Say you have a discrete distribution \(\pi\) that you want to approximate with a small number of weighted particles. Intuitively, it seems like the the best choice of particles would be the outputs of highest probability under \(\pi\), and that the relative weights of these particles should be the same …

In a \(k\)-Nearest Neighbor Gaussian Process, we assume that the input points \(x\) are ordered in such a way that \(f(x_i)\) is independent of \(f(x_j)\) whenever \(i > j + k\). When \(k=2\), for example, this means we can generate the sequence of process values by sampling the …

This notebook looks at a technique for simultaneous localization (finding the position of a robot) and mapping (finding the positions of any obstacles), abbreviated as SLAM. In this model, the probability distribution for the robot's trajectory \(x_{1:t}\) is represented with a set of weighted particles. Let the weight …

For a robot to navigate autonomously, it needs to learn the locations of any potential obsticles around it. One of the standard ways to do this is with an algorithm known as EKF-Slam. Slam stands for "simultaneous localization and mapping", as the algorithm must simultaneously find out where the robot …

This post is about a technique that allows us to use variational message passing on models where the likelihood doesn't have a conjugate prior. There will be a lot of Jax code snippets to make everything as concrete as possible.

The Math

Say \(X\) comes from a distribution with density …

This notebook introduces Fully Independent Training Conditional (FITC) sparse variational Gaussian process model. You shouldn't need any prior knowledge about Gaussian processes- it's enough to know how to condition and marginalize finite dimensional Gaussian distributions. I'll assume you know about variational inference and Pyro, though.

import pyro
import pyro.distributions …