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

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Text Data & NLPStat4ML
Overview

Stat4ML

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

This is the first course from our trio courses:

  1. Statistics Foundation for ML

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

  1. Introduction to Statistical Learning https://github.com/Bellman281/Intro_Statistical_Learning

  2. 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: Moments

   Moments
       Expected Value
       Variance
       Covariance and Correlation
   Moment Generating Functions
       Normal mgf
   Matrix Notation for Moments

Slide 3: Distribution Functions

   Distributions
     Discrete Distribution
       Discrete Uniform Distribution
       Binomial Distribution
       Poisson Distribution
     Continuous Distribution
       Uniform Distribution
       Exponential Distribution
       Normal Distribution
       Lognormal Distribution
       Laplace Distribution
       Beta Distribution

Slide 4: Conditional and Multivariate Distributions

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

Slide 5: Convergence Concepts

Random Samples
   Sums of Random Variable from a Random Sample
Inequalities
Convergence Concepts:
   Almost Sure Convergence
   Convergence in Probability
   Convergence in Distribution
The Delta Method

Slide 6: Maximum Likelihood Estimation

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

Slide 7: Bayesian and posterior distribution Estimation

   Computing the posterior
   Maximum likelihood estimation (MLE)
Maximum a posteriori (MAP) estimation
   Posterior mean
   MAP properties
Bayesian linear regression
Owner
Omid Safarzadeh
Deep Learning Expert, Kaggler
Omid Safarzadeh
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