关于此课程： 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.
此课程适用人群： This class is for students who already have had a class in regression modeling and are familiar with the area who would like to see a more advanced treatment of the topic.
制作方： 约翰霍普金斯大学
教学方： Brian Caffo, PhD, Professor, Biostatistics
Bloomberg School of Public Health
| 级别 | Advanced |
| 承诺学习时间 | 6 weeks of study, 1-2 hours/week |
| 语言 | English |
| 如何通过 | 通过所有计分作业以完成课程。 |
| 用户评分 |
授课大纲
第 1 周
Background
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.
7 视频, 4 阅读材料
- 视频: Introduction
- Reading: Welcome to the class
- Reading: Course textbook
- Reading: Grading
- Reading: In this module
- 视频: Matrix derivatives
- 视频: Coding example
- 视频: Centering by matrix multiplication
- 视频: Coding example
- 视频: Variance via matrix multiplication
- 视频: Coding example
已评分: Background Quiz
第 2 周
One and two parameter regression
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.
6 视频, 2 阅读材料
- Reading: Before you begin
- 视频: Regression through the origin
- 视频: Centering first
- 视频: Coding example
- Reading: Before you begin
- 视频: Connection with linear regression
- 视频: Coding example
- 视频: Fitted values and residuals
已评分: One Parameter Regression Quiz
第 3 周
Linear regression
In this lecture, we focus on linear regression, the most standard technique for investigating unconfounded linear relationships.
8 视频, 2 阅读材料
- Reading: Before you begin
- 视频: Least squares
- 视频: Coding example
- 视频: Prediction
- 视频: Coding example
- 视频: Residuals
- 视频: Coding example
- Reading: Generalizations
- 视频: Generalizations
- 视频: Generalizations example
已评分: Linear Regression Quiz
第 4 周
General least squares
We now move on to general least squares where an arbitrary full rank design matrix is fit to a vector outcome.
6 视频, 1 阅读材料
- Reading: Before you begin
- 视频: Least squares
- 视频: Coding example
- 视频: Second derivation of least squares
- 视频: Projections
- 视频: Third derivation of least squares
- 视频: Coding example
已评分: General Least Squares Quiz
第 5 周
Least squares examples
Here we give some canonical examples of linear models to relate them to techniques that you may already be using.
4 视频
- 视频: Basic examples of design matrices and fits
- 视频: Group effects
- 视频: Change of parameterization
- 视频: ANCOVA
已评分: Least Squares Examples Quiz
第 6 周
Bases and residuals
Here we give a very useful kind of linear model, that is decomposing a signal into a basis expansion.
6 视频
- 视频: Bases, introduction
- 视频: Bases 2, Fourier
- 视频: Bases 3, SVDs
- 视频: Bases, coding example
- 视频: Introduction to residuals
- 视频: Partitioning variability
已评分: Bases Quiz
已评分: Residuals Quiz
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制作方
约翰霍普金斯大学
The mission of The Johns Hopkins University is to educate its students and cultivate their capacity for life-long learning, to foster independent and original research, and to bring the benefits of discovery to the world.
评分和审阅
Very thorough and rigorous. A great review for me.
Great, detailed walk-through of least squares. Linear Algebra is a must for this course. To follow the last part requires knowledge of matrix (eigen?)decomposition, which derailed me somewhat.
Great Course
CL
Very good