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)
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) :
Derivative
Chain rule
Integral
Techniques of Integration
Substitution
Integration by parts
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
Sample Space
Probability Theory Foundation
Axiomatic Foundations
The Calculus of Probabilities
Independence
Conditional Probability
Bayes Theorem
Random Variables
Probability Function
Distribution Functions
Density function
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
Beta Distribution
Joint and Marginal Distribution
Conditional Distributions and Independence
Bivariate Transformations
Hierarchical Models and Mixture Distribution
Bivariate Normal Distribution
Multivariate Distribution
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
Maximum Likelihood Estimation
Motivation and the Main Ideas
Properties of the Maximum Likelihood Estimator
Computing the posterior
Maximum likelihood estimation (MLE)
Maximum a posteriori (MAP) estimation
Posterior mean
MAP properties
Bayesian linear regression