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所在平台: Coursera |
课程主页: https://www.coursera.org/learn/linear-models
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课程名称：高级线性模型与数据科学1：最小二乘法 概述：欢迎参加高级线性模型与数据科学第一期课程：最小二乘法。本课程将从线性代数和数学的角度介绍最小二乘法。在开始课程之前，请确保您具备以下基础知识： - 对线性代数和多变量微积分的基本理解。 - 对统计学和回归模型的基本理解。 - 对于证明性质的数学有一定的熟悉度。 - 基本掌握R编程语言。 完成本课程后，学生将能在回归建模的线性代数处理方面建立坚实的基础，这将极大地增强应用数据科学家对回归模型的整体理解。 课程大纲： - 背景：我们涵盖了一些基础矩阵代数结果，这对整个课程至关重要，包括一些基本的向量导数。此外，还介绍了一些利用矩阵从数据中创建总结统计信息的基本用法，包括计算和从观测值中减去均值（中心化）以及计算方差。 - 单参数与双参数回归：在本模块中，我们介绍了从原点回归和线性回归的基础知识，从原点回归是一个有趣的案例，因为它可以构建所有多元回归的基础。 - 线性回归：本讲座重点关注线性回归，这是调查无混淆线性关系的最标准技术。 - 一般最小二乘法：我们接下来讲解一般最小二乘法，其中任意完全秩设计矩阵与向量结果相适配。 - 最小二乘法实例：在这里，我们给出一些经典的线性模型示例，以便将其与您可能已经使用的技术联系起来。 - 基底与残差：在此我们介绍了一种非常有用的线性模型，即将信号分解为基底扩展。
Name:Background
Description:We cover some basic matrix algebra results that we will need throughout the class. This includes some basic vector derivatives. In addition, we cover some some basic uses of matrices to create summary statistics from data. This includes calculating and subtracting means from observations (centering) as well as calculating the variance.
Name:One and two parameter regression
Description:In this module, we cover the basics of regression through the origin and linear regression. Regression through the origin is an interesting case, as one can build up all of multivariate regression with it.
Name:Linear regression
Description:In this lecture, we focus on linear regression, the most standard technique for investigating unconfounded linear relationships.
Name:General least squares
Description:We now move on to general least squares where an arbitrary full rank design matrix is fit to a vector outcome.
Name:Least squares examples
Description:Here we give some canonical examples of linear models to relate them to techniques that you may already be using.
Name:Bases and residuals
Description:Here we give a very useful kind of linear model, that is decomposing a signal into a basis expansion.
Welcome to the Advanced Linear Models for Data Science Class 1: Least Squares. This class is an introduction to least squares from a linear algebraic and mathematical perspective. Before beginning the class make sure that you have the following: - A basic understanding of linear algebra and multivariate calculus. - A basic understanding of statistics and regression models. - At least a little familiarity with proof based mathematics. - Basic knowledge of the R programming language. After taking this course, students will have a firm foundation in a linear algebraic treatment of regression modeling. This will greatly augment applied data scientists' general understanding of regression models.
