219 research outputs found
Effective and efficient structure learning with pruning and model averaging strategies
Learning the structure of a Bayesian Network (BN) with score-based solutions
involves exploring the search space of possible graphs and moving towards the
graph that maximises a given objective function. Some algorithms offer exact
solutions that guarantee to return the graph with the highest objective score,
while others offer approximate solutions in exchange for reduced computational
complexity. This paper describes an approximate BN structure learning
algorithm, which we call Model Averaging Hill-Climbing (MAHC), that combines
two novel strategies with hill-climbing search. The algorithm starts by pruning
the search space of graphs, where the pruning strategy can be viewed as an
aggressive version of the pruning strategies that are typically applied to
combinatorial optimisation structure learning problems. It then performs model
averaging in the hill-climbing search process and moves to the neighbouring
graph that maximises the objective function, on average, for that neighbouring
graph and over all its valid neighbouring graphs. Comparisons with other
algorithms spanning different classes of learning suggest that the combination
of aggressive pruning with model averaging is both effective and efficient,
particularly in the presence of data noise
Bayesian network structure learning with causal effects in the presence of latent variables.
Latent variables may lead to spurious relationships that can be
misinterpreted as causal relationships. In Bayesian Networks (BNs), this
challenge is known as learning under causal insufficiency. Structure learning
algorithms that assume causal insufficiency tend to reconstruct the ancestral
graph of a BN, where bi-directed edges represent confounding and directed edges
represent direct or ancestral relationships. This paper describes a hybrid
structure learning algorithm, called CCHM, which combines the constraint-based
part of cFCI with hill-climbing score-based learning. The score-based process
incorporates Pearl s do-calculus to measure causal effects and orientate edges
that would otherwise remain undirected, under the assumption the BN is a linear
Structure Equation Model where data follow a multivariate Gaussian
distribution. Experiments based on both randomised and well-known networks show
that CCHM improves the state-of-the-art in terms of reconstructing the true
ancestral graph
Distributional Equivalence and Structure Learning for Bow-free Acyclic Path Diagrams
We consider the problem of structure learning for bow-free acyclic path
diagrams (BAPs). BAPs can be viewed as a generalization of linear Gaussian DAG
models that allow for certain hidden variables. We present a first method for
this problem using a greedy score-based search algorithm. We also prove some
necessary and some sufficient conditions for distributional equivalence of BAPs
which are used in an algorithmic ap- proach to compute (nearly) equivalent
model structures. This allows us to infer lower bounds of causal effects. We
also present applications to real and simulated datasets using our publicly
available R-package
Robust causal structure learning with some hidden variables
We introduce a new method to estimate the Markov equivalence class of a
directed acyclic graph (DAG) in the presence of hidden variables, in settings
where the underlying DAG among the observed variables is sparse, and there are
a few hidden variables that have a direct effect on many of the observed ones.
Building on the so-called low rank plus sparse framework, we suggest a
two-stage approach which first removes the effect of the hidden variables, and
then estimates the Markov equivalence class of the underlying DAG under the
assumption that there are no remaining hidden variables. This approach is
consistent in certain high-dimensional regimes and performs favourably when
compared to the state of the art, both in terms of graphical structure recovery
and total causal effect estimation
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