# Writing

### 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.