74,714 research outputs found
Sparsity with sign-coherent groups of variables via the cooperative-Lasso
We consider the problems of estimation and selection of parameters endowed
with a known group structure, when the groups are assumed to be sign-coherent,
that is, gathering either nonnegative, nonpositive or null parameters. To
tackle this problem, we propose the cooperative-Lasso penalty. We derive the
optimality conditions defining the cooperative-Lasso estimate for generalized
linear models, and propose an efficient active set algorithm suited to
high-dimensional problems. We study the asymptotic consistency of the estimator
in the linear regression setup and derive its irrepresentable conditions, which
are milder than the ones of the group-Lasso regarding the matching of groups
with the sparsity pattern of the true parameters. We also address the problem
of model selection in linear regression by deriving an approximation of the
degrees of freedom of the cooperative-Lasso estimator. Simulations comparing
the proposed estimator to the group and sparse group-Lasso comply with our
theoretical results, showing consistent improvements in support recovery for
sign-coherent groups. We finally propose two examples illustrating the wide
applicability of the cooperative-Lasso: first to the processing of ordinal
variables, where the penalty acts as a monotonicity prior; second to the
processing of genomic data, where the set of differentially expressed probes is
enriched by incorporating all the probes of the microarray that are related to
the corresponding genes.Comment: Published in at http://dx.doi.org/10.1214/11-AOAS520 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Active Sampling-based Binary Verification of Dynamical Systems
Nonlinear, adaptive, or otherwise complex control techniques are increasingly
relied upon to ensure the safety of systems operating in uncertain
environments. However, the nonlinearity of the resulting closed-loop system
complicates verification that the system does in fact satisfy those
requirements at all possible operating conditions. While analytical proof-based
techniques and finite abstractions can be used to provably verify the
closed-loop system's response at different operating conditions, they often
produce conservative approximations due to restrictive assumptions and are
difficult to construct in many applications. In contrast, popular statistical
verification techniques relax the restrictions and instead rely upon
simulations to construct statistical or probabilistic guarantees. This work
presents a data-driven statistical verification procedure that instead
constructs statistical learning models from simulated training data to separate
the set of possible perturbations into "safe" and "unsafe" subsets. Binary
evaluations of closed-loop system requirement satisfaction at various
realizations of the uncertainties are obtained through temporal logic
robustness metrics, which are then used to construct predictive models of
requirement satisfaction over the full set of possible uncertainties. As the
accuracy of these predictive statistical models is inherently coupled to the
quality of the training data, an active learning algorithm selects additional
sample points in order to maximize the expected change in the data-driven model
and thus, indirectly, minimize the prediction error. Various case studies
demonstrate the closed-loop verification procedure and highlight improvements
in prediction error over both existing analytical and statistical verification
techniques.Comment: 23 page
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