Writing
The Copula and 2008
The copula provides a clever means for mixing and matching a set of marginal distributions with the joint-only mechanism of a joint distribution. However, its elegance and utility have been a dangerous lure.
The Matrix Inversion Lemma
The Matrix Inversion Lemma looks intimidating, but it is easy to know when it applies. Doing so offers considerable computational speed ups.
Bayesian Optimization
When optimizing a slow-to-evaluate and non-differentiable function, one may think random sampling is the only option--a naive approach likely to disappoint. However, Bayesian optimization, a clever exploit of the function assumed smoothness, disconfirms these intuitions.
The Fundamental Law of Active Management
The Fundamental Law of Active Management decomposes a well known summarizing metric of an investment strategy. The decomposition yields two dimensions along which all strategies may be judged and suggests avenues for improvement.
The Exponential Family
The exponential family is a generalization of distributions, inclusive of many familiar ones plus a universe of others. The general form brings elegant properties, illuminating all distributions within. In this post, we discuss what it is, how it applies and some of its properties.
Motivating the Gini Impurity Metric
We reveal the gini impurity metric as the destination of a few natural steps.
The Trace as a Measure of Complexity
For a class of models, the trace provides a measure of model complexity that's useful for managing the bias variance trade-off.
The Conjugate Gradient Method
Utilizing a geometric perspective, we find an efficient algorithm for solving a special kind of system of equations.
A Brief Explanation and Application of Gaussian Processes
A clever and useful technique for inferring distributions over infinite functions using finite observations.
Singular Value Decomposition and the Fundamental Theorem of Linear Algebra
Any linear transformation fixes four subspaces, which delineate outputs that can be reached using inputs that matter.