CurvPy is an open-source Python library for automated curve fitting and regression analysis, aiming to make advanced statistical and machine learning techniques more accessible. This paper explores the mathematical foundations and implementation of key CurvPy components for optimization, smoothing, imputation, summarization, visualization, regression, evaluation, and tuning. The methodology leverages well-established statistical and computational algorithms adapted through both simplification and exposure of advanced options to balance usability and customizability. Mathematical techniques utilized include least squares estimation, Savitzky-Golay filtering, matrix completion, gradient descent optimization, regularization, basis function regression, and standard model evaluation metrics.

翻译：CurvPy是一个用于自动化曲线拟合与回归分析的开源Python库，旨在使高级统计与机器学习技术更易于使用。本文探讨了CurvPy在优化、平滑、插补、汇总、可视化、回归、评估与调参等关键组件的数学基础与实现方法。该方法论通过简化和开放高级选项来平衡可用性与可定制性，利用了成熟的统计与计算算法。采用的数学技术包括最小二乘估计、Savitzky-Golay滤波、矩阵补全、梯度下降优化、正则化、基函数回归以及标准模型评估指标。