基于稀疏图码的混合稀疏线性回归参数估计

Parameter Estimation of Hybrid Sparse Linear Regression based on Sparse Graph Codes

由于似然函数的非凸性和局部最优解的存在,混合模型的参数估计是一个非常困难的问题。它通常需要较大的样本量及较高的计算复杂度。针对混合稀疏线性回归的参数估计问题,利用现代编码理论和稀疏线性回归系统之间的关系,提出一种基于稀疏图码构造查询矩阵并进行参数估计的逐步迭代分离算法,从样本测量维度、算法复杂度以及测量性能三个方面进行仿真实验来为查询矩阵的构造和重构算法的设计提供理论支撑。仿真显示,对于固定个数的稀疏参数向量,该算法可以达到顺序最优样本和时间复杂度Θ(K)。

Due to the non-convexity of the likelihood function and the existence of local optimal solutions,the parameter estimation of the mixed model is a very difficult problem.It usually requires a larger sample size and higher computational complexity.Aiming at the parameter estimation problem of hybrid sparse linear regression,by using the relationship between modern coding theory and sparse linear regression system,a stepwise iterative separation algorithm based on sparse graph codes to construct query matrix and estimate parameters is proposed.Simulation experiments are carried out from three aspects of sample measurement dimension,algorithm complexity and measurement performance to provide theoretical support for the construction of query matrix and the design of reconstruction algorithm.The simulation indicates that for a fixed number of sparse parameter vectors,the algorithm can achieve the optimal sample order and time complexityΘ(K).