Hassan Ijaz
Ai, Web & Design
Probability and Statistics for Machine Learning
Interactive visualizations to build intuition for 58 essential probability and statistics concepts
Probability axioms and basic rules
Interactive probability calculator with visual Venn diagrams that update in real-time as users adjust probabilities, showing how addition and multiplication rules work
Conditional probability and independence
Two-box simulator where users can drag colored balls between boxes and see how P(A|B) changes dynamically with visual tree diagrams
Random variables (discrete and continuous)
Dice rolling and spinner simulators that generate histograms in real-time, allowing users to see distributions emerge from repeated sampling
Probability distributions
Interactive distribution playground with sliders for parameters, showing how shapes change and allowing overlay comparisons between different distributions
Joint, marginal, and conditional distributions
3D surface plot that users can rotate and slice to see marginal distributions on axes and conditional distributions as cross-sections
Bayes' theorem and Bayesian inference
Medical test simulator where users adjust disease prevalence and test accuracy sliders to see how posterior probabilities change, with visual prior/posterior distributions
Expectation, variance, and covariance
Visual scatter plot generator where users can drag points and see mean, variance, and covariance update in real-time with geometric interpretations
Measures of central tendency and spread
Interactive dataset builder where users add/remove points and see mean, median, mode, and spread measures update with visual indicators
Data visualization and EDA
Dashboard builder where users drag different chart types and see how same data tells different stories
Correlation and causation
Scatter plot generator with hidden confounders that users must discover, showing how correlation can be misleading
Outlier detection
Interactive scatter plot where users click to add points and see various outlier detection methods highlight anomalies in real-time
Sampling methods comparison
Population visualizer where users apply different sampling strategies and see resulting sample distributions
Sample size determination
Power calculator with visual effect size demonstrations showing required samples for statistical significance
Law of large numbers and central limit theorem
Animated simulation showing sample means converging to population mean, with adjustable sample sizes and various starting distributions
Parameter estimation (MLE, MAP)
Interactive likelihood function visualizer where users guess parameters and see likelihood surface with gradient ascent animation to find MLE
Confidence intervals and credible intervals
Bootstrap simulator that shows confidence interval construction through resampling animations with adjustable confidence levels
Bootstrapping and permutation tests
Card shuffling visualizer showing permutation test logic with drag-and-drop interface for creating null distributions
Hypothesis testing and p-values
Courtroom simulation game where users act as statistical judges, seeing null distribution animations and making accept/reject decisions
Type I and Type II errors
Traffic light decision game showing consequences of false positives/negatives with adjustable threshold slider and error rate tracking
Multiple testing correction
Slot machine simulator demonstrating false discovery rates with and without correction methods applied
A/B testing simulator
Website optimization game where users run tests, see results accumulate, and learn about statistical significance
Linear regression
Drag-and-drop interface where users place points and see regression line update, with residual visualization and R-squared display
Logistic regression
Classification boundary visualizer where users add points of different classes and see decision boundary morph in real-time
Generalized linear models (GLMs)
Link function playground showing how different link functions transform linear predictors for various response types
Model selection and validation
Model comparison dashboard with AIC/BIC calculations and cross-validation performance tracking
Train/validation/test splits
Data partitioning visualizer showing how different split strategies affect model evaluation reliability
Cross-validation visualizer
Dataset splitter showing different CV strategies (k-fold, leave-one-out) with animation of train/test splits
Bias-variance tradeoff
Model complexity slider showing underfitting to overfitting transition with animated decomposition of error into bias and variance
Regularization (L1/L2)
Overfitting playground showing polynomial regression with adjustable regularization strength sliders and train/test error curves
Performance metrics dashboard
Confusion matrix builder where users classify examples and see all metrics (precision, recall, F1) update live
ROC curve generator
Threshold slider showing how TPR/FPR tradeoff creates ROC curve with AUC calculation
Calibration and reliability diagrams
Prediction calibration tool where users adjust model outputs and see reliability plots update
PCA visualization
3D to 2D projection tool where users rotate high-dimensional data clouds and see principal components as projection axes
Linear Discriminant Analysis
Class separation visualizer showing how LDA finds optimal projection for maximum class separation
Factor analysis
Latent variable explorer where users adjust hidden factors and see how they generate observed correlations in data
Feature selection methods
Feature subset explorer showing forward/backward selection and regularization-based selection in action
Feature importance visualizer
Random forest inspector showing feature importance through interactive tree exploration
Prior and posterior distributions
Belief updater where users set priors with sliders, add evidence, and watch posterior distributions evolve
Conjugate priors
Prior-posterior pair matcher showing how certain prior distributions lead to closed-form posterior updates
MCMC visualization
Random walk simulator showing how Markov chains explore probability distributions with acceptance/rejection animations
Variational inference basics
Distribution approximation game where users adjust variational parameters to minimize KL divergence
Hierarchical models
Nested data simulator showing how group-level and individual-level parameters interact in multilevel models
Entropy and information calculator
Message encoding game showing how entropy relates to optimal code length with interactive probability adjustments
KL divergence visualizer
Distribution matcher game where users adjust parameters to minimize KL divergence between two distributions
Information gain
Decision tree builder where users select features and see information gain calculations for splits
Maximum entropy principle
Constraint satisfaction puzzle where users find maximum entropy distributions given moment constraints
Autocorrelation visualization
Time series generator where users draw patterns and see autocorrelation function update, learning about lag relationships
Stationarity and unit root tests
Time series transformer showing effects of differencing and detrending with visual stationarity tests
Seasonality and trend decomposition
Seasonal pattern builder where users draw components (trend, seasonal, residual) and see how they combine
ARIMA model builder
Interactive forecasting tool where users adjust AR, I, MA components and see predictions change on stock-like data
Gaussian Mixture Models
Interactive cluster generator where users click to create data and see GMM fit with adjustable components
EM algorithm animation
Gaussian mixture clustering tool showing expectation and maximization steps iteratively refining clusters
Hidden Markov Models
Weather prediction game with hidden states, showing forward-backward algorithm visualization
Kernel density estimation
Bandwidth tuning tool showing how kernel width affects density estimate smoothness
Imbalanced data simulator
Class rebalancing tool showing effects of different sampling strategies on model performance
Missing data imputation
Data corruption and recovery game showing how different imputation methods affect downstream analysis
Concentration inequalities
Tail probability visualizer showing Hoeffding and Chernoff bounds compared to actual sampling distributions
PAC learning theory basics
Sample complexity calculator showing relationships between error tolerance, confidence, and required samples