Learning Center.
Visual essays, mathematical derivations, and interactive simulations. Follow the pedagogical curriculum from linear regression and classification to tree ensembles, deep neural networks, and sequence models.
Linear Regression: Ordinary Least Squares
Minimizing orthogonal Euclidean residuals in parameter space. Closed-form normal equations versus iterative gradient descent steps.
Logistic Regression & The Sigmoid Curve
Projecting continuous feature combinations onto calibrated probability bounds. Analyzing logit slopes, odds ratios, and linear decision boundaries.
Confusion Matrix, Precision-Recall & F1
Navigating severe class imbalance where baseline accuracy fails. Harmonic balance between false positive alarms, missed detections, and F1 optimization.
ROC & AUC: Diagnostic Power
Mapping the sensitivity vs. specificity tradeoff across continuous decision thresholds with confusion matrix projections and integral AUC estimation.
K-Fold Partitioning & Generalization
Mitigating sample bias and estimating performance variance through rotational holdout splits and out-of-fold validation.
Decision Trees & Random Forests
Recursive feature space partitioning, Gini impurity minimization, and bootstrap aggregation (bagging) with random feature sub-sampling to suppress variance.
Neural Networks: A Visual Introduction
Constructing feed-forward computational graphs from first principles: layer activations, synaptic weights, Adam optimization, and live backpropagation feedback loops.
Convolutional Neural Networks (CNNs)
Spatial receptive fields, 2D discrete convolution kernels, hierarchical feature maps, and spatial invariance through pooling layers.
Recurrent Networks (RNNs, LSTMs & Sequence Models)
Sequential temporal dynamics, Backpropagation Through Time (BPTT), vanishing gradients, LSTM memory gates, and Transformer self-attention.
The Random Forest Algorithm
Bagging, random feature sub-sampling, and majority voting. How averaging many decorrelated trees collapses variance without adding bias.
The Bias-Variance Tradeoff
Decomposing expected error into bias squared, variance, and irreducible noise. Underfitting, overfitting, and the KNN knob that dials between them.
Train, Test & Validation: The Honest Split
Why one dataset must become three, what each partition is actually for, and how a single careless peek turns your final number into fiction.
Double Descent
Error that rises at the interpolation threshold and then falls again. Why over-parameterised models generalise, and what minimum-norm bias has to do with it.
Equality of Odds
Defining and measuring parity in true and false positive rates across groups, the equal-opportunity relaxation, and the three stages at which you can intervene.
Reinforcement Learning
Learning from delayed consequences instead of labels. Markov decision processes, the explore-exploit dilemma, grid worlds, and the Bellman recursion.
The Transformer: Attention Is All You Need
Eliminating recurrence with constant-path multi-head self-attention. Interactive dual-tower architecture, coreference attention simulator, and autoregressive generation.