Causal Models are like Dependency Graphs and Belief Nets in that they provide a structure and a set of assumptions from which a joint distribution can, in principle, be computed. Unlike Dependency Graphs, Causal Models are models of hierarchical and/or parallel processes, rather than models of distributions (partially) known to a model builder through some sort of gestalt. As such, Causal Models are more modular, easier to build, more intuitive, and easier to understand than Dependency Graph Models. Causal Models are formally defined and Dependency Graph Models are shown to be a special case of them. Algorithms supporting inference are presented. Parsimonious methods for eliciting dependent probabilities are presented.

This paper compares three approaches to the problem of selecting among probability models to fit data (1) use of statistical criteria such as Akaike's information criterion and Schwarz's "Bayesian information criterion," (2) maximization of the posterior probability of the model, and (3) maximization of an effectiveness ratio? trading off accuracy and computational cost. The unifying characteristic of the approaches is that all can be viewed as maximizing a penalized likelihood function. The second approach with suitable prior distributions has been shown to reduce to the first. This paper shows that the third approach reduces to the second for a particular form of the effectiveness ratio, and illustrates all three approaches with the problem of selecting the number of components in a mixture of Gaussian distributions. Unlike the first two approaches, the third can be used even when the candidate models are chosen for computational efficiency, without regard to physical interpretation, so that the likelihood and the prior distribution over models cannot be interpreted literally. As the most general and computationally oriented of the approaches, it is especially useful for artificial intelligence applications.

By discussing several examples, the theory of generalized functional models is shown to be very natural for modeling some situations of reasoning under uncertainty. A generalized functional model is a pair (f, P) where f is a function describing the interactions between a parameter variable, an observation variable and a random source, and P is a probability distribution for the random source. Unlike traditional functional models, generalized functional models do not require that there is only one value of the parameter variable that is compatible with an observation and a realization of the random source. As a consequence, the results of the analysis of a generalized functional model are not expressed in terms of probability distributions but rather by support and plausibility functions. The analysis of a generalized functional model is very logical and is inspired from ideas already put forward by R.A. Fisher in his theory of fiducial probability.

The dependency graph is a data architecture that models all the dependencies between the different types of assets in the game. It depicts the dependency-based relationships between the assets of a game. For example, a player must construct an arsenal before he can build weapons. It is vital that the dependency graph of a game is designed logically to ensure a logical sequence of game play. However, a mere logical dependency graph is not sufficient in sustaining the players' enduring interests in a game, which brings the problem of game balancing into picture. The issue of game balancing arises when the players do not feel the chances of winning the game over their AI opponents who are more skillful in the game play. At the current state of research, the architecture of dependency graph is monolithic for the players. The sequence of asset possession is always foreseeable because there is only a single dependency graph. Game balancing is impossible when the assets of AI players are overwhelmingly outnumbering that of human players. This paper proposes a parallel architecture of dependency graph for the AI players and human players. Instead of having a single dependency graph, a parallel architecture is proposed where the dependency graph of AI player is adjustable with that of human player using a support dependency as a game balancing mechanism. This paper exhibits that the parallel dependency graph helps to improve game balancing.

This paper presents a sound and completecalculus for causal relevance, based onPearl's functional models semantics.The calculus consists of axioms and rulesof inference for reasoning about causalrelevance relationships.We extend the set of known axioms for causalrelevance with three new axioms, andintroduce two new rules of inference forreasoning about specific subclasses ofmodels.These subclasses give a more refinedcharacterization of causal models than the one given in Halpern's axiomatizationof counterfactual reasoning.Finally, we show how the calculus for causalrelevance can be used in the task ofidentifying causal structure from non-observational data.

In binary-transaction data-mining, traditional frequent itemset mining often produces results which are not straightforward to interpret. To overcome this problem, probability models are often used to produce more compact and conclusive results, albeit with some loss of accuracy. Bayesian statistics have been widely used in the development of probability models in machine learning in recent years and these methods have many advantages, including their abilities to avoid overfitting. In this paper, we develop two Bayesian mixture models with the Dirichlet distribution prior and the Dirichlet process (DP) prior to improve the previous non-Bayesian mixture model developed for transaction dataset mining. We implement the inference of both mixture models using two methods: a collapsed Gibbs sampling scheme and a variational approximation algorithm. Experiments in several benchmark problems have shown that both mixture models achieve better performance than a non-Bayesian mixture model. The variational algorithm is the faster of the two approaches while the Gibbs sampling method achieves a more accurate results. The Dirichlet process mixture model can automatically grow to a proper complexity for a better approximation. Once the model is built, it can be very fast to query and run analysis on (typically 10 times faster than Eclat, as we will show in the experiment section). However, these approaches also show that mixture models underestimate the probabilities of frequent itemsets. Consequently, these models have a higher sensitivity but a lower specificity.

A very important topic in systems biology is developing statistical methods that automatically find causal relations in gene regulatory networks with no prior knowledge of causal connectivity. Many methods have been developed for time series data. However, discovery methods based on steady-state data are often necessary and preferable since obtaining time series data can be more expensive and/or infeasible for many biological systems. A conventional approach is causal Bayesian networks. However, estimation of Bayesian networks is ill-posed. In many cases it cannot uniquely identify the underlying causal network and only gives a large class of equivalent causal networks that cannot be distinguished between based on the data distribution. We propose a new discovery algorithm for uniquely identifying the underlying causal network of genes. To the best of our knowledge, the proposed method is the first algorithm for learning gene networks based on a fully identifiable causal model called LiNGAM. We here compare our algorithm with competing algorithms using artificially-generated data, although it is definitely better to test it based on real microarray gene expression data.

In case of a plan failure, plan-repair is a more promising solution than replanning from scratch. The effectiveness of plan-repair depends on knowledge of which plan action failed and why. Therefore, in this paper, we propose an Extended Spectrum Based Diagnosis approach that efficiently pinpoints failed actions. Unlike Model Based Diagnosis (MBD), it does not require the fault models and behavioral descriptions of actions. Our approach first computes the likelihood of an action being faulty and subsequently proposes optimal probe locations to refine the diagnosis. We also exploit knowledge of plan steps that are instances of the same plan operator to optimize the selection of the most informative diagnostic probes. In this paper, we only focus on diagnostic aspect of plan-repair process.

Given a partially observable dynamic system and a diagnoser observing its evolution over time, diagnosability analysis formally verifies (at design time) if the diagnosis system will be able to infer (at runtime) the required information on the hidden part of the dynamic state. Diagnosability directly depends on the availability of observations, and can be guaranteed by different sets of sensors, possibly associated with different costs. In this paper, we tackle the problem of synthesizing observability requirements, i.e. automatically discovering a set of observations that is sufficient to guarantee diagnosability. We propose a novel approach with the following characterizing features. First, it fully covers a comprehensive formal framework for diagnosability analysis, and enables ranking configurations of observables in terms of cost, minimality, and diagnosability delay. Second, we propose two complementary algorithms for the synthesis of observables. Third, we describe an efficient implementation that takes full advantage of mature symbolic model checking techniques. The proposed approach is thoroughly evaluated over a comprehensive suite of benchmarks taken from the aerospace domain.

We propose a definition of causality for time series in terms of the effect of an intervention in one component of a multivariate time series on another component at some later point in time. Conditions for identifiability, comparable to the back-door and front-door criteria, are presented and can also be verified graphically. Computation of the causal effect is derived and illustrated for the linear case.