-and-bound MRE algorithm based on a novel upper bound on GBF. The bound is calculated by decomposing the computation of the score to a set of Markov blankets of subsets of evidence variables. Our empirical evaluations show that the proposed algorithm scales up exact MRE inference significantly.

Monte-Carlo Tree Search, especially UCT and its POMDP version POMCP, have demonstrated excellent performanceon many problems. However, to efficiently scale to large domains one should also exploit hierarchical structure if present. In such hierarchical domains, finding rewarded states typically requires to search deeply; covering enough such informative states very far from the root becomes computationally expensive in flat non-hierarchical search approaches. We propose novel, scalable MCTS methods which integrate atask hierarchy into the MCTS framework, specifically lead-ing to hierarchical versions of both, UCT and POMCP. The new method does not need to estimate probabilistic models of each subtask, it instead computes subtask policies purely sample-based. We evaluate the hierarchical MCTS methods on various settings such as a hierarchical MDP, a Bayesian model-based hierarchical RL problem, and a large hierarchical POMDP.

The main computational bottleneck in various sampling based and local-search based inference algorithms for Markov logic networks (e.g., Gibbs sampling, MC-SAT, MaxWalksat, etc.) is computing the number of groundings of a first-order formula that are true given a truth assignment to all of its ground atoms. We reduce this problem to the problem of counting the number of solutions of a constraint satisfaction problem (CSP) and show that during their execution, both sampling based and local-search based algorithms repeatedly solve dynamic versions of this counting problem. Deriving from the vast amount of literature on CSPs and graphical models, we propose an exact junction-tree based algorithm for computing the number of solutions of the dynamic CSP, analyze its properties, and show how it can be used to improve the computational complexity of Gibbs sampling and MaxWalksat. Empirical tests on a variety of benchmarks clearly show that our new approach is several orders of magnitude more scalable than existing approaches.

Lifted probabilistic inference algorithms have been successfully applied to a large number of symmetric graphical models. Unfortunately, the majority of real-world graphical models is asymmetric. This is even the case for relational representations when evidence is given. Therefore, more recent work in the community moved to making the models symmetric and then applying existing lifted inference algorithms. However, this approach has two shortcomings. First, all existing over-symmetric approximations require a relational representation such as Markov logic networks. Second, the induced symmetries often change the distribution significantly, making the computed probabilities highly biased. We present a framework for probabilistic sampling-based inference that only uses the induced approximate symmetries to propose steps in a Metropolis-Hastings style Markov chain. The framework, therefore, leads to improved probability estimates while remaining unbiased. Experiments demonstrate that the approach outperforms existing MCMC algorithms.