主讲人：刘妍岩 教授 （武汉大学）

时  间：2014年12月20日（周六）  16：00-18：00

地  点：必赢76net线路官网北一区文科楼215教室

摘  要：We develop a constructive approach to estimating an approximatelysparse linear regression model in high-dimensions. The proposed approach is a computational algorithm that generates a sequence of solutions iteratively, based on support detection using primal and dual information and root finding according to a modified KKT condition for the `0-penalized least squares criterion. We refer to the proposed algorithm as SDAR for brevity. Under certain di erent regularity conditions on the design matrix and sparsity assumption on the regression coefficients, we show that with high probability, the errors of the solution sequence decay exponentially to the minimax error bounds and to the optimal error bound in more than O(pK log(R)) and O(log(R)) steps respectively, where K is the sparsity level, R is the relative magnitude of the nonzero coecients. Moreover the oracle estimator can be exactly recovered with high probability at the same cost if we know K. Computational complexity analysis shows that the cost of SDAR is O(np) in each step if the regression coefficients are sparse or can be sparsely approximated. Simulation studies support our theoretical results. We also consider ASDAR, an adaptive version of SDAR to make it more practical in applications. Numerical comparisons with Lasso and MCP and several greedy methods indicate that ASDAR is competitive with or outperforms them in accuracy and efficiency