\texttt{Mixture-Models} is an open-source Python library for fitting Gaussian Mixture Models (GMM) and their variants, such as Parsimonious GMMs, Mixture of Factor Analyzers, MClust models, Mixture of Student's t distributions, etc. It streamlines the implementation and analysis of these models using various first/second order optimization routines such as Gradient Descent and Newton-CG through automatic differentiation (AD) tools. This helps in extending these models to high-dimensional data, which is first of its kind among Python libraries. The library provides user-friendly model evaluation tools, such as BIC, AIC, and log-likelihood estimation. The source-code is licensed under MIT license and can be accessed at \url{https://github.com/kasakh/Mixture-Models}. The package is highly extensible, allowing users to incorporate new distributions and optimization techniques with ease. We conduct a large scale simulation to compare the performance of various gradient based approaches against Expectation Maximization on a wide range of settings and identify the corresponding best suited approach.

《Mixture-Models》是一个开源的Python库，用于拟合高斯混合模型及其变种，如Sparimonious GMM、因子分析混合模型、MClust模型、学生t分布混合模型等。它使用各种一阶/二阶优化算法，如梯度下降和牛顿法，通过自动微分工具简化了这些模型的实现和分析，从而帮助扩展这些模型到高维数据。该库提供了用户友好的模型评估工具，如BIC、AIC和对数似然估计。该软件包具有很高的可扩展性，允许用户轻松地添加新的分布和优化技术。我们进行了大规模模拟实验，比较了各种基于梯度的方法与期望最大化算法在各种设置下的性能，并确定相应最适合的方法。

混合模型：一个用于基于模型的聚类的Python一站式库，使用各种混合模型