Improved reduced set density estimator by introducing weighted l1 penalty on the weight coefficients

Reduced set density estimator (RSDE), employing a small percentage of available data samples, is an efficient and important nonparametric technique for probability density function estimation. But it still faces the critical challenge in practical applications when training the estimator on large data sets. Dealing with its high complexity both in time and space, an improved reduced set density estimator with weighted l₁ penalty term (WL1-RSDE) is proposed in this paper. To further reduce the complexity, we introduce the weighted l₁ norm as the additional penalty term on the plug-in estimation of weight coefficients, in which small weight coefficients are more likely to be driven to zero. Then, an iterative algorithm is proposed to solve the corresponding minimization problem efficiently. Several examples are employed to demonstrate that the proposed WL1-RSDE is superior to the related methods including the RSDE in sparsity and complexity.