Model Selection in High-Dimensional Block-Sparse Linear Regression

Model selection is an indispensable part of data analysis dealing very frequently with fitting and prediction purposes. In this paper, we tackle the problem of model selection in a general linear regression where the parameter matrix possesses a block-sparse structure, i.e., the non-zero entries occur in clusters or blocks and the number of such non-zero blocks is very small compared to the parameter dimension. Furthermore, a high-dimensional setting is considered where the parameter dimension is quite large compared to the number of available measurements. To perform model selection in this setting, we present an information criterion that is a generalization of the Extended Bayesian Information Criterion-Robust (EBIC-R) and it takes into account both the block structure and the high-dimensionality scenario. The analytical steps for deriving the EBIC-R for this setting are provided. Simulation results show that the proposed method performs considerably better than the existing state-of-the-art methods and achieves empirical consistency at large sample sizes and/or at high-SNR.Comment: 5 pages, 2 figure

Evidence Theory based Cooperative Energy Detection under Noise Uncertainty

Noise power uncertainty is a major issue in energy-based spectrum sensors. Any uncertainty in the noise power leads to significant reduction in the detection performance of the energy detector and also results in a performance limitation in the form of SNR walls. In this paper, we propose an evidence theory (also called Dempster-Shafer theory (DST)) based cooperative energy detection (CED) for spectrum sensing. The noise variance is modeled as a random variable with a known distribution. The analyzed system model is similar to a distributed parallel detection network where each secondary user (SU) evaluates the energy from its received signal samples and sends it to a fusion center (FC), which makes the final decision. However, in the proposed DST-based method, the SUs sends computed belief-values instead of actual energy value to the FC. The uncertainty in the noise variance is accounted for by discounting the belief values based on the amount of uncertainty associated with each SU. Finally, the discounted belief values are combined using Dempster rule to reach at a global decision. Simulation results indicate that the proposed DST scheme significantly improves the detection probability under low average signal-to-noise ratio(ASNR) compared to the traditional sum fusion rule in the presence of noise uncertainty.Peer reviewe