Machine Learning: Visualization

Chapters

• 2.1 Statistics Summary
• 2.2 Measure of Spread
• 2.3 Pre-Processing

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2.1 Statistics Summary

Symbols

Symbol	Definition
$\sum$	Sum of
$\prod$	Mult of
$^{^{T}}$	Transpose
$\sigma^{2}$	Variance
$s^{2}$	Sample Variance
$\hat{y}$	Prediction of y
$\bar{x}$	Sample Mean
$L(w)$	Likelyhood of w
$\Theta$	Scalar value

• Sample
  • Sample Mean:    $\bar{x} = \frac{\sum x_{i}}{n}$
  • Sample Variance:    $s^{2} = \frac {\sum(x_{i}-\bar{x})^2}{n-1}$
  • Sample std:    $s = \sqrt{s^{2}}$
  • Sample Covariance;    $cov = \frac{\sum(x-\bar{x})^2 (y-\bar{y})^2}{n-1}$

• Population
  • Population Mean:    $\mu = \frac {\sum(x_{i})^2}{N}$
  • Population Variance:    $\sigma^{2} = \frac {\sum(x_{i}-\mu)^2}{N}$
  • Population Std:    $\sigma = \sqrt{\sigma^{2}}$
  • Population Covariance:    $cov = \frac{\sum(x - \mu_{x})^2(y - \mu_{x})^2}{N}$

• Correlation:    $p (X,Y) = \frac{Cov(X,Y)}{\sigma_{x}\sigma_{y}}$
• Mean Absolute Deviation (MAD):    $MAD = \frac{\sum|X_{i}-\bar{X}|}{n}$
• Standard error of mean:    $\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}}$

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