Motivation: disease progression modelling Motivation: disease progression modelling Motivation: disease progression modelling
GPLVM maps latent to observed data using GP mappings
Covariate-GPLVM
zi ∼ N (0, 1) Y y(j)
i
= f (j)(zi) + εij
GPLVM maps latent to observed data using GP mappings Covariate-GPLVM extends GPLVM by:
- 1. Incorporating covariates
Covariate-GPLVM
zi ∼ N (0, 1) Y y(j)
i
= f (j)(zi) + εij x y(j)
i
= f (j)(xi, zi) + εij
GPLVM maps latent to observed data using GP mappings Covariate-GPLVM extends GPLVM by:
- 1. Incorporating covariates
- 2. Providing a feature-level decomposition
Covariate-GPLVM
zi ∼ N (0, 1) Y y(j)
i
= f (j)(zi) + εij x y(j)
i
= f (j)(xi, zi) + εij y
(j) i
= μ(j) + f (j)
z (z) + f (j) x (x) + f (j) zx (z, x) + εij
Feature-level decomposition
Readily available for linear models, otherwise challenging:
y(j)
i
= μ(j) + f (j)
z (z) + f (j) x (x) + f (j) zx (z, x) + εij
Feature-level decomposition
Readily available for linear models, otherwise challenging: Naive decompositions (with standard GP priors) can lead to misleading conclusions With appropriate functional constraints we learn an identifiable non-linear decomposition
y(j)
i
= μ(j) + f (j)
z (z) + f (j) x (x) + f (j) zx (z, x) + εij
Decomposing feature-level variation with Decomposing feature-level variation with Covariate Gaussian Process Latent Variable Models Covariate Gaussian Process Latent Variable Models
@kasparmartens @kasparmartens kasparmartens.rbind.io kasparmartens.rbind.io Poster #261 Poster #261
Decomposing feature-level variation with Decomposing feature-level variation with Covariate Gaussian Process Latent Variable Models Covariate Gaussian Process Latent Variable Models
Kaspar Märtens, Kieran Campbell, Christopher Yau Kaspar Märtens, Kieran Campbell, Christopher Yau @kasparmartens @kasparmartens kasparmartens.rbind.io kasparmartens.rbind.io