DocumentCode :
592575
Title :
Nonsmooth regression and state estimation using piecewise quadratic log-concave densities
Author :
Aravkin, Aleksandr Y. ; Burke, James V. ; Pillonetto, G.
Author_Institution :
Dept. of Earth & Ocean Sci., Univ. of British Columbia, Vancouver, BC, Canada
fYear :
2012
fDate :
10-13 Dec. 2012
Firstpage :
4101
Lastpage :
4106
Abstract :
We demonstrate that many robust, sparse and nonsmooth identification and Kalman smoothing problems can be studied using a unified statistical framework. This framework is built on a broad sub-class of log-concave densities, which we call PLQ densities, that include many popular models for regression and state estimation, e.g. ℓ1, ℓ2, Vapnik and Huber penalties. Using the dual representation for PLQ penalties, we review conditions that permit interpreting them as negative logs of true probability densities. This allows construction of non-smooth multivariate distributions with specified means and variances from simple scalar building blocks. The result is a flexible statistical modelling framework for a variety of identification and learning applications, comprising models whose solutions can be computed using interior point (IP) methods. For the special case of Kalman smoothing, the complexity of this method scales linearly with the number of time-points, exactly as in the quadratic (Gaussian) case.
Keywords :
probability; regression analysis; state estimation; Huber penalty; Kalman smoothing problem; PLQ density; PLQ penalty; Vapnik penalty; flexible statistical modelling framework; interior point method; nonsmooth identification; nonsmooth multivariate distribution; nonsmooth regression; piecewise quadratic log concave density; probability density; state estimation; unified statistical framework; Estimation; IP networks; Kalman filters; Optimization; Robustness; Smoothing methods; Vectors; Kalman smoothing; interior point methods; nonsmooth optimization; robust and sparse estimation; statistical modeling;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Decision and Control (CDC), 2012 IEEE 51st Annual Conference on
Conference_Location :
Maui, HI
ISSN :
0743-1546
Print_ISBN :
978-1-4673-2065-8
Electronic_ISBN :
0743-1546
Type :
conf
DOI :
10.1109/CDC.2012.6426893
Filename :
6426893
Link To Document :
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