In my recent article on optimizing set diversity I mentioned the primary abstraction was of “diminishing returns” and is formalized by the theory of monotone submodular functions (though I did call out some of my own work which used a different abstraction). A proof that appears again and again in […]

Estimated reading time: 19 minutes

The mathematical concept of set diversity is a somewhat neglected topic in current applied decision sciences and optimization. We take this opportunity to discuss the issue. The problem Consider the following problem: for a number of items U = {x_1, … x_n} pick a small set of them X = […]

Estimated reading time: 28 minutes

From time to time we work on projects that would benefit from a free lightweight pure Java linear programming library. That is a library unencumbered by a bad license, available cheaply, without an infinite amount of file format and interop cruft and available in Java (without binary blobs and JNI […]

Estimated reading time: 11 minutes

We have been writing for a while about the convergence of Newton steps applied to a logistic regression (See: What does a generalized linear model do?, How robust is logistic regression? and Newton-Raphson can compute an average). This is all based on our principle of working examples for understanding. This […]

Estimated reading time: 14 minutes