In krisrs1128/LFExpers: Experiments in Latent Factor Modeling

Setup

library("knitr")
read_chunk("spline_sim.R")

Preliminary plots

First, we can plot result of the example spline latent factor model. There isn't that much noise in the example, so of course the reconstruction is good.

Beware overinterpreting the latent sources though! They are only unique up to rotations.

Simulations

A natural question is how well we can reconstruct the data, in different noise and missigness regimes, this is simulated below. We might have also wanted to know performance changes when the true number of latent sources or complexity of the basis changes, but these are omitted for now. We might also be interested in how the model performs under various misspecifications (incorrect basis, wrong number of sources, nongaussianity, outliers, etc.), but this is also omitted.

In a few cases, the coordinate descent estimates blew up. Really, we should be tuning the step-sizes according to the noise level, or at least do a line search. So, in practice, this kind of behavior can be avoided.

The fact that it seems like the RSS is going down with higher missingness is misleading, it should be averaged only over observed points.

krisrs1128/LFExpers documentation built on May 20, 2019, 1:25 p.m.