(8/8) Check out the paper here: arxiv.org/abs/2402.09122
It was a pleasure working with James Odgers, Chrysoula Kappatou, Ruth Misener and Sarah Filippi on this project! If you are interested in knowing more, we’d love to hear from you.

(7/8) We demonstrate this approach on a synthetic test case, a spectroscopy dataset and oil flow data. Compared to baselines like inverse linear model of coregionalisation, classical least squares and partial least squares, WS-GPLVM achieves competitive or better performance.

(6/8) This means not only do we get predictions of the component weights, but also a measure of uncertainty in these values. The Bayesian component weights and latent variables make the calculation of the evidence lower bound more challenging, and we show how this can be done.

(5/8) At the core of this approach is the idea that each pure signal depends on a latent variable, and these signals combine linearly. We also treat the component weights in a Bayesian way, allowing for the inclusion of useful priors, such as summing-to-one.

(4/8) This variability makes the separation task much harder. Most existing methods assume fixed pure signals. We introduce WS-GPLVM - a Bayesian nonparametric model that relaxes those assumptions.

(3/8) Take spectroscopy for example: following Beer-Lambert’s law, the observed spectra is a linear combination of the spectra of the pure components, but these pure component spectra vary depending on experimental conditions.

(2/8) In many real-world datasets, each observation is a mixture of underlying signals, with no observations of the pure signals. Think: chemical spectra, audio sources, hyperspectral images.
But what happens when the pure signals vary between samples due to some unobserved variables?