Sparse signal recovery under poisson statistics for online marketing applications

We are motivated by many applications such as problems that arise in online marketing applications, where the observations are governed by non-homogeneous Poisson models. We analyze the performance of a Maximum Likelihood (ML) decoder. We prove consistency and show an exponential rate of converge for sparse recovery in the high-dimensional Poisson setting. After verifying the efficiency of ML estimator empirically, we apply the ML decoder to study the dynamics of online marketing methods over time.

[1]  Jöran Bela Erik Beel,et al.  Academic Search Engine Optimization (ASEO ): Optimizing Scholarly Literature for Google Scholar & Co. , 2010 .

[2]  S. Geer,et al.  On the conditions used to prove oracle results for the Lasso , 2009, 0910.0722.

[3]  S. Portnoy Asymptotic Behavior of Likelihood Methods for Exponential Families when the Number of Parameters Tends to Infinity , 1988 .

[4]  Venkatesh Saligrama,et al.  Sparse signal recovery under Poisson statistics , 2013, 2013 51st Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[5]  B. Hoadley Asymptotic Properties of Maximum Likelihood Estimators for the Independent Not Identically Distributed Case , 1971 .

[6]  Erik Wilde,et al.  Academic Search Engine Optimization (ASEO) , 2010 .

[7]  I. Rish,et al.  Sparse signal recovery with exponential-family noise , 2009, 2009 47th Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[8]  Shuheng Zhou Restricted Eigenvalue Conditions on Subgaussian Random Matrices , 2009, 0912.4045.

[9]  I. Rubin,et al.  Random point processes , 1977, Proceedings of the IEEE.

[10]  Ambuj Tewari,et al.  Learning Exponential Families in High-Dimensions: Strong Convexity and Sparsity , 2009, AISTATS.

[11]  Martin J. Wainwright,et al.  A unified framework for high-dimensional analysis of $M$-estimators with decomposable regularizers , 2009, NIPS.

[12]  Roummel F. Marcia,et al.  Compressed Sensing Performance Bounds Under Poisson Noise , 2009, IEEE Transactions on Signal Processing.

[13]  Mohamed-Jalal Fadili,et al.  A Proximal Iteration for Deconvolving Poisson Noisy Images Using Sparse Representations , 2008, IEEE Transactions on Image Processing.

[14]  Peter I. Frazier,et al.  Distance dependent Chinese restaurant processes , 2009, ICML.

[15]  W. Newey,et al.  Uniform Convergence in Probability and Stochastic Equicontinuity , 1991 .

[16]  Bin Yu,et al.  THE LASSO UNDER POISSON-LIKE HETEROSCEDASTICITY , 2013 .

[17]  P. Bickel,et al.  SIMULTANEOUS ANALYSIS OF LASSO AND DANTZIG SELECTOR , 2008, 0801.1095.

[18]  Zachary T. Harmany,et al.  Sparse poisson intensity reconstruction algorithms , 2009, 2009 IEEE/SP 15th Workshop on Statistical Signal Processing.

[19]  Jean-Luc Starck,et al.  Deconvolution under Poisson noise using exact data fidelity and synthesis or analysis sparsity priors , 2011, 1103.2213.

[20]  Martin J. Wainwright,et al.  Restricted Eigenvalue Properties for Correlated Gaussian Designs , 2010, J. Mach. Learn. Res..

[21]  Christoph Trattner,et al.  Social stream marketing on Facebook: a case study , 2013, Int. J. Soc. Humanist. Comput..