Adaptive sparse logistic regression with application to neuronal plasticity analysis

We consider the problem of estimating the time-varying parameters of a sparse logistic regression model in an online setting. We introduce two adaptive filters based on proximal gradient algorithms for recursive estimation of the model parameters by maximizing an ℓ1-regularized version of the observation log-likelihood, as well as an efficient online procedure for computing statistical confidence intervals around the estimates. We evaluate the performance of the proposed algorithms through simulation studies as well as application to real spiking data from the ferret's primary auditory cortex during a series of auditory tasks.

[1]  Vahid Tarokh,et al.  SPARLS: The Sparse RLS Algorithm , 2010, IEEE Transactions on Signal Processing.

[2]  N. Meinshausen,et al.  High-dimensional graphs and variable selection with the Lasso , 2006, math/0608017.

[3]  S. Geer,et al.  On asymptotically optimal confidence regions and tests for high-dimensional models , 2013, 1303.0518.

[4]  Shihab A. Shamma,et al.  Recursive Sparse Point Process Regression With Application to Spectrotemporal Receptive Field Plasticity Analysis , 2015, IEEE Transactions on Signal Processing.

[5]  P. Bühlmann,et al.  The group lasso for logistic regression , 2008 .

[6]  Stuart Barber,et al.  All of Statistics: a Concise Course in Statistical Inference , 2005 .

[7]  I. Daubechies,et al.  An iterative thresholding algorithm for linear inverse problems with a sparsity constraint , 2003, math/0307152.

[8]  Cun-Hui Zhang,et al.  Confidence intervals for low dimensional parameters in high dimensional linear models , 2011, 1110.2563.

[9]  J. Fritz,et al.  Active listening: Task-dependent plasticity of spectrotemporal receptive fields in primary auditory cortex , 2005, Hearing Research.

[10]  Robert D. Nowak,et al.  An EM algorithm for wavelet-based image restoration , 2003, IEEE Trans. Image Process..

[11]  Adel Javanmard,et al.  Confidence intervals and hypothesis testing for high-dimensional regression , 2013, J. Mach. Learn. Res..

[12]  Michael Elad,et al.  From Sparse Solutions of Systems of Equations to Sparse Modeling of Signals and Images , 2009, SIAM Rev..