Generalized Linear Models and Nonparametric Regression

所在平台: Coursera

课程主页: https://www.coursera.org/learn/generalized-linear-models-and-nonparametric-regression

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课程简介

课程名称：广义线性模型与非参数回归 课程概述：在数据科学统计建模项目的最后一门课程中，学习者将研究一系列更高级的统计建模工具。这些工具包括广义线性模型（GLMs），将通过逻辑回归引入分类；非参数建模，包括核估计、平滑样条；以及半参数广义加性模型（GAMs）。课程将强调对这些工具的概念理解，并关注使用复杂统计模型所引发的伦理问题。这门课程可以作为科罗拉多大学博尔德分校数据科学硕士（MS-DS）学位的一部分进行学分学习。MS-DS是一个跨学科的学位，结合了博尔德分校应用数学、计算机科学、信息科学等多个学科的教师资源。该项目具有基于表现的招生标准且无申请流程，适合具有计算机科学、信息科学、数学和统计等广泛本科教育和/或专业经验的个人。更多信息请访问：https://www.coursera.org/degrees/master-of-science-data-science-boulder。 课程大纲： 1. **广义线性模型简介与二项回归**：介绍广义线性模型（GLMs），重点研究二项数据，讨论GLMs的必要性，二项回归模型，包括常见的二项链接函数，正确解读二项回归模型，评估模型拟合度和预测能力的方法。 2. **计数数据模型**：探讨如何建模计数数据，描述Poisson回归及其在真实数据中的应用，以及在不适用Poisson回归的场景下的解决方案。 3. **非参数回归简介**：介绍非参数回归模型，与之前学习的参数模型进行对比，研究特定的非参数回归模型，如核估计和平滑样条，最终引入加性模型作为参数与非参数方法的结合。 4. **广义加性模型简介**：探讨广义加性模型（GAMs），其在灵活性和可解释性之间的平衡，学习GAMs的基本数学方法，并在模拟和真实数据中使用R实现它们。

课程大纲

Name:An Introduction to Generalized Linear Models Through Binomial Regression

Description:In this module, we will introduce generalized linear models (GLMs) through the study of binomial data. In particular, we will motivate the need for GLMs; introduce the binomial regression model, including the most common binomial link functions; correctly interpret the binomial regression model; and consider various methods for assessing the fit and predictive power of the binomial regression model.

Name:Models for Count Data

Description:In this module, we will consider how to model count data. When the response variable is a count of some phenomenon, and when that count is thought to depend on a set of predictors, we can use Poisson regression as a model. We will describe the Poisson regression in some detail and use Poisson regression on real data. Then, we will describe situations in which Poisson regression is not appropriate, and briefly present solutions to those situations.

Name:Introduction to Nonparametric Regression

Description:In this module, we will introduce the concept of a nonparametric regression model. We will contrast this notion with the parametric models that we have studied so far. Then, we’ll study particular nonparametric regression models: kernel estimators and splines. Finally, we will introduce additive models as a blending of parametric and nonparametric methods.

Name:Introduction to Generalized Additive Models

Description:Some models, such as linear regression, are easily interpretable, but inflexible, in that they don't capture many real-world relationships accurately. Other models, such as neural networks, are quite flexible, but very difficult to interpret. Generalized additive models (GAMs) are a nice balance between flexibility and interpretability. In this module, we will further motivate GAMs, learn the basic mathematics of fitting GAMs, and implementing them on simulated and real data in R.

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