machine-learning-algorithms

Machine-Learning Algorithms

Overview

Machine-learning-algorithm answers must separate the textbook model from production machine-learning practice. Use the chapter mechanisms for their invariants, regret potentials, and convex-optimization proof moves; do not silently replace them with modern defaults such as k-means++ initialization, randomized exponential weights, or library-regression pipelines unless the prompt asks for production advice.

Core principle: first identify whether the task is clustering, online expert prediction, or convex optimization, then state the model assumptions that make the chapter theorem true before giving an algorithm, bound, or engineering recommendation.

Shared CLRS Conventions

Follow the parent clrs skill for mathematical formatting, direct polished answers, theorem preconditions, and formula-free headings. Keep tables verbal and put objectives, updates, bounds, and potentials in display blocks adjacent to the table.

Answer Formatting Guardrail

Machine-learning prompts often invite verification tables after theorem statements. A verification table is still a table: do not put parameter ranges, update factors, objective values, asymptotic bounds, theorem inequalities, or potential expressions in its cells.

Use this safe pattern instead:

1. In the table, use verbal labels such as "chapter penalty range," "prefix mistake theorem," "expert lower bound," or "projected-gradient guarantee."
2. Immediately before or after the table, put the exact expression in a display block.
3. If several expressions must be checked, use a numbered list with one display block per item instead of a table.

When reviewing your own answer, scan tables separately. If a table cell contains a symbol-heavy expression, move the expression out of the table before responding.

When to Use

Use this skill for:

• k-means clustering, squared Euclidean dissimilarity, Lloyd's procedure, centroid updates, empty clusters, and vector quantization;
• online prediction from binary experts, deterministic weighted majority, multiplicative weights, mistake bounds, and regret-style potential arguments;
• convex gradient descent, projected gradient descent, average-iterate guarantees, line search, and amortized potential proofs;
• least-squares linear regression as convex optimization over weights, including norm-constrained regularization.