Monday, November 30, 2015

ML - Mathematics Notes

Statistics: 

Basics:
  • Mean 
    • Average = Total of Value / Total No of Values
  • Median 
    • Middle Value to divide the Value Set in middle (n/2 or n/2+1)
  • Mode
    • Most Frequent Value - Highest Score in Value Set 
  • Standard Deviation 
    •  Measure to understand data value spread from central tendency
  • Variances 
    • Average of Squired value of means  
  • Technique 
    • Squired - Penalizes Higher Difference in Summation
    • Square Root - Normalizes SME on Same Scale  
Advances:
  • Linear Regression 
    • Finding Exploratory Variable (Y) based on relationship with  Dependent Variable (X) 
    • Multi-value Regression - More than 1 Dependent Variable and Exploratory variables  
  • Permutation and Combination 
    • Permutation: Total no of Selection without consideration for Order 
    • Combination: Total no of Selection with consideration for Order   

Calculus: 

  • Derivative: 
    • Slope of Curve
    • Degree of Change Effect with marginal change in wrt values. 
  • Integration 
    • All Area under Change Value of wrt value
    • Change in Slop and full value of Y.
Ref: 

Probability: 

  • Intersection Probability
    • U - Probability of two events happening together  
    • Exclusion - Probability of two events NOT happening together
    • P (A U B) = P(A) + P(B) - P(A Exclusion B) 
  • Conditional Probability
    • If we know P(B) event, then Conditional Probability P(A|B)
    • P(A|B) = P (A Intersection B) / P (B) 
  • Bayesian Probability 
    • Bayes Theorem: P(B|A) = P(A|B) P(B) / P(A)  

Algebra

Linear Algebra:
  • Matrix : row by column 
  • Vector : row by 1 
  • Addition/Subtraction: Simple Element by element: Similar Matrix only
  • Multiplication/Division: Right Side matrix column maps to Left side Row ; Column of left = Row of right
  • Competitive: A * B = B * A
  • Transitive : A * B * C
  • Identity Matrix : All 0 except 1 on diagonal 
    • In order to find bottom (Global/Local Minimum)
  • Identity Vector  - ?? 
  • Transpose - T - Changing Row to Column = m * n >  n * m
  • Inverse - A * A` = I 

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