Supplementary Material The Nonparametric Metadata Dependent Relational Model

1.1. Independence Sampler for Topic Activations V The posterior of v:i does not have a closed analytical form due to the nonlinearity associated with the logistic mapping of our stick-breaking weights π:i. We instead perform a Metropolis-Hastings update with an independence proposal q(v∗ :i | v:i, η, φ:i, λV ) = N(v∗ :i | ηφ:i, λ −1 V IK), which represents a sample from our prior. Since our proposal distributions are equal to the prior we need to evaluate in our acceptance ratio A(v∗ :i, v:i), these terms cancel and we are left with a simple ratio between our likelihood terms so that A(v∗ :i, v:i) is now: