🌌 Manifold Learning, MDS, and PCA Unsupervised Learning – Dimensionality Reduction Lecture-style notes with full mathematical derivations ✨ 🌌 Data Manifold What is a Manifold? A manifol...

🌳 Hierarchical Clustering & 📦 K-Means Unsupervised Learning – Clustering Algorithms (Lecture Notes) 🌳 Hierarchical Clustering 🔁 Agglomerative Clustering (Bottom-Up) Level 0: S...

🧠 Unsupervised Learning & Clustering Lecture-style structured notes with intuition, examples, and math 📌 Why Unsupervised Learning? 🎯 Goal Unsupervised learning aims to discover intere...

📘 Support Vector Machines — Kernels, Logistic Comparison, and Multi‑Class ⚔️ SVM vs Logistic Regression When classes are well separated SVM tends to perform better because it maximizes the mar...

📘 Margin-Based Loss Functions 🎯 What is a Loss Function? A loss function measures how wrong a model prediction is. Given prediction $\hat{y}$ and label $y$: [\mathcal{L}(\hat{y}, y)] If $...

📘 Support Vector Machine (SVM) — Soft Margin with Slack Variables 🌪️ Noisy & Non‑Separable Data Real-world data are often not perfectly separable due to noise, overlap, or outliers. The cla...

🧠✨ Support Vector Machine (SVM) 🎯 Goal: Find the maximum-margin hyperplane that separates two classes. 📦 1. Problem Setup Training data: [{(x_i, y_i)}_{i=1}^n,\quad x_i \in \mathbb{R}^p,\...

🔁 Computational Graphs & Backpropagation (with Vectors & Matrices) Goal: Understand backpropagation as systematic application of the chain rule on a computational graph — from scalars →...

🟨 Limitations of Linear Classifier & Probabilistic Interpretation From raw scores to probabilities, and why loss functions like cross-entropy naturally arise. Full derivations included, no ...

🌲 Bagged Trees & 🌳 Random Forests 🎯 1. Bagged Trees (Bootstrap Aggregation) Bagging = Train many decision trees on bootstrap samples and combine predictions. Procedure Sample many boot...