Compiling graphical models has recently been under intense investigation, especially for probabilistic modeling and processing. We present here a novel data structure for compiling weighted graphical models (in particular, probabilistic models), called AND/OR Multi-Valued Decision Diagram (AOMDD). This is a generalization of our previous work on constraint networks, to weighted models. The AOMDD is based on the frameworks of AND/OR search spaces for graphical models, and Ordered Binary Decision Diagrams (OBDD). The AOMDD is a canonical representation of a graphical model, and its size and compilation time are bounded exponentially by the treewidth of the graph, rather than pathwidth as is known for OBDDs. We discuss a Variable Elimination schedule for compilation, and present the general APPLY algorithm that combines two weighted AOMDDs, and also present a search based method for compilation method. The preliminary experimental evaluation is quite encouraging, showing the potential of the AOMDD data structure.

We present a graphical criterion for reading dependencies from the minimal directed independence map G of a graphoid p when G is a polytree and p satisfies composition and weak transitivity. We prove that the criterion is sound and complete. We argue that assuming composition and weak transitivity is not too restrictive.

We present the mixture-of-parents maximum entropy Markov model (MoP-MEMM), a class of directed graphical models extending MEMMs. The MoP-MEMM allows tractable incorporation of long-range dependencies between nodes by restricting the conditional distribution of each node to be a mixture of distributions given the parents. We show how to efficiently compute the exact marginal posterior node distributions, regardless of the range of the dependencies. This enables us to model non-sequential correlations present within text documents, as well as between interconnected documents, such as hyperlinked web pages. We apply the MoP-MEMM to a named entity recognition task and a web page classification task. In each, our model shows significant improvement over the basic MEMM, and is competitive with other long-range sequence models that use approximate inference.

Most real-world dynamic systems are composed of different components that often evolve at very different rates. In traditional temporal graphical models, such as dynamic Bayesian networks, time is modeled at a fixed granularity, generally selected based on the rate at which the fastest component evolves. Inference must then be performed at this fastest granularity, potentially at significant computational cost. Continuous Time Bayesian Networks (CTBNs) avoid time-slicing in the representation by modeling the system as evolving continuously over time. The expectation-propagation (EP) inference algorithm of Nodelman et al. (2005) can then vary the inference granularity over time, but the granularity is uniform across all parts of the system, and must be selected in advance. In this paper, we provide a new EP algorithm that utilizes a general cluster graph architecture where clusters contain distributions that can overlap in both space (set of variables) and time. This architecture allows different parts of the system to be modeled at very different time granularities, according to their current rate of evolution. We also provide an information-theoretic criterion for dynamically re-partitioning the clusters during inference to tune the level of approximation to the current rate of evolution. This avoids the need to hand-select the appropriate granularity, and allows the granularity to adapt as information is transmitted across the network. We present experiments demonstrating that this approach can result in significant computational savings.

We present a memory-bounded optimization approach for solving infinite-horizon decentralized POMDPs. Policies for each agent are represented by stochastic finite state controllers. We formulate the problem of optimizing these policies as a nonlinear program, leveraging powerful existing nonlinear optimization techniques for solving the problem. While existing solvers only guarantee locally optimal solutions, we show that our formulation produces higher quality controllers than the state-of-the-art approach. We also incorporate a shared source of randomness in the form of a correlation device to further increase solution quality with only a limited increase in space and time. Our experimental results show that nonlinear optimization can be used to provide high quality, concise solutions to decentralized decision problems under uncertainty.

Although a number of related algorithms have been developed to evaluate influence diagrams, exploiting the conditional independence in the diagram, the exact solution has remained intractable for many important problems. In this paper we introduce decision circuits as a means to exploit the local structure usually found in decision problems and to improve the performance of influence diagram analysis. This work builds on the probabilistic inference algorithms using arithmetic circuits to represent Bayesian belief networks [Darwiche, 2003]. Once compiled, these arithmetic circuits efficiently evaluate probabilistic queries on the belief network, and methods have been developed to exploit both the global and local structure of the network. We show that decision circuits can be constructed in a similar fashion and promise similar benefits.

We describe the semantic foundations for elicitation of generalized additively independent (GAI) utilities using the minimax regret criterion, and propose several new query types and strategies for this purpose. Computational feasibility is obtained by exploiting the local GAI structure in the model. Our results provide a practical approach for implementing preference-based constrained configuration optimization as well as effective search in multiattribute product databases.

In this paper we introduce a new network reachability problem where the goal is to find the most reliable path between two nodes in a network, represented as a directed acyclic graph. Individual edges within this network may fail according to certain probabilities, and these failure probabilities may depend on the values of one or more hidden variables. This problem may be viewed as a generalization of shortest-path problems for finding minimum cost paths or Viterbi-type problems for finding highest-probability sequences of states, where the addition of the hidden variables introduces correlations that are not handled by previous algorithms. We give theoretical results characterizing this problem including an NP-hardness proof. We also give an exact algorithm and a more efficient approximation algorithm for this problem.

Remote sensors are becoming the standard for observing and recording ecological data in the field. Such sensors can record data at fine temporal resolutions, and they can operate under extreme conditions prohibitive to human access. Unfortunately, sensor data streams exhibit many kinds of errors ranging from corrupt communications to partial or total sensor failures. This means that the raw data stream must be cleaned before it can be used by domain scientists. In our application environment|the H.J. Andrews Experimental Forest|this data cleaning is performed manually. This paper introduces a Dynamic Bayesian Network model for analyzing sensor observations and distinguishing sensor failures from valid data for the case of air temperature measured at 15 minute time resolution. The model combines an accurate distribution of long-term and short-term temperature variations with a single generalized fault model. Experiments with historical data show that the precision and recall of the method is comparable to that of the domain expert. The system is currently being deployed to perform real-time automated data cleaning.

The ways in which an agent's actions affect the world can often be modeled compactly using a set of relational probabilistic planning rules. This paper addresses the problem of learning such rule sets for multiple related tasks. We take a hierarchical Bayesian approach, in which the system learns a prior distribution over rule sets. We present a class of prior distributions parameterized by a rule set prototype that is stochastically modified to produce a task-specific rule set. We also describe a coordinate ascent algorithm that iteratively optimizes the task-specific rule sets and the prior distribution. Experiments using this algorithm show that transferring information from related tasks significantly reduces the amount of training data required to predict action effects in blocks-world domains.