CP-nets: A Tool for Representing and Reasoning withConditional Ceteris Paribus Preference Statements

Information about user preferences plays a key role in automated decision making. In many domains it is desirable to assess such preferences in a qualitative rather than quantitative way. In this paper, we propose a qualitative graphical representation of preferences that reflects conditional dependence and independence of preference statements under a ceteris paribus (all else being equal) interpretation. Such a representation is often compact and arguably quite natural in many circumstances. We provide a formal semantics for this model, and describe how the structure of the network can be exploited in several inference tasks, such as determining whether one outcome dominates (is preferred to) another, ordering a set outcomes according to the preference relation, and constructing the best outcome subject to available evidence

Cutset Sampling for Bayesian Networks

The paper presents a new sampling methodology for Bayesian networks that samples only a subset of variables and applies exact inference to the rest. Cutset sampling is a network structure-exploiting application of the Rao-Blackwellisation principle to sampling in Bayesian networks. It improves convergence by exploiting memory-based inference algorithms. It can also be viewed as an anytime approximation of the exact cutset-conditioning algorithm developed by Pearl. Cutset sampling can be implemented efficiently when the sampled variables constitute a loop-cutset of the Bayesian network and, more generally, when the induced width of the networks graph conditioned on the observed sampled variables is bounded by a constant w. We demonstrate empirically the benefit of this scheme on a range of benchmarks

Efficient inference in Bayes networks as a combinatorial optimization problem

AbstractA number of exact algorithms have been developed in recent years to perform probabilistic inference in Bayesian belief networks. The techniques used in these algorithms are closely related to network structures, and some of them are not easy to understand and implement. We consider the problem from the combinatorial optimization point of view and state that efficient probabilistic inference in a belief network is a problem of finding an optimal factoring given a set of probability distributions. From this viewpoint, previously developed algorithms can be seen as alternative factoring strategies. In this paper, we define a combinatorial optimization problem, the optimal factoring problem, and discuss application of this problem in belief networks. We show that optimal factoring provides insight into the key elements of efficient probabilistic inference, and demonstrate simple, easily implemented algorithms with excellent performance

A probabilistic reasoning and learning system based on Bayesian belief networks

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Structure and Complexity in Planning with Unary Operators

Unary operator domains -- i.e., domains in which operators have a single effect -- arise naturally in many control problems. In its most general form, the problem of STRIPS planning in unary operator domains is known to be as hard as the general STRIPS planning problem -- both are PSPACE-complete. However, unary operator domains induce a natural structure, called the domain's causal graph. This graph relates between the preconditions and effect of each domain operator. Causal graphs were exploited by Williams and Nayak in order to analyze plan generation for one of the controllers in NASA's Deep-Space One spacecraft. There, they utilized the fact that when this graph is acyclic, a serialization ordering over any subgoal can be obtained quickly. In this paper we conduct a comprehensive study of the relationship between the structure of a domain's causal graph and the complexity of planning in this domain. On the positive side, we show that a non-trivial polynomial time plan generation algorithm exists for domains whose causal graph induces a polytree with a constant bound on its node indegree. On the negative side, we show that even plan existence is hard when the graph is a directed-path singly connected DAG. More generally, we show that the number of paths in the causal graph is closely related to the complexity of planning in the associated domain. Finally we relate our results to the question of complexity of planning with serializable subgoals

From 'tree' based Bayesian networks to mutual information classifiers : deriving a singly connected network classifier using an information theory based technique

For reasoning under uncertainty the Bayesian network has become the representation of choice. However, except where models are considered 'simple' the task of construction and inference are provably NP-hard. For modelling larger 'real' world problems this computational complexity has been addressed by methods that approximate the model. The Naive Bayes classifier, which has strong assumptions of independence among features, is a common approach, whilst the class of trees is another less extreme example. In this thesis we propose the use of an information theory based technique as a mechanism for inference in Singly Connected Networks. We call this a Mutual Information Measure classifier, as it corresponds to the restricted class of trees built from mutual information. We show that the new approach provides for both an efficient and localised method of classification, with performance accuracies comparable with the less restricted general Bayesian networks. To improve the performance of the classifier, we additionally investigate the possibility of expanding the class Markov blanket by use of a Wrapper approach and further show that the performance can be improved by focusing on the class Markov blanket and that the improvement is not at the expense of increased complexity. Finally, the two methods are applied to the task of diagnosing the 'real' world medical domain, Acute Abdominal Pain. Known to be both a different and challenging domain to classify, the objective was to investigate the optiniality claims, in respect of the Naive Bayes classifier, that some researchers have argued, for classifying in this domain. Despite some loss of representation capabilities we show that the Mutual Information Measure classifier can be effectively applied to the domain and also provides a recognisable qualitative structure without violating 'real' world assertions. In respect of its 'selective' variant we further show that the improvement achieves a comparable predictive accuracy to the Naive Bayes classifier and that the Naive Bayes classifier's 'overall' performance is largely due the contribution of the majority group Non-Specific Abdominal Pain, a group of exclusion