A fancy image for capturing the reader's interest. Alludes to linear regression
Linear Algebra, Probability and Statistics

Linear Regression: Statistical vs Machine Learning View

Is linear regression a statistical model or a machine learning algorithm? While often used as the “Hello World” of deep learning, the method is deeply rooted in 18th-century statistics. The confusion arises because both fields tackle the same problem from different perspectives, using different terms for the same concepts. This article serves as a bridge between these two worlds. We will break down why certain terms are favored in one domain over the other, giving you a ‘translation layer’ that makes reading both statistical papers and machine learning textbooks much more intuitive.

A comic illustration of Principal Component Analysis (PCA) auditioning four features (f1, f2, f3, f4). PCA decides to merge parts of features 3 and 4 into a "superfeature" while discarding the rest to reduce noise.
Linear Algebra

A Brain-Friendly Guide to PCA: Math, Visuals, Code

In this brain-friendly deep dive, we’re stripping Principle Component Analysis down to its first principles. You won’t just learn how to use it; you’ll master the underlying logic and the math that makes it work—no hand-waving or vague metaphors required. By pairing theory with practical code, we’ll move beyond simply calling libraries to achieving a true, foundational understanding of the ‘why’ behind the ‘how.

A diagram of the Singular Value Decomposition (SVD) formula showing matrix A being decomposed into matrices U, Sigma, and V-star. The image displays the dimensions of each matrix and uses color-coding to show how specific columns of U, diagonal values of Sigma, and rows of V-star are linked together as sets of triplets.
Linear Algebra

Deriving the Singular Value Decomposition (SVD) from First Principles

The Singular Value Decomposition (SVD) is “a highlight of linear algebra” to quote Prof. Strang ( [1] p. 371). However, I must confess that when I studied it I had a difficult time understanding it and this was due to how it was presented. The SVD is often introduced as a given formula which is then shown to just work. But it always felt very unsatisfying to me not knowing why. So – here is the SVD explained the way I wish I had been taught, which is deriving it from first principles.

Four line graphs on a white background showing 2D geometric transformations of a letter 'E'. From left to right: Rotation (45°), Reflection (X-flip), Inversion (X & Y flip), and Stretch (1.6, 0.6).
Linear Algebra

Understanding the Geometry of Orthogonal and Diagonal Matrices

Why do orthogonal matrices rotate while diagonal matrices stretch?
In this deep dive into linear algebra, we prove the geometric intuition behind the Singular Value Decomposition (SVD). By examining how inner products are preserved and how basis vectors are scaled, I demonstrate why linear transformations are restricted to these specific movements.

Scroll to Top
Cookie Consent with Real Cookie Banner