This paper addresses the problem of predicting the k events that are most likely to occur next, over historical real-time event streams. Existing approaches to causal prediction queries have a number of limitations. First, they exhaustively search over an acyclic causal network to find the most likely k effect events; however, data from real event streams frequently reflect cyclic causality. Second, they contain conservative assumptions intended to exclude all possible non-causal links in the causal network; it leads to the omission of many less-frequent but important causal links. We overcome these limitations by proposing a novel event precedence model and a run-time causal inference mechanism. The event precedence model constructs a first order absorbing Markov chain incrementally over event streams, where an edge between two events signifies a temporal precedence relationship between them, which is a necessary condition for causality. Then, the run-time causal inference mechanism learns causal relationships dynamically during query processing. This is done by removing some of the temporal precedence relationships that do not exhibit causality in the presence of other events in the event precedence model. This paper presents two query processing algorithms -- one performs exhaustive search on the model and the other performs a more efficient reduced search with early termination. Experiments using two real datasets (cascading blackouts in power systems and web page views) verify the effectiveness of the probabilistic top-k prediction queries and the efficiency of the algorithms. Specifically, the reduced search algorithm reduced runtime, relative to exhaustive search, by 25-80 (depending on the application) with only a small reduction in accuracy.
In addition, there has been some work (e.g., @cite_40 @cite_34 @cite_19 ) to support Bayesian network which aims to handle the cyclic causality in Bayesian networks. This work, however, still carries the drawbacks inherent in the Bayesian network approach -- that is, the ambiguity of equivalence classes and the inability to meet the requirement of a causal network that the parent node in the network should always represent the direct cause -- and hence is not useful in our work.
@cite_19 @cite_40 @cite_34
2126653228 1641347315 2950873347 2129564794
A new method is proposed for exploiting causal independencies in exact Bayesian network inference. A Bayesian network can be viewed as representing a factorization of a joint probability into the multiplication of a set of conditional probabilities. We present a notion of causal independence that enables one to further factorize the conditional probabilities into a combination of even smaller factors and consequently obtain a finer-grain factorization of the joint probability. The new formulation of causal independence lets us specify the conditional probability of a variable given its parents in terms of an associative and commutative operator, such as "or", "sum" or "max", on the contribution of each parent. We start with a simple algorithm VE for Bayesian network inference that, given evidence and a query variable, uses the factorization to find the posterior distribution of the query. We show how this algorithm can be extended to exploit causal independence. Empirical studies, based on the CPCS networks for medical diagnosis, show that this method is more efficient than previous methods and allows for inference in larger networks than previous algorithms. Whereas acausal Bayesian networks represent probabilistic independence, causal Bayesian networks represent causal relationships. In this paper, we examine Bayesian methods for learning both types of networks. Bayesian methods for learning acausal networks are fairly well developed. These methods often employ assumptions to facilitate the construction of priors, including the assumptions of parameter independence, parameter modularity, and likelihood equivalence. We show that although these assumptions also can be appropriate for learning causal networks, we need additional assumptions in order to learn causal networks. We introduce two sufficient assumptions, called mechanism independence and component independence. We show that these new assumptions, when combined with parameter independence, parameter modularity, and likelihood equivalence, allow us to apply methods for learning acausal networks to learn causal networks. We present a hybrid constraint-based Bayesian algorithm for learning causal networks in the presence of sparse data. The algorithm searches the space of equivalence classes of models (essential graphs) using a heuristic based on conventional constraint-based techniques. Each essential graph is then converted into a directed acyclic graph and scored using a Bayesian scoring metric. Two variants of the algorithm are developed and tested using data from randomly generated networks of sizes from 15 to 45 nodes with data sizes ranging from 250 to 2000 records. Both variations are compared to, and found to consistently outperform two variations of greedy search with restarts. In recent years, Bayesian networks have become highly successful tool for diagnosis, analysis, and decision making in real-world domains. We present an efficient algorithm for learning Bayes networks from data. Our approach constructs Bayesian networks by first identifying each node's Markov blankets, then connecting nodes in a maximally consistent way. In contrast to the majority of work, which typically uses hill-climbing approaches that may produce dense and causally incorrect nets, our approach yields much more compact causal networks by heeding independencies in the data. Compact causal networks facilitate fast inference and are also easier to understand. We prove that under mild assumptions, our approach requires time polynomial in the size of the data and the number of nodes. A randomized variant, also presented here, yields comparable results at much higher speeds.