TY - GEN
T1 - Rate analysis for detection of sparse mixtures
AU - Ligo, Jonathan G.
AU - Moustakides, George V.
AU - Veeravalli, Venugopal V.
N1 - Publisher Copyright:
© 2016 IEEE.
PY - 2016/5/18
Y1 - 2016/5/18
N2 - In this paper, we study the rate of decay of the probability of error for distinguishing between a sparse signal with noise, modeled as a sparse mixture, from pure noise. This problem has many applications in signal processing, evolutionary biology, bioinformatics, astrophysics and feature selection for machine learning. We let the mixture probability tend to zero as the number of observations tends to infinity and derive oracle rates at which the error probability can be driven to zero for a general class of signal and noise distributions. In contrast to the problem of detection of non-sparse signals, we see the log-probability of error decays sublinearly rather than linearly and is characterized through the x2-divergence rather than the Kullback-Leibler divergence. This work provides the first characterization of the rate of decay of the error probability for this problem.
AB - In this paper, we study the rate of decay of the probability of error for distinguishing between a sparse signal with noise, modeled as a sparse mixture, from pure noise. This problem has many applications in signal processing, evolutionary biology, bioinformatics, astrophysics and feature selection for machine learning. We let the mixture probability tend to zero as the number of observations tends to infinity and derive oracle rates at which the error probability can be driven to zero for a general class of signal and noise distributions. In contrast to the problem of detection of non-sparse signals, we see the log-probability of error decays sublinearly rather than linearly and is characterized through the x2-divergence rather than the Kullback-Leibler divergence. This work provides the first characterization of the rate of decay of the error probability for this problem.
KW - Detection theory
KW - error exponents
KW - large deviations
KW - likelihood ratio test
KW - sparse detection
UR - http://www.scopus.com/inward/record.url?scp=84973304464&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84973304464&partnerID=8YFLogxK
U2 - 10.1109/ICASSP.2016.7472477
DO - 10.1109/ICASSP.2016.7472477
M3 - Conference contribution
AN - SCOPUS:84973304464
T3 - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
SP - 4244
EP - 4248
BT - 2016 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016 - Proceedings
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 41st IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016
Y2 - 20 March 2016 through 25 March 2016
ER -