1,580 research outputs found
Adaptive Lasso and group-Lasso for functional Poisson regression
International audienceHigh dimensional Poisson regression has become a standard framework for the analysis of massive counts datasets. In this work we estimate the intensity function of the Poisson regression model by using a dictionary approach, which generalizes the classical basis approach , combined with a Lasso or a group-Lasso procedure. Selection depends on penalty weights that need to be calibrated. Standard methodologies developed in the Gaussian framework can not be directly applied to Poisson models due to heteroscedasticity. Here we provide data-driven weights for the Lasso and the group-Lasso derived from concentration inequalities adapted to the Poisson case. We show that the associated Lasso and group-Lasso procedures satisfy fast and slow oracle inequalities. Simulations are used to assess the empirical performance of our procedure, and an original application to the analysis of Next Generation Sequencing data is provided
Combining Quadratic Penalization and Variable Selection via Forward Boosting
Quadratic penalties can be used to incorporate external knowledge about the association structure among regressors. Unfortunately, they do not enforce single estimated regression coefficients to equal zero. In this paper we propose a new approach to combine quadratic penalization and variable selection within the framework of generalized linear models. The new method is called Forward Boosting and is related to componentwise boosting techniques. We demonstrate in simulation studies and a real-world data example that the new approach competes well with existing alternatives especially when the focus is on interpretable structuring of predictors
Locally adaptive smoothing with Markov random fields and shrinkage priors
We present a locally adaptive nonparametric curve fitting method that
operates within a fully Bayesian framework. This method uses shrinkage priors
to induce sparsity in order-k differences in the latent trend function,
providing a combination of local adaptation and global control. Using a scale
mixture of normals representation of shrinkage priors, we make explicit
connections between our method and kth order Gaussian Markov random field
smoothing. We call the resulting processes shrinkage prior Markov random fields
(SPMRFs). We use Hamiltonian Monte Carlo to approximate the posterior
distribution of model parameters because this method provides superior
performance in the presence of the high dimensionality and strong parameter
correlations exhibited by our models. We compare the performance of three prior
formulations using simulated data and find the horseshoe prior provides the
best compromise between bias and precision. We apply SPMRF models to two
benchmark data examples frequently used to test nonparametric methods. We find
that this method is flexible enough to accommodate a variety of data generating
models and offers the adaptive properties and computational tractability to
make it a useful addition to the Bayesian nonparametric toolbox.Comment: 38 pages, to appear in Bayesian Analysi
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