We use the implicitization procedure to generate polynomial equality constraints on the set of distributions induced by local interventions on variables governed by a causal Bayesian network with hidden variables. We show how we may reduce the complexity of the implicitization problem and make the problem tractable in certain causal Bayesian networks. We also show some preliminary results on the algebraic structure of polynomial constraints. The results have applications in distinguishing between causal models and in testing causal models with combined observational and experimental data.

Searching the complete space of possible Bayesian networks is intractable for problems of interesting size, so Bayesian network structure learning algorithms, such as the commonly used Sparse Candidate algorithm, employ heuristics. However, these heuristics also restrict the types of relationships that can be learned exclusively from data. They are unable to learn relationships that exhibit "correlation-immunity", such as parity. To learn Bayesian networks in the presence of correlation-immune relationships, we extend the Sparse Candidate algorithm with a technique called "skewing". This technique uses the observation that relationships that are correlation-immune under a specific input distribution may not be correlation-immune under another, sufficiently different distribution. We show that by extending Sparse Candidate with this technique we are able to discover relationships between random variables that are approximately correlation-immune, with a significantly lower computational cost than the alternative of considering multiple parents of a node at a time.

The paper evaluates the power of best-first search over AND/OR search spaces for solving the Most Probable Explanation (MPE) task in Bayesian networks. The main virtue of the AND/OR representation of the search space is its sensitivity to the structure of the problem, which can translate into significant time savings. In recent years depth-first AND/OR Branch-and- Bound algorithms were shown to be very effective when exploring such search spaces, especially when using caching. Since best-first strategies are known to be superior to depth-first when memory is utilized, exploring the best-first control strategy is called for. The main contribution of this paper is in showing that a recent extension of AND/OR search algorithms from depth-first Branch-and-Bound to best-first is indeed very effective for computing the MPE in Bayesian networks. We demonstrate empirically the superiority of the best-first search approach on various probabilistic networks.

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.

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.

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.

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.

We propose a new method for parameter learning in Bayesian networks with qualitative influences. This method extends our previous work from networks of binary variables to networks of discrete variables with ordered values. The specified qualitative influences correspond to certain order restrictions on the parameters in the network. These parameters may therefore be estimated using constrained maximum likelihood estimation. We propose an alternative method, based on the isotonic regression. The constrained maximum likelihood estimates are fairly complicated to compute, whereas computation of the isotonic regression estimates only requires the repeated application of the Pool Adjacent Violators algorithm for linear orders. Therefore, the isotonic regression estimator is to be preferred from the viewpoint of computational complexity. Through experiments on simulated and real data, we show that the new learning method is competitive in performance to the constrained maximum likelihood estimator, and that both estimators improve on the standard estimator.