This paper deals with the problem of identifying direct causal effects in recursive linear structural equation models. The paper establishes a sufficient criterion for identifying individual causal effects and provides a procedure computing identified causal effects in terms of observed covariance matrix.

We present a functional framework for automated mechanism design based on a two-stage game model of strategic interaction between the designer and the mechanism participants, and apply it to several classes of two-player infinite games of incomplete information. At the core of our framework is a black-box optimization algorithm which guides the selection process of candidate mechanisms. Our approach yields optimal or nearly optimal mechanisms in several application domains using various objective functions. By comparing our results with known optimal mechanisms, and in some cases improving on the best known mechanisms, we provide evidence that ours is a promising approach to parametric design of indirect mechanisms.

Relational Markov Decision Processes are a useful abstraction for complex reinforcement learning problems and stochastic planning problems. Recent work developed representation schemes and algorithms for planning in such problems using the value iteration algorithm. However, exact versions of more complex algorithms, including policy iteration, have not been developed or analyzed. The paper investigates this potential and makes several contributions. First we observe two anomalies for relational representations showing that the value of some policies is not well defined or cannot be calculated for restricted representation schemes used in the literature. On the other hand, we develop a variant of policy iteration that can get around these anomalies. The algorithm includes an aspect of policy improvement in the process of policy evaluation and thus differs from the original algorithm. We show that despite this difference the algorithm converges to the optimal policy.

Ranking objects is a simple and natural procedure for organizing data. It is often performed by assigning a quality score to each object according to its relevance to the problem at hand. Ranking is widely used for object selection, when resources are limited and it is necessary to select a subset of most relevant objects for further processing. In real world situations, the object's scores are often calculated from noisy measurements, casting doubt on the ranking reliability. We introduce an analytical method for assessing the influence of noise levels on the ranking reliability. We use two similarity measures for reliability evaluation, Top-K-List overlap and Kendall's tau measure, and show that the former is much more sensitive to noise than the latter. We apply our method to gene selection in a series of microarray experiments of several cancer types. The results indicate that the reliability of the lists obtained from these experiments is very poor, and that experiment sizes which are necessary for attaining reasonably stable Top-K-Lists are much larger than those currently available. Simulations support our analytical results.

Instrumentation and measurement technology is, by and large, keeping pace with this development and growth. However, the algorithms, tools, and technology required to transform the data into relevant information for decision making are not. The claim in this paper (and the invited talk) is that the line of research conducted in Uncertainty in Artificial Intelligence is very well suited to address the challenges and close this gap. I will support this claim and discuss open problems using recent examples in diagnosis, model discovery, and policy optimization on three real life distributed systems.

Relational Markov Random Fields are a general and flexible framework for reasoning about the joint distribution over attributes of a large number of interacting entities. The main computational difficulty in learning such models is inference. Even when dealing with complete data, where one can summarize a large domain by sufficient statistics, learning requires one to compute the expectation of the sufficient statistics given different parameter choices. The typical solution to this problem is to resort to approximate inference procedures, such as loopy belief propagation. Although these procedures are quite efficient, they still require computation that is on the order of the number of interactions (or features) in the model. When learning a large relational model over a complex domain, even such approximations require unrealistic running time. In this paper we show that for a particular class of relational MRFs, which have inherent symmetry, we can perform the inference needed for learning procedures using a template-level belief propagation. This procedure's running time is proportional to the size of the relational model rather than the size of the domain. Moreover, we show that this computational procedure is equivalent to sychronous loopy belief propagation. This enables a dramatic speedup in inference and learning time. We use this procedure to learn relational MRFs for capturing the joint distribution of large protein-protein interaction networks.

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.

When observational data is available from practical studies and a directed cyclic graph for how various variables affect each other is known based on substantive understanding of the process, we consider a problem in which a control plan of a treatment variable is conducted in order to bring a response variable close to a target value with variation reduction. We formulate an optimal control plan concerning a certain treatment variable through path coefficients in the framework of linear nonrecursive structural equation models. Based on the formulation, we clarify the properties of causal effects when conducting a control plan. The results enable us to evaluate the effect of a control plan on the variance from observational 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.