This paper concerns the assessment of the effects of actions or policy interventions from a combination of: (i) nonexperimental data, and (ii) substantive assumptions. The assumptions are encoded in the form of a directed acyclic graph, also called "causal graph", in which some variables are presumed to be unobserved. The paper establishes a necessary and sufficient criterion for the identifiability of the causal effects of a singleton variable on all other variables in the model, and a powerful sufficient criterion for the effects of a singleton variable on any set of variables.

Introduction The introduction of Bayesian networks (Pearl 1986b) and associated local computation algorithms (Lauritzen and Spiegelhalter 1988, Shenoy and Shafer 1990, Jensen, Lauritzen and Olesen 1990) has initiated a renewed interest for understanding causal concepts in connection with modelling complex stochastic systems. It has become clear that graphical models, in particular those based upon directed acyclic graphs, have natural causal interpretations and thus form a base for a language in which causal concepts can be discussed and analysed in precise terms. As a consequence there has been an explosion of writings, not primarily within mainstream statistical literature, concerned with the exploitation of this language to clarify and extend causal concepts. Among these we mention in particular books by Spirtes, Glymour and Scheines (1993), Shafer (1996), and Pearl (2000) as well as the collection of papers in Glymour and Cooper (1999). Very briefly, but fundamentally,

The direct effect of one event on another can be defined and measured by holding constant all intermediate variables between the two. Indirect effects present conceptual and practical difficulties (in nonlinear models), because they cannot be isolated by holding certain variables constant. This paper presents a new way of defining the effect transmitted through a restricted set of paths, without controlling variables on the remaining paths. This permits the assessment of a more natural type of direct and indirect effects, one that is applicable in both linear and nonlinear models and that has broader policy-related interpretations. The paper establishes conditions under which such assessments can be estimated consistently from experimental and nonexperimental data, and thus extends path-analytic techniques to nonlinear and nonparametric models.

The task of causal structure discovery from empirical data is a fundamental problem in many areas. Experimental data is crucial for accomplishing this task. However, experiments are typically expensive, and must be selected with great care. This paper

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Probabilistic models based on directed acyclic graphs have a long and rich tradition, beginning with work by the geneticist Sewall Wright in the 1920s. Variants have appeared in many fields. Within statistics, such models are known as directed graphical models; within cognitive science and artificial intelligence, such models are known as Bayesian networks.

Traditional database systems, particularly those focused on capturing and managing data from the real world, are poorly equipped to deal with the noise, loss, and uncertainty in data. We discuss a suite of techniques based on probabilistic models that are designed to allow database to tolerate noise and loss. These techniques are based on exploiting correlations to predict missing values and identify outliers. Interestingly, correlations also provide a way to give approximate answers to users at a significantly lower cost and enable a range of new types of queries over the correlation structure itself. We illustrate a host of applications for our new techniques and queries, ranging from sensor networks to network monitoring to data stream management. We also present a unified architecture for integrating such models into database systems, focusing in particular on acquisitional systems where the cost of capturing data (e.g., from sensors) is itself a significant part of the query processing cost.

Declarative queries are proving to be an attractive paradigm for interacting with networks of wireless sensors. The metaphor that “the sensornet is a database” is problematic, however, because sensors do not exhaustively represent the data in the real world. In order to map the raw sensor readings onto physical reality, a model of that reality is required to complement the readings. In this article, we enrich interactive sensor querying with statistical modeling techniques. We demonstrate that such models can help provide answers that are both more meaningful, and, by introducing approximations with probabilistic confidences, significantly more efficient to compute in both time and energy. Utilizing the combination of a model and live data acquisition raises the challenging optimization problem of selecting the best sensor readings to acquire, balancing the increase in the confidence of our answer against the communication and data acquisition costs in the network. We describe an exponential time algorithm for finding the optimal solution to this optimization problem, and a polynomial-time heuristic for identifying solutions that perform well in practice. We evaluate our approach on several real-world sensor-network data sets, taking into account the real measured data and communication quality, demonstrating that our model-based approach provides a high-fidelity representation of the real phenomena and leads to significant performance gains versus traditional data acquisition techniques.

We present a generalization of independent component analysis (ICA), where instead of looking for a linear transform that makes the data components independent, we look for a transform that makes the data components well fit by a tree-structured graphical model. This tree-dependent component analysis (TCA) provides a tractable and flexible approach to weakening the assumption of independence in ICA. In particular, TCA allows the underlying graph to have multiple connected components, and thus the method is able to find “clusters ” of components such that components are dependent within a cluster and independent between clusters. Finally, we make use of a notion of graphical models for time series due to Brillinger (1996) to extend these ideas to the temporal setting. In particular, we are able to fit models that incorporate tree-structured dependencies among multiple time series.

We consider a Bayesian method for learning the Bayesian network structure from complete data. Recently, Koivisto and Sood (2004) presented an algorithm that for any single edge computes its marginal posterior probability in O(n2 n) time, where n is the number of attributes; the number of parents per attribute is bounded by a constant. In this paper we show that the posterior probabilities for all the n(n−1) potential edges can be computed in O(n2 n) total time. This result is achieved by a forward–backward technique and fast Möbius transform algorithms, which are of independent interest. The resulting speedup by a factor of about n 2 allows us to experimentally study the statistical power of learning moderate-size networks. We report results from a simulation study that covers data sets with 20 to 10,000 records over 5 to 25 discrete attributes. 1