Adaptive Nonparametric Density Estimation with B-Spline Bases

• DOI: 10.3390/math11020291
• Publication Date: 2023-01-06T07:20:30Z
• Authors: Yanchun Zhao; Mengzhu Zhang; Qian Ni; Xuhui Wang
• Keywords: Overfitting; B-spline; Kernel density estimation; Density estimation; Spline (mechanical)

Learning density estimation is important in probabilistic modeling and reasoning with uncertainty. Since B-spline basis functions are piecewise polynomials local support, B-splines shows its advantages when intensive numerical computations involved the subsequent applications. To obtain an optimal B-splines, we need to select bandwidth (i.e., distance of two adjacent knots) for uniform B-splines. However, selection challenging, computation costly. On other hand, nonuniform can improve on approximation capability Based this observation, perform By introducing error indicator attached each interval, propose adaptive strategy generate knot vector. The information entropy locally, which closely related number kernels construct estimator. experiments show that, compared B-spline, not only achieves better results but also effectively alleviates overfitting phenomenon caused by comparison existing procedures, including state-of-the-art kernel estimators, demonstrates accuracy our new method.