Mathematics for Machine Learning + JAVA

Download source code @ https://sites.fastspring.com/prototypeprj/instant/ai

• Probability+JAVA (Prototype Project 01)

  • Download source code @ https://sites.fastspring.com/prototypeprj/instant/ai

  • use a custom JAVA app. to explain the following:

    • what is 'marginal probability', 'joint probability', and 'conditional probability'

    • what is 'and', 'or', and probability of intersection between 2 disjoint events

    • what is a sample space, an event

    • what are the 3 probability axioms

    • what is the probability of an event

    • what is the definition of conditional probability

• Probability+Independence+Conditional Independence+JAVA (Prototype Proj 02)

  • Download source code @ https://sites.fastspring.com/prototypeprj/instant/ai

  • use a custom JAVA app. to explain the following:

    • what are independent and conditionally independent events

    • when are 2 events independent

    • when are 2 events conditionally independent given a third event

    • how to generalize 'event independence check' to more than 2 events

    • can independent events be disjoint?

    • does conditional independence imply independence and vice versa

• Linear Algebra + JAVA (Prototype Project 01)

  • Download source code @ https://sites.fastspring.com/prototypeprj/instant/ai

  • use a custom JAVA app. to explain the following:

    • add 2 matrices (both must have same size. add elements in same position)

    • subtract 2 matrices (both must have same size. subtract elements in same position)

    • multiply 2 matrices (both must have matching inner dimension. size of resulting matrix obtained by dropping middle dimension)

    • step by step example of multiplying 2 matrices

    • scalar add (operation applied to each element in matrix)

    • scalar subtract (operation applied to each element in matrix)

    • scalar multiply (operation applied to each element in matrix)

    • scalar divide (operation applied to each element in matrix)

• Linear Algebra + JAVA (Prototype Project 02)

  • Download source code @ https://sites.fastspring.com/prototypeprj/instant/ai

  • use a custom JAVA app. to explain the following:

    • identity matrix contains all 0s except diagonal is 1s (multiply matrix by identity matrix and obtain original matrix)

    • transpose matrix by flipping it along diagonal. rows become columns and columns become rows

    • dot product happens between 2 vectors (here we do element-wise multiplication than sum up results)