Course: Mastering Data Analysis in Excel

[jeremy886]

Coursera 6 weeks

• About This Course
• Binary Classification
• Information Measures
• Linear Regression
• Additional Skills for Model Building
• Final Course Project

[jeremy886]

week 2

Note: Interesting to further explore how to find the equivalent and write down example code of the linear equations and solver functionality in Python.

https://www.safaribooksonline.com/library/view/data-science-essentials/9781680502237/f_0080.xhtml

[jeremy886]

Week 3

• quantify
• probability: mutually exclusive and exhaustive to sum up to 1
• entropy H(x): measure of the uncertainty of the whole probability distribution

• bit information: 0/1, it is sum([ p[i] * log2(1/p[i]) for i in range(1, n+1) ])
• uniform distribution and n outcomes, H(x) = log(n)
• once you rolled the dice with an outcome of HEAD, the P(HEAD) is 1 and H(x) goes to 0.
• the higher uncertainty you have, the higher entropy you have.

• H(x|y) = P(y=y1)H(x|y=y1) + P(y=y2)H(x|y=y2)
• Mutual information: I(x; y) = H(x) - H(x|y)

Confusion matrix

actual class / prediction class	c	d
a	e=ac TP	f=ad FN
b	g=bc FP	h=bd TN

If independent, P(x, y) = P(x) * P(y)
I(x; y) = 0

Monty Hall Problem (three doors, one prize) 🤗🏆

• x - the door with a prize, P(1/3, 1/3, 1/3)
• H(x) = 1/3log2(3) + 1/3log2(3) + 1/3*log2(3) = log2(3) = 1.585 bits
• y - what Monty told us
• H(x|y) = (1/3, 2/3) = 1/3 * log2(3/1) + 2/3 * log2 (3/2) = 0.918 bits
• I(x;y) = H(x) - H(x|y) = 1.585 - 0.918 = 0.667 bits
• P.I.G. = .667/1.585 = 42.1 %

Learning from One Coin Toss

• Probability of A given B: P(A, B) = P(A|B) * P(B)

• To get P(B|A)

  • P(B, A) = P(A, B)
  • P(B|A) * P(A) = P(A|B) * P(B) so P(B|A) = P(A|B) * P(B) / P(A) Bayes Theorem

• Learn from Facts: toss a coin, figure out if it's a fair or crooked coin.

  • inverse probability, use Bayes THeorem

A: the coin comes up tails
~A: the coin comes up heads
B: the coin is fair
~B: the coin is crooked

P(Y=B) = 0.5
P(Y=~B) = 0.5

P(X=A | Y=B) = 0.5
P(X=A| Y=~B) = 0.4

P(B|A) = P(A|B)P(B) / P(A)

P(A) = P(A, B) + P(A, ~B) = P(A | B) * P(B) + P(A | ~B) * P(~B) = .5 * .5 + .4  * .5 = .45

P( coin is fair | observe TAILs) = p(B | A) = p(A | B) P(B) / P(A) = .5 * .5 / .45 = .556
P( coin is crooked | observe TAILs) = P (~B | A) = P(A | ~B) * P(~B) / P(A) = .4 * .5 / .45 = .444

(P fair, P crooked): (.5, .5) --data: TAILs--> (.556, .444)

H(.5, .5) - H(X|Y) = H(.5, .5) - H(.556, .444) = 1 - .9909 = .0091 bits
PIG = .0091 / 1 = .91 %

[jeremy886]

Week 4

Gaussian

• Gaussian Probability Density Function: the most common model for noise or uncertainty
• Gaussian distribution
  • f(x) = 1/sqrt(2*pi) * exp(-x**2 / 2)
• Normal distribution, area =1, mean = 0, variance = 1

Standardization

• mean, variance, standard deviation
• z-score

Central Limit Theorem

• distribution of the sample mean

Algebra with Gaussian

variance = δ**2

1. covariance == 0 (independent distribution)

• sum:
  • new mean = mean1 + mean2
  • new variance = variance1 + variance2
• multiply by constant ß
  • new mean = mean * ß
  • new variance = ß**2 * variance

2. covariance != 0

• ...

Markowitz Portfolio Optimization