Various things... Yves-Laurent Kom Samo Ibrahim Almosallam Stephen - - PowerPoint PPT Presentation

Various things...

Yves-Laurent Kom Samo Ibrahim Almosallam Stephen Roberts University of Oxford

String & membrane GPs

Easy to consider a GP over a function and its derivative String GPs easy to construct – each GP is conditionally independent given the boundary values for the function and its derivative – so string GPs are C1 continuous

(Joint work with Yves-Laurent Kom Samo)

String GPs are (often) just GPs...

Inference

Can place boundary points arbitrarily,

• r can infer – using eg Pitman-Yor etc

We use MCMC for this What we gain is that each string can be inferred independently subject to message passing at boundaries

Scaling

Airline delay data set GP* - no inferred break points (r)BCM – (robust) Bayesian Committee Machine (Marc D) SVIGP – James H & Neil L big data GP Darn... SVIGP does better, but we are 10x faster 6 million data points in < 1 CPU day (scales as 1/cores)

Pipeline for string GPs

Generalized Spectral Kernels

Lebesgue decomposition theorem Sparse spectrum kernels Random Fourier features e.g. Spectral mixture kernels

(Joint work with Yves-Laurent Kom Samo)

Stationary GSK

• r Matérn GSK

Examples

Non-stationary Extensions

recover Bochner Generalized non-stationary spectral kernels

Sparse spectrum Spectral mixture

Sparse GP things

(joint work with Ibrahim Almosallam) Galactic redshift inference

TPZ: random forest

ANNz: (deep) net

GPz: sparse GP

Rejection Performance

Input & output uncertainty

Without input uncertainty

With input uncertainty

Deep nets, kernels etc.

(Joint work with Yves-Laurent Kom Samo)

Deep nets, kernels etc.

Deep nets, kernels etc.