Generalized Probability Density Function Estimation via Convex Optimization
Generalized Probability Density Function Estimation via Convex Optimization
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DOI：
10.1109/isit50566.2022.9834583
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发表时间：
2022-06
期刊：
影响因子：
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通讯作者：
Arian Eamaz;Farhang Yeganegi;M. Soltanalian;N. Devroye
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文献类型：
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作者：
Arian Eamaz;Farhang Yeganegi;M. Soltanalian;N. Devroye
统计学中一个长期存在的问题与从有限样本集估计连续随机变量的概率密度函数有关。本文提出了一种新的基于凸规划的参数概率密度函数估计。我们的公式将未知分布分解为一个高斯罚函数加上一个误差函数，然后用多尺度小波函数(特别是框架)展开，如B-Spline和墨西哥帽子小波。为了恢复误差函数中的小波系数，通过线性约束，建立了考虑概率密度函数正性的凸二次规划。所提出的分解模型有助于准确估计感兴趣的概率密度函数。
A longstanding problem in statistics pertains to the estimation of probability density functions of continuous random variables from a finite set of their samples. In this paper, we propose a new parametric probability density function estimator based on convex programming. Our formulation decomposes the unknown distribution as a Gaussian penalty function plus an error function, which is then expanded by multi-scale wavelet functions (specifically frames) such as B-Spline and Mexican Hat wavelets. To recover the wavelet coefficients in the error function, a convex quadratic program is formulated which takes into account the positivity of the probability density function-through a linear constraint. The proposed decomposition model is shown to facilitate an accurate estimation of the probability density functions of interest.