Hop Lists are a novel retroactive set data-structure that allow for a branching timeline.
read moreGraph SLAM
For a robot to navigate autonomously, it needs to learn both its own location, as well as the locations of any potential obsticles around it, given its sensors' observations of the world. We'll create a probabilistic model of our environment and get a MAP estimate of these unknown quantities.
- Let …
Diagnosing Lack of Independence in Exogenous Variables
This post outlines a simple workflow for diagnosing lack of independence in
read morestatsmodels.Finite Basis Gaussian Processes
By Mercer's theorem, every positive definite kernel \(k(x, y) : \mathcal{X} \to \mathcal{X} \to \mathbb{R}\) that we might want to use in a Gaussian Process corresponds to some inner product \(\langle \phi(x), \phi(y) \rangle\), where \(\phi : \mathcal{X} \to \mathcal{V}\) maps our inputs into …
read moreFinite Particle Approximations
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 …
read moreNearest Neighbor Gaussian Processes
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 …
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