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Linear trees in LightGBM: how to use
What are linear trees? This was originally written as a "Hello world" kind of program aimed at giving my team at the DataLab some help getting started with less noisy variants of GBDTs. From this post: Not everybody knows simple yet effective variations of the Decision Tree algorithm. These are… Read more
September 21st, 2022 · 3 min read -
A ROC AUC partial to misclassification cost
Context This was originally written as a quick intro to partial AUCs, aimed at giving my team at the DataLab some insights into cost-based classification. Below, we consider the standard binary classification problem. Assume we pay a cost in case we classify a point of the positive class as a… Read more
September 20th, 2022 · 5 min read -
The Carr-Madan decomposition of arbitrary payoff functions
Context The Carr-Madan decomposition is used in quant finance to break any payoff into a (continuous) combination of calls and puts, plus a forward. Namely, for any twice differentiable function: where is the positive part function. This result translates what quants intuitively know: for a… Read more
September 20th, 2022 · 2 min read -
A vector space structure for probabilities
Rethinking probabilities This post is based on this article. Does it even make sense to discuss about adding two probabilities? Probabilities definitely look like vectors: they are arrays of numbers. For example, it could make sense that a coin toss would be described by an array with two numbers,… Read more
September 18th, 2022 · 6 min read