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是一个开源的Python库，用于自动曲线拟合与回归分析，旨在使先进的统计和机器学习技术更易于使用。本文探究了CurvPy关键组件的数学基础及其在优化、平滑、插补、汇总、可视化、回归、评估和调参中的实现。该方法利用既有的统计学与计算算法，通过简化与暴露高级选项的平衡策略，兼顾可用性与可定制性。所涉及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。