DeepAI AI Chat
Log In Sign Up

Simultaneous Signal Subspace Rank and Model Selection with an Application to Single-snapshot Source Localization

by   Muhammad Naveed Tabassum, et al.

This paper proposes a novel method for model selection in linear regression by utilizing the solution path of ℓ_1 regularized least-squares (LS) approach (i.e., Lasso). This method applies the complex-valued least angle regression and shrinkage (c-LARS) algorithm coupled with a generalized information criterion (GIC) and referred to as the c-LARS-GIC method. c-LARS-GIC is a two-stage procedure, where firstly precise values of the regularization parameter, called knots, at which a new predictor variable enters (or leaves) the active set are computed in the Lasso solution path. Active sets provide a nested sequence of regression models and GIC then selects the best model. The sparsity order of the chosen model serves as an estimate of the model order and the LS fit based only on the active set of the model provides an estimate of the regression parameter vector. We then consider a source localization problem, where the aim is to detect the number of impinging source waveforms at a sensor array as well to estimate their direction-of-arrivals (DoA-s) using only a single-snapshot measurement. We illustrate via simulations that, after formulating the problem as a grid-based sparse signal reconstruction problem, the proposed c-LARS-GIC method detects the number of sources with high probability while at the same time it provides accurate estimates of source locations.


page 1

page 2

page 3

page 4


Sequential adaptive elastic net approach for single-snapshot source localization

This paper proposes efficient algorithms for accurate recovery of direct...

Bolasso: model consistent Lasso estimation through the bootstrap

We consider the least-square linear regression problem with regularizati...

Model Selection for High-Dimensional Regression under the Generalized Irrepresentability Condition

In the high-dimensional regression model a response variable is linearly...

Nested Model Averaging on Solution Path for High-dimensional Linear Regression

We study the nested model averaging method on the solution path for a hi...

Cluster Regularization via a Hierarchical Feature Regression

Prediction tasks with high-dimensional nonorthogonal predictor sets pose...

A LASSO-Inspired Approach for Localizing Power System Infeasibility

A method is proposed to identify and localize the cause of network colla...

A Unified Dynamic Approach to Sparse Model Selection

Sparse model selection is ubiquitous from linear regression to graphical...