At NeurIPS 2021 this year, Pierpaolo Tomassi and I have a demonstrator that brings together a few ideas on surrogates, bayesian networks, and model understanding. The system (while its still up!

Integer programming approaches to set partitioning

I stumbled across Binary Decision Diagrams (BDDs) by chance. They are an efficient data structure to represent sets of graphs. While a graph $G$ is a set of vertices $V$ along with a set of edges $E$ that connect the vertices, a graph set is a collection of subgraphs over the universe $V$.

So you think you need CPLEX? To find out more, you review the marketing material. After you wade past that you get to the technical documentation. The links lead you in loops.

Suppose you have a list of objects that you need to iterate over two consecutive items at a time.
An old stackoverflow question for this leads to the a quote from the documentation that reads:

A 4.2 kilometre road cuts the 2000 acres of Phoenix Park neatly in half. Chesterfield Avenue doesn’t have a single pedestrian crossing, yield sign, or any amenity that isn’t designed for the car.

In this post, I’ll review a paper from 2018 that deals with generating boolean decision rules and uses column generation. The paper is well worth the read if you are interested in explainable AI models.

Recently, I had the need to compute maximum weighted cliques on very dense large graphs. This is a well studied problem, and a nice survey paper from 90’s by Pardalos and Xue gives a good overview of approaches.

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