13,571 research outputs found
Efficient computational strategies to learn the structure of probabilistic graphical models of cumulative phenomena
Structural learning of Bayesian Networks (BNs) is a NP-hard problem, which is
further complicated by many theoretical issues, such as the I-equivalence among
different structures. In this work, we focus on a specific subclass of BNs,
named Suppes-Bayes Causal Networks (SBCNs), which include specific structural
constraints based on Suppes' probabilistic causation to efficiently model
cumulative phenomena. Here we compare the performance, via extensive
simulations, of various state-of-the-art search strategies, such as local
search techniques and Genetic Algorithms, as well as of distinct regularization
methods. The assessment is performed on a large number of simulated datasets
from topologies with distinct levels of complexity, various sample size and
different rates of errors in the data. Among the main results, we show that the
introduction of Suppes' constraints dramatically improve the inference
accuracy, by reducing the solution space and providing a temporal ordering on
the variables. We also report on trade-offs among different search techniques
that can be efficiently employed in distinct experimental settings. This
manuscript is an extended version of the paper "Structural Learning of
Probabilistic Graphical Models of Cumulative Phenomena" presented at the 2018
International Conference on Computational Science
Model selection and local geometry
We consider problems in model selection caused by the geometry of models
close to their points of intersection. In some cases---including common classes
of causal or graphical models, as well as time series models---distinct models
may nevertheless have identical tangent spaces. This has two immediate
consequences: first, in order to obtain constant power to reject one model in
favour of another we need local alternative hypotheses that decrease to the
null at a slower rate than the usual parametric (typically we will
require or slower); in other words, to distinguish between the
models we need large effect sizes or very large sample sizes. Second, we show
that under even weaker conditions on their tangent cones, models in these
classes cannot be made simultaneously convex by a reparameterization.
This shows that Bayesian network models, amongst others, cannot be learned
directly with a convex method similar to the graphical lasso. However, we are
able to use our results to suggest methods for model selection that learn the
tangent space directly, rather than the model itself. In particular, we give a
generic algorithm for learning Bayesian network models
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