# Mathematics behind Machine Learning – The Concepts you Need to Know

https://www.analyticsvidhya.com/blog/2019/10/mathematics-behind-machine-learning/

Data Science & Machine Learning (AI is a sub-discipline) overlap but not the same:  # Statistical Significance Explained

“Statistical Significance Explained” by Will Koehrsen

https://towardsdatascience.com/statistical-significance-hypothesis-testing-the-normal-curve-and-p-values-93274fa32687

Normal Distribution

Convert to Z-score p-Value vs Alpha (0.05% = noise)   # Data Science: 5 Statistics & Math tools

1. MEAN / MEDIUM

2. PERCENTILE

3. SKEWNESS

4. STANDARD DEVIATION

5. PCA = Pricinpal Component Analysis

1. Probability & Statistics

2. Linear Algebra (Matrix, Eigenvectors, Eigenvalues)

3. Optimisation : eg. Gradient Descent, etc.

4. Discrete Math in Computing

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# “No, Machine Learning is not just glorified Statistics” “No, Machine Learning is not just glorified Statistics” by Joe Davison https://link.medium.com/fv3z50FDYY  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