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.

The traditional way of obtaining models from data, inductive learning, has proved itself both in theory and in many practical applications. However, in domains where data is difficult or expensive to obtain, e.g., medicine, deep transfer learning is a more promising technique. It circumvents the model acquisition difficulties caused by scarce data in a target domain by carrying over structural properties of a model learned in a source domain where training data is ample. Nonetheless, the lack of a principled view of transfer learning so far has limited its adoption. In this paper, we address this issue by regarding transfer learning as a process that biases learning in a target domain in favor of patterns useful in a source domain. Specifically, we consider a first-order logic model of the data as an instantiation of a set of second-order templates. Hence, the usefulness of a model is partly determined by the learner's prior distribution over these template sets. The main insight of our work is that transferring knowledge amounts to acquiring a posterior over the second-order template sets by learning in the source domain and using this posterior when learning in the target setting. Our experimental evaluation demonstrates our approach to outperform the existing transfer learning techniques in terms of accuracy and runtime.

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.

Image clustering and visual codebook learning are two fundamental problems in computer vision and they are tightly related. On one hand, a good codebook can generate effective feature representations which largely affect clustering performance. On the other hand, class labels obtained from image clustering can serve as supervised information to guide codebook learning. Traditionally, these two processes are conducted separately and their correlation is generally ignored.In this paper, we propose a Double Layer Gaussian Mixture Model (DLGMM) to simultaneously perform image clustering and codebook learning. In DLGMM, two tasks are seamlessly coupled and can mutually promote each other. Cluster labels and codebook are jointly estimated to achieve the overall best performance. To incorporate the spatial coherence between neighboring visual patches, we propose a Spatially Coherent DLGMM which uses a Markov Random Field to encourage neighboring patches to share the same visual word label.We use variational inference to approximate the posterior of latent variables and learn model parameters.Experiments on two datasets demonstrate the effectiveness of two models.

Recent advances in Symbolic Dynamic Programming (SDP) combined withthe extended algebraic decision diagram (XADD) have provided exactsolutions for expressive subclasses of finite-horizon Hybrid MarkovDecision Processes (HMDPs) with mixed continuous and discrete stateand action parameters. Unfortunately, SDP suffers from two majordrawbacks: (1) it solves for all states and can be intractable formany problems that inherently have large optimal XADD value functionrepresentations; and (2) it cannot maintain compact (pruned) XADDrepresentations for domains with nonlinear dynamics and reward due tothe need for nonlinear constraint checking. In this work, wesimultaneously address both of these problems by introducing real-timeSDP (RTSDP). RTSDP addresses (1) by focusing the solution and valuerepresentation only on regions reachable from a set of initial statesand RTSDP addresses (2) by using visited states as witnesses ofreachable regions to assist in pruning irrelevant or unreachable(nonlinear) regions of the value function. To this end, RTSDP enjoysprovable convergence over the set of initial states and substantialspace and time savings over SDP as we demonstrate in a variety of hybrid domains ranging from inventory to reservoir to traffic control.

We consider partially observable Markov decision processes (POMDPs) with a set of target states and every transition is associated with an integer cost. The optimization objective we study asks to minimize the expected total cost till the target set is reached, while ensuring that the target set is reached almost-surely (with probability 1). We show that for integer costs approximating the optimal cost is undecidable. For positive costs, our results are as follows: (i) we establish matching lower and upper bounds for the optimal cost and the bound is double exponential; (ii) we show that the problem of approximating the optimal cost is decidable and present approximation algorithms developing on the existing algorithms for POMDPs with finite-horizon objectives. While the worst-case running time of our algorithm is double exponential, we present efficient stopping criteria for the algorithm and show experimentally that it performs well in many examples of interest.

Twitter, as a popular microblogging service, has become a new information channel for users to receive and exchange the mostup-to-date information on current events. However, since there is no control on how users can publish messages on Twitter, finding newsworthy events from Twitter becomes a difficult task like "finding a needle in a haystack". In this paper we propose a general unsupervised framework to explore events from tweets, which consists of a pipeline process of filtering, extraction and categorization. To filter out noisy tweets, the filtering step exploits a lexicon-based approach to separate tweets that are event-related from those that are not. Then, based on these event-related tweets, the structured representations of events are extracted and categorized automatically using an unsupervised Bayesian model without the use of any labelled data. Moreover, the categorized events are assigned with the event type labels without human intervention. The proposed framework has been evaluated on over 60 millions tweets which were collected for one month in December 2010. A precision of 70.49% is achieved in event extraction, outperforming a competitive baseline by nearly 6%. Events are also clustered into coherence groups with the automatically assigned event type label.

Latent author attribute prediction in social media provides a novel set of conditions for the construction of supervised classification models. With individual authors as training and test instances, their associated content ("features") are made available incrementally over time, as they converse over discussion forums. We propose various approaches to handling this dynamic data, from traditional batch training and testing, to incremental bootstrapping, and then active learning via crowdsourcing. Our underlying model relies on an intuitive application of Bayes rule, which should be easy to adopt by the community, thus allowing for a general shift towards online modeling for social media.

We present a probabilistic model for tensor decomposition where one or more tensor modes may have side-information about the mode entities in form of their features and/or their adjacency network. We consider a Bayesian approach based on the Canonical PARAFAC (CP) decomposition and enrich this single-layer decomposition approach with a two-layer decomposition. The second layer fits a factor model for each layer-one factor matrix and models the factor matrix via the mode entities' features and/or the network between the mode entities. The second-layer decomposition of each factor matrix also learns a binary latent representation for the entities of that mode, which can be useful in its own right. Our model can handle both continuous as well as binary tensor observations. Another appealing aspect of our model is the simplicity of the model inference, with easy-to-sample Gibbs updates. We demonstrate the results of our model on several benchmarks datasets, consisting of both real and binary tensors.

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.