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

### Related tags

Text Data & NLP Stat4ML

# 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

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
``````

### 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
``````
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