Stat4ML

Statistics and Mathematics for Machine Learning, Deep Learning , Deep NLP

This is the first course from our trio courses:

Statistics Foundation for ML

https://github.com/Bellman281/Stat4ML/

Introduction to Statistical Learning https://github.com/Bellman281/Intro_Statistical_Learning
Advanced Statistical Learning for DL ( to be anounced)

Registration Form for cohort 2 of STAT4ML:

https://forms.gle/ZqLJLmv1K5nGVx3m7

Notes about the course:

Instructor : Omid Safarzadeh,

LinkedIn: https://www.linkedin.com/in/omidsafarzadeh/

IG : @deepdatascientists

Course Text Book: Statistical Inference 2nd Edition by George Casella (Author), Roger L. Berger (Author) :

https://www.amazon.com/Statistical-Inference-George-Casella-dp-0534243126/dp/0534243126/ref=mt_other?_encoding=UTF8&me=&qid=

Pre Requisitives

Recall from Calculus:

    Derivative
          Chain rule
    Integral
          Techniques of Integration
          Substitution
    Integration by parts

Matrix Algebra Review:

    Matrix operations
    Matrix Multiplication
       Properties of determinants
       Inverse Matrix
       Matrix Transpose
       Properties of transpose
    Partioned Matrices
    Eigenvalues and Eigenvectors
    Matrix decomposition
       LU decomposition
       Cholesky decomposition
       QR decomposition
       SVD
    Matrix Differentiation

Course 1 :

Slide 1 : Probability Theory Foundation

 Sample Space
 Probability Theory Foundation
    Axiomatic Foundations
    The Calculus of Probabilities
 Independence
 Conditional Probability
    Bayes Theorem
 Random Variables
 Probability Function
    Distribution Functions
    Density function

Slide 2: Distribution Functions

   Moments
       Expected Value
       Variance
       Covariance and Correlation
   Moment Generating Functions
       Normal mgf
   Matrix Notation for Moments
   
   Distributions
     Discrete Distribution
       Discrete Uniform Distribution
       Binomial Distribution
       Poisson Distribution
     Continuous Distribution
       Uniform Distribution
       Exponential Distribution
       Normal Distribution
       Lognormal Distribution
       Laplace distribution

Slide 3: Conditional and Multivariate Distributions

Joint and Marginal Distribution
Conditional Distributions and Independence
Bivariate Transformations
Hierarchical Models and Mixture Distribution
Bivariate Normal Distribution
Multivariate Distribution
Inequalities

Slide 4: Convergence Concepts

Sums of Random Variable from a Random Sample
Convergence Concepts
Almost Sure Convergence
Convergence in Probability
Convergence in Distribution
The Delta Method
Some More Large Sample Results

Slide 5: Maximum Likelihood Estimation

Maximum Likelihood Estimation
  Motivation and the Main Ideas
  Properties of the Maximum Likelihood Estimator

RIALI-MOUAD / Stat4ML