Statistics And Data Analysis

In this course, we study some basic probility and sampling theories which are commonly used in machine learning.

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Syllabus

1. Statistics review - Random Variable
- pdf/cdf/pmf
- Joint distribution
- Expectation/covariance
- Conditional expectation
Probability theory Review - Chernoff bound
2. common distributions - Discrete
- Continuous
Useful distribution
Conjugate Prior
Normal - Gamma Conjugate
- expoential family
3. sample and limit theory - sampling mean and variance
- order statistics distribution
- weak and strong law of large numbers
- central limit theorem
sample and limit theory
4. T and F distribution - $\chi^2$ distribution
- $t$ distribution
- $F$ distribution
T and F distribution
5. Sampling - Sample Random sampling
- Confident interval
- MCMC
- Gibbs Sampling
Survey Sampling - 拒绝采样
- 别名采样
- MCMC
6. Estimation of Parameters&Fitting of Probability Distribution - MLE（parameter）
- MLE for exponential family
- Conjugate family （Bayes）
- EM algorithm
LDA思考与总结 - 文本主题模型之LDA(一) LDA基础
7. Testing Hypotheses and assessing Goodness of fit - Neyman-Perason lemma
- Likelihood Ratio Tests
8. Testing and Summarizing Testing and Summarizing)
9. The analysis of Variance The Analysis Of Variance
10. notes for exam Notes For Exam
@Last updated at 1/23/2021