We present a method for unsupervised learning of event classes from videos in which multiple actions might occur simultaneously. It is assumed that all such activities are produced from an underlying set of event class generators. The learning task is then to recover this generative process from visual data. A set of event classes is derived from the most likely decomposition of the tracks into a set of labelled events involving subsets of interacting tracks. Interactions between subsets of tracks are modelled as a relational graph structure that captures qualitative spatio-temporal relationships between these tracks. The posterior probability of candidate solutions favours decompositions in which events of the same class have a similar relational structure, together with other measures of well-formedness. A Markov Chain Monte Carlo (MCMC) procedure is used to efficiently search for the MAP solution. This search moves between possible decompositions of the tracks into sets of unlabelled events and at each move adds a close to optimal labelling (for this decomposition) using spectral clustering. Experiments on real data show that the discovered event classes are often semantically meaningful and correspond well with groundtruth event classes assigned by hand.

Trial-based approaches offer an efficient way to solve single-agent MDPs and POMDPs. These approaches allow agents to focus their computations on regions of the environment they encounter during the trials, leading to significant computational savings. We present a novel trial-based dynamic programming (TBDP) algorithm for DEC-POMDPs that extends these benefits to multi-agent settings. The algorithm uses trial-based methods for both belief generation and policy evaluation. Policy improvement is implemented efficiently using linear programming and a sub-policy reuse technique that helps bound the amount of memory. The results show that TBDP can produce significant value improvements and is much faster than the best existing planning algorithms.

Constructing models of mobile agents can be difficult without domain-specific knowledge. Parametric models flexible enough to capture all mobility patterns that an expert believes are possible are often large, requiring a great deal of training data. In contrast, nonparametric models are extremely flexible and can generalize well with relatively little training data. We propose modeling the mobility patterns of moving agents as a mixture of Gaussian processes (GP) with a Dirichlet process (DP) prior over mixture weights. The GP provides a flexible representation for each individual mobility pattern, while the DP assigns observed trajectories to particular mobility patterns. Both the GPs and the DP adjust the model's complexity based on available data, implicitly avoiding issues of over-fitting or under-fitting. We apply our model to a helicopter-based tracking task, where the mobility patterns of the tracked agents — cars — are learned from real data collected from taxis in the greater Boston area.

Ontology matching is the problem of determining correspondences between concepts, properties, and individuals of different heterogeneous ontologies. With this paper we present a novel probabilistic-logical framework for ontology matching based on Markov logic. We define the syntax and semantics and provide a formalization of the ontology matching problem within the framework. The approach has several advantages over existing methods such as ease of experimentation, incoherence mitigation during the alignment process, and the incorporation of a-priori confidence values. We show empirically that the approach is efficient and more accurate than existing matchers on an established ontology alignment benchmark dataset.

With the development of Web 2.0, sentiment analysis has now become a popular research problem to tackle. Recently, topic models have been introduced for the simultaneous analysis for topics and the sentiment in a document. These studies, which jointly model topic and sentiment, take the advantage of the relationship between topics and sentiment, and are shown to be superior to traditional sentiment analysis tools. However, most of them make the assumption that, given the parameters, the sentiments of the words in the document are all independent. In our observation, in contrast, sentiments are expressed in a coherent way. The local conjunctive words, such as “and” or “but”, are often indicative of sentiment transitions. In this paper, we propose a major departure from the previous approaches by making two linked contributions. First, we assume that the sentiments are related to the topic in the document, and put forward a joint sentiment and topic model, i.e. Sentiment-LDA. Second, we observe that sentiments are dependent on local context. Thus, we further extend the Sentiment-LDA model to Dependency-Sentiment-LDA model by relaxing the sentiment independent assumption in Sentiment-LDA. The sentiments of words are viewed as a Markov chain in Dependency-Sentiment-LDA. Through experiments, we show that exploiting the sentiment dependency is clearly advantageous, and that the Dependency-Sentiment-LDA is an effective approach for sentiment analysis.

Relational Markov Decision Processes (MDP) are a useful abstraction for stochastic planning problems since one can develop abstract solutions for them that are independent of domain size or instantiation. While there has been an increased interest in developing relational fully observable MDPs, there has been very little work on relational partially observable MDPs (POMDP), which deal with uncertainty in problem states in addition to stochastic action effects. This paper provides a concrete formalization of relational POMDPs making several technical contributions toward their solution. First, we show that to maintain correctness one must distinguish between quantification over states and quantification over belief states; this implies that solutions based on value iteration are inherently limited to the finite horizon case. Second, we provide a symbolic dynamic programing algorithm for finite horizon relational POMDPs, solving them at an abstract level, by lifting the propositional incremental pruning algorithm. Third, we show that this algorithm can be implemented using first order decision diagrams, a compact representation for functions over relational structures, that has been recently used to solve relational MDPs.

Partially Observable Markov Decision Processes (POMDPs) are a well-established and rigorous framework for sequential decision-making under uncertainty. POMDPs are well-known to be intractable to solve exactly, and there has been significant work on finding tractable approximation methods. One well-studied approach is to find a compression of the original POMDP by projecting the belief states to a lower-dimensional space. We present a novel dimensionality reduction method for POMDPs based on locality preserving non-negative matrix factorization. Unlike previous approaches, such as Krylov compression and regular non-negative matrix factorization, our approach preserves the local geometry of the belief space manifold. We present results on standard benchmark POMDPs showing improved performance over previously explored compression algorithms for POMDPs.

Partially-observable Markov decision processes (POMDPs) provide a powerful model for sequential decision-making problems with partially-observed state and are known to have (approximately) optimal dynamic programming solutions. Much work in recent years has focused on improving the efficiency of these dynamic programming algorithms by exploiting symmetries and factored or relational representations. In this work, we show that it is also possible to exploit the full expressive power of first-order quantification to achieve state, action, and observation abstraction in a dynamic programming solution to relationally specified POMDPs. Among the advantages of this approach are the ability to maintain compact value function representations, abstract over the space of potentially optimal actions, and automatically derive compact conditional policy trees that minimally partition relational observation spaces according to distinctions that have an impact on policy values. This is the first lifted relational POMDP solution that can optimally accommodate actions with a potentially infinite relational space of observation outcomes.

Recent research has shown that surprisingly rich models of human behavior can be learned from GPS (positional) data. However, most research to date has concentrated on modeling single individuals or aggregate statistical properties of groups of people. Given noisy real-world GPS data, we---in contrast---consider the problem of modeling and recognizing activities that involve multiple related individuals playing a variety of roles. Our test domain is the game of capture the flag---an outdoor game that involves many distinct cooperative and competitive joint activities. We model the domain using Markov logic, a statistical relational language, and learn a theory that jointly denoises the data and infers occurrences of high-level activities, such as capturing a player. Our model combines constraints imposed by the geometry of the game area, the motion model of the players, and by the rules and dynamics of the game in a probabilistically and logically sound fashion. We show that while it may be impossible to directly detect a multi-agent activity due to sensor noise or malfunction, the occurrence of the activity can still be inferred by considering both its impact on the future behaviors of the people involved as well as the events that could have preceded it. We compare our unified approach with three alternatives (both probabilistic and nonprobabilistic) where either the denoising of the GPS data and the detection of the high-level activities are strictly separated, or the states of the players are not considered, or both. We show that the unified approach with the time window spanning the entire game, although more computationally costly, is significantly more accurate.

The precise specification of reward functions for Markov decision processes (MDPs) is often extremely difficult, motivating research into both reward elicitation and the robust solution of MDPs with imprecisely specified reward (IRMDPs). We develop new techniques for the robust optimization of IRMDPs, using the minimax regret decision criterion, that exploit the set of nondominated policies, i.e., policies that are optimal for some instantiation of the imprecise reward function. Drawing parallels to POMDP value functions, we devise a Witness-style algorithm for identifying nondominated policies. We also examine several new algorithms for computing minimax regret using the nondominated set, and examine both practically and theoretically the impact of approximating this set. Our results suggest that a small subset of the nondominated set can greatly speed up computation, yet yield very tight approximations to minimax regret.