Deep Gaussian Processes II

Robot Wireless Data

Robot WiFi Data

Gaussian Process Fit to Robot Wireless Data

Robot WiFi Data GP

Robot WiFi Data Deep GP

Robot WiFi Data Deep GP

Robot WiFi Data Latent Space

Robot WiFi Data Latent Space

GPy: A Gaussian Process Framework in Python

GPy: A Gaussian Process Framework in Python

• BSD Licensed software base.
• Wide availability of libraries, ‘modern’ scripting language.
• Allows us to set projects to undergraduates in Comp Sci that use GPs.
• Available through GitHub https://github.com/SheffieldML/GPy
• Reproducible Research with Jupyter Notebook.

Features

• Probabilistic-style programming (specify the model, not the algorithm).
• Non-Gaussian likelihoods.
• Multivariate outputs.
• Dimensionality reduction.
• Approximations for large data sets.

Olympic Marathon Data

Gold medal times for Olympic Marathon since 1896. Marathons before 1924 didn’t have a standardized distance. Present results using pace per km. In 1904 Marathon was badly organized leading to very slow times.

Image from Wikimedia Commons http://bit.ly/16kMKHQ

Olympic Marathon Data

Alan Turing

Probability Winning Olympics?

• He was a formidable Marathon runner.
• In 1946 he ran a time 2 hours 46 minutes.
  • That’s a pace of 3.95 min/km.
• What is the probability he would have won an Olympics if one had been held in 1946?

Gaussian Process Fit

Olympic Marathon Data GP

Deep GP Fit

• Can a Deep Gaussian process help?

• Deep GP is one GP feeding into another.

Olympic Marathon Data Deep GP

Olympic Marathon Data Deep GP

Olympic Marathon Data Latent 1

Olympic Marathon Data Latent 2

Olympic Marathon Pinball Plot

Della Gatta Gene Data

• Given given expression levels in the form of a time series from Della Gatta et al. (2008).

Della Gatta Gene Data

Gene Expression Example

• Want to detect if a gene is expressed or not, fit a GP to each gene Kalaitzis and Lawrence (2011).

TP53 Gene Data GP

TP53 Gene Data GP

TP53 Gene Data GP

Multiple Optima

Della Gatta Gene Data Deep GP

Della Gatta Gene Data Deep GP

Della Gatta Gene Data Latent 1

Della Gatta Gene Data Latent 2

TP53 Gene Pinball Plot

Step Function Data

Step Function Data GP

Step Function Data Deep GP

Step Function Data Deep GP

Step Function Data Latent 1

Step Function Data Latent 2

Step Function Data Latent 3

Step Function Data Latent 4

Step Function Pinball Plot

Motorcycle Helmet Data

Motorcycle Helmet Data GP

Motorcycle Helmet Data Deep GP

Motorcycle Helmet Data Deep GP

Motorcycle Helmet Data Latent 1

Motorcycle Helmet Data Latent 2

Motorcycle Helmet Pinball Plot

‘High Five’ Motion Capture Data

• ‘High five’ data.
• From CMU Mocap Database (CMU Motion Capture Lab, 2003).
• Model learns structure between two interacting subjects.

Shared LVM

Subsample of the MNIST Data

Fitting a Deep GP to a the MNIST Digits Subsample

Deep Health