• 

  How Cartesian can we make coordinates on Earth?

  What we already know: Earth is locally flat. This is true not only for the (surface of) the Earth, but for any so-called Riemannian manifold, a generalization of surfaces to any number of dimensions. Even though there is curvature, if one zooms enough into a point, curvature disappears and their… Read more

  May 11th, 2023 · 29 min read
• 

  My favorite math problem

  Background Back in the second year of high school, a friend shared with me a problem that his geometry teacher had shown him. I was going through a small crisis regarding my future career. I couldn't decide whether I wanted to pursue a major in the Humanities (Arts or Design were on the top of the… Read more

  April 16th, 2023 · 4 min read
• 

  AUC as Loss: directly fitting to optimize ROC AUC

  The AUC in the real world A common application of binary classification models is ranking, more than classification itself. The difference between the two is subtle: In classification, you want to say how likely a point is to belong to class 1 or class 0; In ranking, you care whether point A, who… Read more

  January 27th, 2023 · 15 min read
• 

  Dribbling through Jensen's inequality

  Context I recently published a short discussion (in Portuguese) on LinkedIn about how Jensen's inequality complicates the process of building regressions for transformations of an original variable. More specifically, we discussed how This is due to being concave and both it and its inverse, ,… Read more

  September 25th, 2022 · 9 min read
• 

  Variance of the ROC AUC: a full derivation

  AUC status quo The ROC AUC is the most used statistic to assess the predictive power of a classification model. However, few working data scientists know theoretical results about its statistical fluctuations. Here, we show in detail a derivation of a commonly found result on the variance of the… Read more

  September 22nd, 2022 · 22 min read