Machine learning practice problems

Expectation, variance, Bayes' rule and entropy — computed from their definitions, so that the notation in later sections reads as arithmetic rather than decoration.

Master the fundamental data structure of numerical computing in Python. Learn to create, index, and manipulate n-dimensional arrays efficiently.

Raw data is messy. Learn normalization, standardization, and feature engineering, the critical steps that happen before any model sees data.

Build your intuition for deep learning from scratch. Understand layers, activations, and why depth enables hierarchical feature learning.

A work cell as closed forms: homogeneous transforms and their inverse, camera-to-base point transfer, the four ways a controller writes an orientation (Rodrigues, roll-pitch-yaw, axis-angle, quaternion), Denavit-Hartenberg links and whole chains, forward and inverse kinematics of a 2-link arm, its Jacobian and manipulability, a damped least-squares velocity step, the statics that Jacobian transpose gives you, gravity compensation, a differential-drive base and its odometry, PID, and the cubic, trapezoidal and speed-limited moves a planner actually emits.

The maths behind the collapsing-canyon drone, one formula per failure: returns to go, why a reward that is negative everywhere makes crashing the best move, potential-based shaping and the geodesic distance it should be measured on, the lidar fan and the stacked scans that turn it into motion, running observation normalisation, then the TD error, GAE, explained variance, the PPO clipped objective and the policy entropy that keeps it exploring.

The simplest unsupervised algorithm: assign points to the nearest centroid and update centroids until convergence. Deceptively powerful in practice.

Training from scratch is expensive. Pre-trained models encode rich representations that transfer across tasks, the backbone of modern applied ML.

Real-world data arrives with outliers, duplicates, missing values, and evolving schemas. Mastering cleaning pipelines is the unglamorous work that makes or breaks model performance.