Broyden’s Method in Python

In a previous post we looked at root-finding methods for single variable equations. In this post we’ll look at the expansion of Quasi-Newton methods to the multivariable case and look at one of the more widely-used algorithms today: Broyden’s Method.

Root-Finding Algorithms Tutorial in Python: Line Search, Bisection, Secant, Newton-Raphson, Inverse Quadratic Interpolation, Brent’s Method

Motivation

How do you find the roots of a continuous polynomial function? Well, if we want to find the roots of something like:

$f(x) = x^2 + 3x - 4$

I recently did some A/B testing work through the Facebook advertising platform, and gave a quick presentation on the pros and cons of the platform. Here’s a summary.

PRO

• Microtargeting
• Optimization
• Inexpensive, low ceilings
• Demonstrated to work at scale, sophisticated distribution

CON

• Click bots
• Opaque

To clarify my perspective on the platform, some background on the work we did:

We ran some A/B tests through the platform targeting a specific population, evaluating different levels of resulting engagement for statistical significance. I assure you, nothing fancy. Continue reading “Understanding Facebook Ads: Pros and Cons”