Motivation: disease progression modellingMotivation: disease progression modellingMotivation: 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 ModelsCovariate Gaussian Process Latent Variable Models

@kasparmartens @kasparmartens

kasparmartens.rbind.io kasparmartens.rbind.io

Poster #261Poster #261

Decomposing feature-level variation with Decomposing feature-level variation with Covariate Gaussian Process Latent Variable ModelsCovariate Gaussian Process Latent Variable Models

Kaspar Märtens, Kieran Campbell, Christopher YauKaspar Märtens, Kieran Campbell, Christopher Yau

@kasparmartens @kasparmartens

kasparmartens.rbind.io kasparmartens.rbind.io

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 ModelsCovariate Gaussian Process Latent Variable Models

@kasparmartens @kasparmartens

kasparmartens.rbind.io kasparmartens.rbind.io

Poster #261Poster #261