524 research outputs found
Reasoning about Independence in Probabilistic Models of Relational Data
We extend the theory of d-separation to cases in which data instances are not
independent and identically distributed. We show that applying the rules of
d-separation directly to the structure of probabilistic models of relational
data inaccurately infers conditional independence. We introduce relational
d-separation, a theory for deriving conditional independence facts from
relational models. We provide a new representation, the abstract ground graph,
that enables a sound, complete, and computationally efficient method for
answering d-separation queries about relational models, and we present
empirical results that demonstrate effectiveness.Comment: 61 pages, substantial revisions to formalisms, theory, and related
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A Logical Characterization of Constraint-Based Causal Discovery
We present a novel approach to constraint-based causal discovery, that takes
the form of straightforward logical inference, applied to a list of simple,
logical statements about causal relations that are derived directly from
observed (in)dependencies. It is both sound and complete, in the sense that all
invariant features of the corresponding partial ancestral graph (PAG) are
identified, even in the presence of latent variables and selection bias. The
approach shows that every identifiable causal relation corresponds to one of
just two fundamental forms. More importantly, as the basic building blocks of
the method do not rely on the detailed (graphical) structure of the
corresponding PAG, it opens up a range of new opportunities, including more
robust inference, detailed accountability, and application to large models
Graphical models for mediation analysis
Mediation analysis seeks to infer how much of the effect of an exposure on an
outcome can be attributed to specific pathways via intermediate variables or
mediators. This requires identification of so-called path-specific effects.
These express how a change in exposure affects those intermediate variables
(along certain pathways), and how the resulting changes in those variables in
turn affect the outcome (along subsequent pathways). However, unlike
identification of total effects, adjustment for confounding is insufficient for
identification of path-specific effects because their magnitude is also
determined by the extent to which individuals who experience large exposure
effects on the mediator, tend to experience relatively small or large mediator
effects on the outcome. This chapter therefore provides an accessible review of
identification strategies under general nonparametric structural equation
models (with possibly unmeasured variables), which rule out certain such
dependencies. In particular, it is shown which path-specific effects can be
identified under such models, and how this can be done
Vector Autoregressions, Policy Analysis, and Directed Acyclic Graphs: An Application to the U.S. Economy
The paper considers the use of directed acyclic graphs (DAGs), and their construction from observational data with PC-algorithm TETRAD II, in providing over-identifying restrictions on the innovations from a vector autoregression. Results from Sims’ 1986 model of the US economy are replicated and compared using these data-driven techniques. The directed graph results show Sims’ six-variable VAR is not rich enough to provide an unambiguous ordering at usual levels of statistical significance. A significance level in the neighborhood of 30 % is required to find a clear structural ordering. Although the DAG results are in agreement with Sims’ theory-based model for unemployment, differences are noted for the other five variables: income, money supply, price level, interest rates, and investment. Overall the DAG results are broadly consistent with a monetarist view with adaptive expectations and no hyperinflation.vector autoregression; directed graphs; policy analysis
Identifying Independence in Relational Models
The rules of d-separation provide a framework for deriving conditional
independence facts from model structure. However, this theory only applies to
simple directed graphical models. We introduce relational d-separation, a
theory for deriving conditional independence in relational models. We provide a
sound, complete, and computationally efficient method for relational
d-separation, and we present empirical results that demonstrate effectiveness.Comment: This paper has been revised and expanded. See "Reasoning about
Independence in Probabilistic Models of Relational Data"
http://arxiv.org/abs/1302.438
On the Foundations of Cycles in Bayesian Networks
Bayesian networks (BNs) are a probabilistic graphical model widely used for
representing expert knowledge and reasoning under uncertainty. Traditionally,
they are based on directed acyclic graphs that capture dependencies between
random variables. However, directed cycles can naturally arise when
cross-dependencies between random variables exist, e.g., for modeling feedback
loops. Existing methods to deal with such cross-dependencies usually rely on
reductions to BNs without cycles. These approaches are fragile to generalize,
since their justifications are intermingled with additional knowledge about the
application context. In this paper, we present a foundational study regarding
semantics for cyclic BNs that are generic and conservatively extend the
cycle-free setting. First, we propose constraint-based semantics that specify
requirements for full joint distributions over a BN to be consistent with the
local conditional probabilities and independencies. Second, two kinds of limit
semantics that formalize infinite unfolding approaches are introduced and shown
to be computable by a Markov chain construction.Comment: Full version with an appendix containing the proof
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