Mathematics of AI

Math fundamentals in AI:

  • Linear Algebra: will teach you how to represent and manipulate data.
  • Calculus and optimization, how to measure and improve performance.
  • Statistics:
    • Statistics, how to extract meaning from numerical data using data collection, analysis, interpretation and presentation of data.
    • Probability, how to make decisions under uncertainty, by calculation of how likely an event may occur.
  • Discreet Mathematics
    • Graph Theory

Mastery of AI Mathematics allows:

  • Intuitive model design
  • intuitive understanding of model behaviors.
    It’s also a requirement for those who wish to create new machine learning algorithms.

Concepts:

  • Continuous variables: are variables that have an infinite number of values, such as speed and distance.
  • Vectors: are used to represent numeric characteristics known as features in a mathematical and easily analyzable form.
  • Dependent Variable(input value, explanatory variable, X): the variable that is measured and is affected by the independent variable.
  • Independent Variable(response variable , target variable , Y): the variable that can manipulate or have a direct effect on the dependent variable.
  • Nominal Variable: a type of the variable used to name, label, or categorize particular attributes that are being measured.
  • Ordinal Variable: variables that have discrete values with some form of order involved.
  • Predictor variable: the variable used to make a prediction for dependent variables.
  • Monte Carlo method: a mathematical technique used to estimate the possible outcomes of an uncertain event by learning from experience(states, actions, and rewards).
  • Multivariate analysis: the process of comparing and analyzing the dependency of multiple variables over one another.
  • Regression: a technique used for investigating the relationship between independent variables or features and a dependent variable or outcome.
  • Euclidian Distance: Eucladian Distance is the most used and standard measure for the distance between two points.
  • Correlation Coefficient: IT is a measure of the strength(closeness) and direction of a linear association(linear relationship) between data points and is denoted by . it is always calculated in the range of -1 to +1.
    • A correlation coefficient close to 0 is considered very weak and suggests little or no correlation.
    • A correlation coefficient close to +1 or -1 is considered very strong and suggests high level of association.
    • A correlation coefficient of +1 is considered perfect positive and suggests very high level of association.
    • A correlation coefficient of -1 is considered perfect negative and suggests very high level of association.

Learning Material: