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03 · Algorithms

Machine Learning

A practical and theoretical guide to supervised, unsupervised, and ensemble learning—from objective to deployment.

Academic pathway3 curated papersReadable formulas
Learning outcomes
  • Select models by task, inductive bias, and data regime
  • Explain bias–variance trade-offs and evaluation leakage
  • Compare interpretable baselines with high-capacity models
Core equations · rendered for reading, not code
Logistic regression
P(y=1|x) = σ(wᵀx + b)

Maps a linear score to a calibrated probability through the sigmoid function.

Gini impurity
Gini = 1 − Σᵢ pᵢ²

Measures class mixing inside a decision-tree node; zero means perfectly pure.

Support-vector margin
min ½ ‖w‖² subject to yᵢ(wᵀxᵢ+b) ≥ 1

Finds the widest separating margin while satisfying the training constraints.

Deep study guide

A reusable technical reading framework for moving from vocabulary to working understanding. Use it alongside the formulas and papers below.

4-part knowledge map
01

Conceptual map

A practical and theoretical guide to supervised, unsupervised, and ensemble learning—from objective to deployment. Start by naming the representation, objective, and source of evidence in any system you study. This habit separates a useful model explanation from a list of buzzwords.

02

Technical reasoning

Use the learning outcomes as checks for understanding: Select models by task, inductive bias, and data regime; Explain bias–variance trade-offs and evaluation leakage; Compare interpretable baselines with high-capacity models. For each claim, ask what assumptions make it true, what data it needs, and how it could fail.

03

Equations to implementation

Translate each equation into a small experiment before treating it as memorized knowledge. Logistic regression: Maps a linear score to a calibrated probability through the sigmoid function. Gini impurity: Measures class mixing inside a decision-tree node; zero means perfectly pure. Support-vector margin: Finds the widest separating margin while satisfying the training constraints.

04

Evidence and research practice

Read primary work with a repeatable lens: problem, method, data, measurement, limits, and what would change your mind. This section starts with “Random Forests”, “A Tutorial on Support Vector Machines”, “XGBoost: A Scalable Tree Boosting System”. Follow citations outward only after you can explain the central claim in your own words.

Build exercise

Implement a minimal example using Logistic regression; record inputs, outputs, and a failure case.

Evaluate exercise

Define a baseline, a success metric, a stress test, and the evidence required before you trust an improvement.

Extend exercise

Choose one paper from the library, reproduce a small claim, then write down the questions its evaluation leaves open.

Research library

Primary sources and peer-reviewed work to deepen this page.

Each card includes a summary and direct paper link
Machine Learning2001

Random Forests

Leo Breiman

Defines an ensemble of randomized decision trees with strong accuracy and robust generalization.

#ensembles#trees
Read paper / source
Data Mining and Knowledge Discovery1998

A Tutorial on Support Vector Machines

C. J. C. Burges

A clear mathematical treatment of maximum-margin classification and kernel methods.

#kernels#classification
Read paper / source
KDD2016

XGBoost: A Scalable Tree Boosting System

T. Chen · C. Guestrin

Presents a scalable, regularized gradient-boosting system that became a standard tabular baseline.

#boosting#systems
Read paper / source
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