The objective of this compilation is to bring together a variety of resources that provide straightforward and accessible explanations of fundamental principles in statistics and machine learning.
Set theory
Venn Diagrams
Probability Axioms
pdf,cdf,ppt
Quantiles
Experiment, Sample space, Event, Probability function, Random variable
Properties of cdf and pdf
Transformations of Random Variables
Joint Probability Distribution
Expected Values,
Properties of Expected Value
Variance Values,
Properties of Variance
Bayes Rule
Univariate distributions
Bernoulli distribution
Binomial distribution
Continous Uniform Distribution
Poission distribution
Exponential distribution
Probablity vs Statistics
Likelihoodist, Bayesian, and Frequentist Methods
Mathematical Basis of Bayesian vs Frequentist Debate
Covariance and Correlation
Pearson Correlation
Partial Correlation
Kendall Rank Correlation
Wald Wolfowitz Run Test
Estimators
Difference between estimator and statistics
Maximum Likelihood Estimation
MLE vs MAP Estimation
MLE vs MAP Bayesian Inference
Law of Large Numbers
Difference between Strong and Weak laws of large numbers
Central Limit Theorem
Effect Size
p-value
Right, Left, and Two tailed test
Type I and Type II Errors
SVD and PCA
Z-Score
One Proportion Z-test
Two Sample Z-test
t-distribution
Paired t-test
UnPaird t-test, Pooled t-test, Welch's t-test
Chi-square distribution
Pearson's Theorem
Chi-square test
Nonparametric Tests vs. Parametric Tests
Mann Whitney U Test (Wilcoxon Rank Sum Test)
Wilcoxon Signed Rank Test
Sign Test
The Kruskal-Wallis Test
Permutation Test
Ordinary Least Squares through minimising the sum of square errors
Projection and Orthogonality
Method of Moments
Linear Regression as Maximum Likelihoods
Regression vs Correlation coefficients
Bayesian Linear Regression
Applying SVD to Linear Regression
Linear Regression Metrics
Variance Inflation Factors
Multi Linear Regression and multicollinearityand also
Bias-Variance Decomposition of the Squared Loss
Bias-Variance Trade-off and Double Descent
Regualization: the path to Bias-Variance Trade-off
F-distribution
General Linear F-test
Calculating F-Statistic
Coding Systems For Categorical Variables
What is ANOVA
One Way Anova
ANOVA mathematical model
ANOVA Assumptions
Linear Combinations and Contrasts
Fixed Effect, Random Effect and Mixed Effect models
Factorial and Unbalanced ANOVA
ANCOVA
Multiple Comparison Problem
Bonferroni’s Correction
Holm’s Step-Down and Hochberg’s Step-Up Procedure
Studentized range distribution
Turkey's Range Test
MANOVA
PCA
Factor Analysis
Canonical Analysis
Bayesian Learning
A/B testing, Bayesian
Hierarchical Modeling
Rejection Sampling
Importance Sampling
Inverse Transform Sampling
The Metropolis-hasting algorithm and also
Gibbs Sampling
Gibbs Sampling as a Special Case of Metropolis–Hastings
Structural Causal Models
Chains, and Forks
Colliders
d-separation
Model Testing and Causal Search
Interventions
The Adjustment Formula
Backdoor Criterion
Front-door Criterion
Gaussian Process
Bootstrapping
Decision Trees
ID3, C4.5, C5.0, CART decision tree difference
C4.5 and C5.0 Algorithm
ID3 Algorithm
Pruning
Gini Impurity, Entropy, Classification Error
K-means clustering
Gaussian Mixture Modeling
Support Vector Machine
SVM vs logisitic regression
Ensemble methods: bagging, boosting and stacking
Adaboost
Gradient Boosting
Lime
Shapley and Shap
Counterfactual Explanations
Global Surrogate
Arima
Sarima, Sarimax
Prophet
Forecasting: Principles and Practice
General Introduction
Isolation Forest
One Class SVM
Local Outlier Factor
Robust Covariance Estimator
Data Cleaning
Imbalanced datasets
Data Set Shift
Covariate Shift
The Importance of Data Splitting
Training, Development and Test errors
My sides on Convolutional Neural Networks
My sides on Sequence Modles
Mechanics of Seq2seq Models With Attention
The illustrated transformer
Line-by-line implementation of “Attention is All You Need”
Illustrated GPT-2
Decoding Strategies