Data Science: 5 Statistics & Math tools

【掌握这五大统计学知识,让你笑傲数据科学界】
https://m.toutiaocdn.com/group/6723020943871967751/?app=news_article_lite&timestamp=1565375984&req_id=20190810023944010152028205708822C&group_id=6723020943871967751&tt_from=android_share&utm_medium=toutiao_android&utm_campaign=client_share

1. MEAN / MEDIUM

2. PERCENTILE

3. SKEWNESS

4. STANDARD DEVIATION

5. PCA = Pricinpal Component Analysis

【学习大数据,我不会数学怎么办?还要不要学啦?】
https://m.toutiaocdn.com/group/6706386149763449356/?app=news_article_lite&timestamp=1565378178&req_id=20190810031618010152042134003992B&group_id=6706386149763449356&tt_from=android_share&utm_medium=toutiao_android&utm_campaign=client_share

1. Probability & Statistics

2. Linear Algebra (Matrix, Eigenvectors, Eigenvalues)

3. Optimisation : eg. Gradient Descent, etc.

4. Discrete Math in Computing

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A Programmer’s Regret: Neglecting Math at University – Adenoid Adventures

Advanced Programming needs Advanced Math: eg.

Video Game Animation: Verlet Integration

AI: Stats, Probability, Calculus, Linear Algebra

Search Engine : PageRank: Linear Algebra

Abstraction in Program “Polymorphism” : Monoid, Category, Functor, Monad

Program “Proof” : Propositions as Types, HoTT

https://awalterschulze.github.io/blog/post/neglecting-math-at-university/

Abstraction: Monoid, Category

Category

Unknown German Retiree Proved The “Gaussian Correlation Inequality” Conjecture

https://www.wired.com/2017/04/elusive-math-proof-found-almost-lost

\boxed {P (a + b) \geq P (a) \times P (b)}

Case “=” : if (a, b) independent 
Case “>” : if (a, b) dependent

Thomas Royen used only high-school math (function, derivative) in his proof in 2014. He then published it in arxiv.org website – like Perelman did with the “Poincaré Conjecture”.

Statistics detects cheat

Statistics & Truth [by CR Rao]:

RedCross hires local food contractors to supply rice, salt, water to N unknown survived victims of a recent Earthquake.

The bill shows they supply quantities R, S, W, resp, per day.
Assume average daily consumption per person be r, s, w resp.

To verify any cheating of overbill by contractors:

R/r = S/s = W/w = N