There is no excerpt because this is a protected post.
Developmental – Welcoming The Gamma Function
"The art of doing mathematics consists in finding that special case which contains all germs of generality." -- David Hilbert. The Gamma function appears in many areas of mathematics, physics, and engineering. This post will not only provide motivation for studying the Gamma function but also present several methods for deriving it, including an introduction … Continue reading Developmental – Welcoming The Gamma Function
OPERATION GRADIENT: MY 15A EXPERIENCE (Part I)
What is a gradient? Many students plowing their way through Calculus III can readily answer this question. In fact I would have, before attending the esteemed Operations Research Analyst course (15A) for incoming officers in the US Air Force. Now I consider this question as much philosophically as I do mathematically, especially in terms of … Continue reading OPERATION GRADIENT: MY 15A EXPERIENCE (Part I)
Developmental – DMD Meets Space City (Part I)
Imagine being able to detect subtle patterns in Earth's landscape using mathematical tools. With NASA's API for obtaining LANDSAT Imagery and the Dynamic Mode Decomposition (DMD) technique, this becomes not only possible but accessible to anyone with enough curiosity and a reasonable understanding of python. Here are the highlights: LANDSAT Summary Accessing NASA's API DMD … Continue reading Developmental – DMD Meets Space City (Part I)
Protected: Advanced – Symmetries Reimagined: Generalized Subset Mappings and Extensions of Symmetry Groups
There is no excerpt because this is a protected post.
Developmental – What About Those Pesky Integrals?
So what about those pesky definite integrals? I mean the ones integrating over a high number of dimensions. Many ML problems, especially in Bayesian statistics, involve computing probabilities or expectations over high-dimensional spaces. For this reason, we're gonna need a clever way to compute these integrals. Enter Monte Carlo Integration! This technique isn't just a … Continue reading Developmental – What About Those Pesky Integrals?
Advanced – Ridge Regression Notes (Module 3)
Welcome to the final module of our comprehensive study of Ridge Regression! In Module 1, we uncovered various facets of Ridge Regression, starting with SVD (Singular Value Decomposition) approach. We carefully dissected the formula for the Ridge estimator: $latex w_{Ridge} = (X^{T}X + \lambda I)^{-1}X^{T}y$, unraveling its intricacies through calculus. Our previous discussions in Module … Continue reading Advanced – Ridge Regression Notes (Module 3)
Advanced – Ridge Regression Notes (Module 2): A Closer Look at the Ridge Estimator
With a clear understanding of the framework of Ridge Regression, we are now well-equipped to delve deeper into some of its nuances. A key aspect of this exploration involves examining the parameters of the distribution over the Ridge weights, denoted as $latex w_{Ridge}$. Through this, we will uncover a crucial property: while Ridge Regression helps … Continue reading Advanced – Ridge Regression Notes (Module 2): A Closer Look at the Ridge Estimator
BGecko 