Thomas HughesinTowards Data ScienceThe Vandermonde Determinant, A Novel ProofApplications of the Vandermonde Matrix and An Original Proof of the DeterminantAug 9, 20203Aug 9, 20203
Thomas HughesinThe StartupGradient DescentThere certainly isn’t any shortage of gradient descent articles floating around the internet, so perhaps I add nothing new by writing this…Jun 25, 20201Jun 25, 20201
Thomas HughesChebyshev’s InequalityChebyshev’s Inequality is the most delightful result I’ve yet seen in my studies of Probability and Statistics. At first, it seemed as…Jun 25, 2020Jun 25, 2020
Thomas HughesMinimizing the Sum of Squared Deviations with High School AlgebraPreviously we saw how we can use linear algebra to show that the arithmetic mean minimizes the sum of squared deviations (SSD). Typically…Jun 25, 2020Jun 25, 2020
Thomas HughesThe Mean as an Orthogonal ProjectionLet’s start with the simplest case. Suppose we are given a pair of real numbers:Mar 30, 2019Mar 30, 2019