This paper concerns learning and prediction with probabilistic models where the domain sizes of latent variables have no a priori upper-bound. Current approaches represent prior distributions over latent variables by stochastic processes such as the Dirichlet process, and rely on Monte Carlo sampling to estimate the model from data. We propose an alternative approach that searches over the domain size of latent variables, and allows arbitrary priors over the their domain sizes. We prove error bounds for expected probabilities, where the error bounds diminish with increasing search scope. The search algorithm can be truncated at any time . We empirically demonstrate the approach for topic modelling of text documents.

We study the marginal-MAP problem on graphical models, and present a novel approximation method based on direct approximation of the sum operation. A primary difficulty of marginal-MAP problems lies in the non-commutativity of the sum and max operations, so that even in highly structured models, marginalization may produce a densely connected graph over the variables to be maximized, resulting in an intractable potential function with exponential size. We propose a chain decomposition approach for summing over the marginalized variables, in which we produce a structured approximation to the MAP component of the problem consisting of only pairwise potentials. We show that this approach is equivalent to the maximization of a specific variational free energy, and it provides an upper bound of the optimal probability. Finally, experimental results demonstrate that our method performs favorably compared to previous methods.

The presence of non-symmetric evidence has been a barrier for the application of lifted inference since the evidence destroys the symmetry of the first-order probabilistic model. In the extreme case, if distinct soft evidence is obtained about each individual object in the domain then, often, all current exact lifted inference methods reduce to traditional inference at the ground level. However, it is of interest to ask whether the symmetry of the model itself before evidence is obtained can be exploited. We present new results showing that this is, in fact, possible. In particular, we show that both exact maximum a posteriori (MAP) and marginal inference can be lifted for the case of distinct soft evidence on a unary Markov Logic predicate. Our methods result in efficient procedures for MAP and marginal inference for a class of graphical models previously thought to be intractable.

Recent work in the field of probabilistic inference demonstrated the efficiency of weighted model counting (WMC) enginesfor exact inference in propositional and, very recently, first order models. To date, these methods have not been applied to decision making models, propositional or first order, such as influence diagrams, and Markov decision networks (MDN). In this paper we show how this technique can be applied to such models. First, we show how WMC can be used to solve (propositional) MDNs. Then, we show how this can be extended to handle a first-order model — the Markov Logic Decision Network (MLDN). WMC offers two central benefits: it is a very simple and very efficient technique. This is particularly true for the first-order case, where the WMC approach is simpler conceptually, and, in many cases, more effective computationally than the existing methods for solving MLDNs via first-order variable elimination, or via propositionalization. We demonstrate the above empirically.

Many real-world decision-theoretic planning problemsare naturally modeled using both continuous state andaction (CSA) spaces, yet little work has provided ex-act solutions for the case of continuous actions. Inthis work, we propose a symbolic dynamic program-ming (SDP) solution to obtain the optimal closed-formvalue function and policy for CSA-MDPs with mul-tivariate continuous state and actions, discrete noise,piecewise linear dynamics, and piecewise linear (or re-stricted piecewise quadratic) reward. Our key contribu-tion over previous SDP work is to show how the contin-uous action maximization step in the dynamic program-ming backup can be evaluated optimally and symboli-cally — a task which amounts to symbolic constrainedoptimization subject to unknown state parameters; wefurther integrate this technique to work with an efficientand compact data structure for SDP — the extendedalgebraic decision diagram (XADD). We demonstrateempirical results on a didactic nonlinear planning exam-ple and two domains from operations research to showthe first automated exact solution to these problems.

We consider symbolic dynamic programming (SDP) for solving Markov Decision Processes (MDP) with factored state and action spaces, where both states and actions are described by sets of discrete variables. Prior work on SDP has considered only the case of factored states and ignored structure in the action space, causing them to scale poorly in terms of the number of action variables. Our main contribution is to present the first SDP-based planning algorithm for leveraging both state and action space structure in order to compute compactly represented value functions and policies. Since our new algorithm can potentially require more space than when action structure is ignored, our second contribution is to describe an approach for smoothly trading-off space versus time via recursive conditioning. Finally, our third contribution is to introduce a novel SDP approximation that often significantly reduces planning time with little loss in quality by exploiting action structure in weakly coupled MDPs. We present empirical results in three domains with factored action spaces that show that our algorithms scale much better with the number of action variables as compared to state-of-the-art SDP algorithms.

Current computer involvement in adolescent social networks (youth between the ages of 11 and 17) provides new opportunities to study group dynamics, interactions amongst peers, and individual preferences. Nevertheless, most of the research in this area focuses on efficiently retrieving information that is explicit in large social networks (e.g., properties of the graph structure), but not on how to use the dynamics of the virtual social network to discover latent characteristics of the real-world social network. In this paper, we present the analysis of a game designed to take advantage of the familiarity of adolescents with online social networks, and describe how the data generated by the game can be used to identify bullies in 5th grade classrooms. We present a probabilistic model of the game and using the in-game interactions of the players (i.e., content of chat messages) infer their social role within their classroom (either a bully or non-bully). The evaluation of our model is done by using previously collected data from psychological surveys on the same 5th grade population and by comparing the performance of the new model with off-the-shelf classifiers.

Problem-solving procedures have been typically aimed at achieving well-defined goals or satisfying straightforward preferences. However, learners and solvers may often generate rich multiattribute results with procedures guided by sets of controls that define different dimensions of quality. We explore methods that enable people to explore and express preferences about the operation of classification models in supervised multiclass learning. We leverage a leave-one-out confusion matrix that provides users with views and real-time controls of a model space. The approach allows people to consider in an interactive manner the global implications of local changes in decision boundaries. We focus on kernel classifiers and show the effectiveness of the methodology on a variety of tasks.

We introduce a new task-independent framework to model top-down overt visual attention based on graph-ical models for probabilistic inference and reasoning. We describe a Dynamic Bayesian Network (DBN) that infers probability distributions over attended objects and spatial locations directly from observed data. Probabilistic inference in our model is performed over object-related functions which are fed from manual annotations of objects in video scenes or by state-of-the-art object detection models. Evaluating over ∼3 hours (appx. 315,000 eye fixations and 12,600 saccades) of observers playing 3 video games (time-scheduling, driving, and flight combat), we show that our approach is significantly more predictive of eye fixations compared to: 1) simpler classifier-based models also developed here that map a signature of a scene (multi-modal information from gist, bottom-up saliency, physical actions, and events) to eye positions, 2) 14 state-of-the-art bottom-up saliency models, and 3) brute-force algorithms such as mean eye position. Our results show that the proposed model is more effective in employing and reasoning over spatio-temporal visual data.

We consider an infinite mixture model of Gaussian processes that share mixture components between non-local clusters in data. Meeds and Osindero (2006) use a single Dirichlet process prior to specify a mixture of Gaussian processes using an infinite number of experts. In this paper, we extend this approach to allow for experts to be shared non-locally across the input domain. This is accomplished with a hierarchical double Dirichlet process prior, which builds upon a standard hierarchical Dirichlet process by incorporating local parameters that are unique to each cluster while sharing mixture components between them. We evaluate the model on simulated and real data, showing that sharing Gaussian process components non-locally can yield effective and useful models for richly clustered non-stationary, non-linear data.