Monthly Archives: November 2025

Problem: Distinguish between Las Vegas methods and Monte Carlo methods. Solution: Both are umbrella terms referring to broad classes of methods that draw (repeatedly) from (not necessarily i.i.d.) random variables to compute the value of some deterministic variable. Here, “compute” … Continue reading →

Problem: What does it mean for a topological space \(X\) to be locally homeomorphic to a topological space \(Y\)? Hence, what does it mean for a topological space \(X\) to be locally Euclidean? Solution: \(X\) is said to be locally … Continue reading →

Problem: Explain how a hard-margin support vector machine would perform binary classification. Solution: Conceptually, it’s simple. Given a training set of \(N\) feature vectors \(\mathbf x_1,…,\mathbf x_N\in\mathbf R^n\) each associated with some binary target label \(y_1,…,y_N\in\{-1,1\}\) (notice the \(2\) binary … Continue reading →