6,085 research outputs found
Structural Agnostic Modeling: Adversarial Learning of Causal Graphs
A new causal discovery method, Structural Agnostic Modeling (SAM), is
presented in this paper. Leveraging both conditional independencies and
distributional asymmetries in the data, SAM aims at recovering full causal
models from continuous observational data along a multivariate non-parametric
setting. The approach is based on a game between players estimating each
variable distribution conditionally to the others as a neural net, and an
adversary aimed at discriminating the overall joint conditional distribution,
and that of the original data. An original learning criterion combining
distribution estimation, sparsity and acyclicity constraints is used to enforce
the end-to-end optimization of the graph structure and parameters through
stochastic gradient descent. Besides the theoretical analysis of the approach
in the large sample limit, SAM is extensively experimentally validated on
synthetic and real data
Two Optimal Strategies for Active Learning of Causal Models from Interventional Data
From observational data alone, a causal DAG is only identifiable up to Markov
equivalence. Interventional data generally improves identifiability; however,
the gain of an intervention strongly depends on the intervention target, that
is, the intervened variables. We present active learning (that is, optimal
experimental design) strategies calculating optimal interventions for two
different learning goals. The first one is a greedy approach using
single-vertex interventions that maximizes the number of edges that can be
oriented after each intervention. The second one yields in polynomial time a
minimum set of targets of arbitrary size that guarantees full identifiability.
This second approach proves a conjecture of Eberhardt (2008) indicating the
number of unbounded intervention targets which is sufficient and in the worst
case necessary for full identifiability. In a simulation study, we compare our
two active learning approaches to random interventions and an existing
approach, and analyze the influence of estimation errors on the overall
performance of active learning
Reversible MCMC on Markov equivalence classes of sparse directed acyclic graphs
Graphical models are popular statistical tools which are used to represent
dependent or causal complex systems. Statistically equivalent causal or
directed graphical models are said to belong to a Markov equivalent class. It
is of great interest to describe and understand the space of such classes.
However, with currently known algorithms, sampling over such classes is only
feasible for graphs with fewer than approximately 20 vertices. In this paper,
we design reversible irreducible Markov chains on the space of Markov
equivalent classes by proposing a perfect set of operators that determine the
transitions of the Markov chain. The stationary distribution of a proposed
Markov chain has a closed form and can be computed easily. Specifically, we
construct a concrete perfect set of operators on sparse Markov equivalence
classes by introducing appropriate conditions on each possible operator.
Algorithms and their accelerated versions are provided to efficiently generate
Markov chains and to explore properties of Markov equivalence classes of sparse
directed acyclic graphs (DAGs) with thousands of vertices. We find
experimentally that in most Markov equivalence classes of sparse DAGs, (1) most
edges are directed, (2) most undirected subgraphs are small and (3) the number
of these undirected subgraphs grows approximately linearly with the number of
vertices. The article contains supplement arXiv:1303.0632,
http://dx.doi.org/10.1214/13-AOS1125SUPPComment: Published in at http://dx.doi.org/10.1214/13-AOS1125 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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