13,678 research outputs found
Likelihood Adaptively Modified Penalties
A new family of penalty functions, adaptive to likelihood, is introduced for
model selection in general regression models. It arises naturally through
assuming certain types of prior distribution on the regression parameters. To
study stability properties of the penalized maximum likelihood estimator, two
types of asymptotic stability are defined. Theoretical properties, including
the parameter estimation consistency, model selection consistency, and
asymptotic stability, are established under suitable regularity conditions. An
efficient coordinate-descent algorithm is proposed. Simulation results and real
data analysis show that the proposed method has competitive performance in
comparison with existing ones.Comment: 42 pages, 4 figure
Adaptive First-Order Methods for General Sparse Inverse Covariance Selection
In this paper, we consider estimating sparse inverse covariance of a Gaussian
graphical model whose conditional independence is assumed to be partially
known. Similarly as in [5], we formulate it as an -norm penalized maximum
likelihood estimation problem. Further, we propose an algorithm framework, and
develop two first-order methods, that is, the adaptive spectral projected
gradient (ASPG) method and the adaptive Nesterov's smooth (ANS) method, for
solving this estimation problem. Finally, we compare the performance of these
two methods on a set of randomly generated instances. Our computational results
demonstrate that both methods are able to solve problems of size at least a
thousand and number of constraints of nearly a half million within a reasonable
amount of time, and the ASPG method generally outperforms the ANS method.Comment: 19 pages, 1 figur
Adaptive LASSO estimation for functional hidden dynamic geostatistical models
We propose a novel model selection algorithm based on a penalized maximum likelihood estimator (PMLE) for functional hidden dynamic geostatistical models (f-HDGM). These models employ a classic mixed-effect regression structure with embedded spatiotemporal dynamics to model georeferenced data observed in a functional domain. Thus, the regression coefficients are functions. The algorithm simultaneously selects the relevant spline basis functions and regressors that are used to model the fixed effects. In this way, it automatically shrinks to zero irrelevant parts of the functional coefficients or the entire function for an irrelevant regressor. The algorithm is based on an adaptive LASSO penalty function, with weights obtained by the unpenalised f-HDGM maximum likelihood estimators. The computational burden of maximisation is drastically reduced by a local quadratic approximation of the log-likelihood. A Monte Carlo simulation study provides insight in prediction ability and parameter estimate precision, considering increasing spatiotemporal dependence and cross-correlations among predictors. Further, the algorithm behaviour is investigated when modelling air quality functional data with several weather and land cover covariates. Within this application, we also explore some scalability properties of our algorithm. Both simulations and empirical results show that the prediction ability of the penalised estimates are equivalent to those provided by the maximum likelihood estimates. However, adopting the so-called one-standard-error rule, we obtain estimates closer to the real ones, as well as simpler and more interpretable models
Convex and non-convex regularization methods for spatial point processes intensity estimation
This paper deals with feature selection procedures for spatial point
processes intensity estimation. We consider regularized versions of estimating
equations based on Campbell theorem derived from two classical functions:
Poisson likelihood and logistic regression likelihood. We provide general
conditions on the spatial point processes and on penalty functions which ensure
consistency, sparsity and asymptotic normality. We discuss the numerical
implementation and assess finite sample properties in a simulation study.
Finally, an application to tropical forestry datasets illustrates the use of
the proposed methods
Rejoinder: One-step sparse estimates in nonconcave penalized likelihood models
We would like to take this opportunity to thank the discussants for their
thoughtful comments and encouragements on our work [arXiv:0808.1012]. The
discussants raised a number of issues from theoretical as well as computational
perspectives. Our rejoinder will try to provide some insights into these issues
and address specific questions asked by the discussants.Comment: Published in at http://dx.doi.org/10.1214/07-AOS0316REJ the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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