jamesrobertlloyd / gp-structure-search

This is part of the automatic statistician project

Gaussian Process Structure Search

Code for automatically searching through compositions of covariance functions for Gaussian process regression, described in

Structure Discovery in Nonparametric Regression through Compositional Kernel Search by David Duvenaud, James Robert Lloyd, Roger Grosse, Joshua B. Tenenbaum, Zoubin Ghahramani

Abstract:

Despite its importance, choosing the structural form of the kernel in nonparametric regression remains a black art. We define a space of kernel structures which are built compositionally by adding and multiplying a small number of base kernels. We present a method for searching over this space of structures which mirrors the scientific discovery process. The learned structures can often decompose functions into interpretable components and enable long-range extrapolation on time-series datasets. Our structure search method outperforms many widely used kernels and kernel combination methods on a variety of prediction tasks.

Feel free to email us with any questions:
James Lloyd ([email protected])
David Duvenaud ([email protected])
Roger Grosse ([email protected])

We welcome pull requests and feature suggestions!

Instructions:

You'll need Matlab and Python 2.7 with numpy.

You'll also need to create source/cblparallel/config.py - follow the format of the example file in the same directory.

To check whether the framework runs, go to the source directory and run demo.py.

There are some example experiment scripts source/examples/.

Many helper functions to summarize results are in postprocessing.py. For example, to produce nice plots of your decomposition, call make_all_1d_figures()

If you have any questions about getting this running on your machine or cluster, please let us know.

If describe your problem to us, we'll also happy to give advice about running the method.

Known issues:

Windows users will need to make a change

• All strings in config files are not sanitized, therefore backslashes and other special characters should be delimited e.g. C:\\ProgramFiles\\Matlab

Updated Repository and Paper:

Development on this project has now moved to https://github.com/jamesrobertlloyd/gpss-research/.

Further developments are described in the paper: Automatic Construction and Natural-Language Description of Nonparametric Regression Models by James Robert Lloyd, David Duvenaud, Roger Grosse, Joshua B. Tenenbaum and Zoubin Ghahramani, appearing in AAAI 2014.

Abstract:

This paper presents the beginnings of an automatic statistician, focusing on regression problems. Our system explores an open-ended space of statistical models to discover a good explanation of a data set, and then produces a detailed report with figures and natural-language text. Our approach treats unknown regression functions nonparametrically using Gaussian processes, which has two important consequences. First, Gaussian processes can model functions in terms of high-level properties (e.g. smoothness, trends, periodicity, changepoints). Taken together with the compositional structure of our language of models this allows us to automatically describe functions in simple terms. Second, the use of flexible nonparametric models and a rich language for composing them in an open-ended manner also results in state-of-the-art extrapolation performance evaluated over 13 real time series data sets from various domains.

gp-structure-search's Issues

Zip loop

Zipping/unzipping occasionally results in perhaps unreadable files - they have a job id of 'access' - clearly something is wrong

In general, there is a risk of constant looping when a job is submitted but it doesn't show up on qstat yet - need to detect this looping behaviour

Miscellaneous notes

Hessian delta of 1e-6 will not always be appropriate e.g. location parameters for unscaled data

Fix intro

Make it read as well as abstract and Jaynes quotation

Fix the optimisation

This means both

• ensuring local extrema are reached so Laplace approx valid
• jittering previously learned parameter values to avoid having to multiply by constant kernels

Add Roger's ideas about improving the Structure Search section

Sanity Check Frobenius norm

Is it well-calibrated across different scales?

Implement taboo search

Might be useful when removing kernels - not sure - seemed sensible a while back

Remove kernel / pruning operation in 'expansion'

Keep track of mean or add to kernel

I prefer the kernel conceptually - but need to check if numerically stable

Inference fail loop

If any code fails (e.g. ill conditioned covariance matrix) the experiment can get stuck in an infinite loop

I observed this in the prediction code once - quick fix was to change the starting noise parameter very slightly.

Expand 'extrapolation' results writeup

Automatic plots of 1D posterior decomposition

Write code to plot separately the posterior mean and marginal variance of each component of the signal.

Fix random seeds for reproducibility

Add a changepoint kernel

This would let us make a lot more interesting claims in the paper - we could claim to address nonstationarity. It would also make the decomposition algorithm more interesting than simply distributing terms.

LOCAL / REMOTE / HOME

Merge LOCAL and HOME - and put fully within cblparallel

Check noise model in additive paper and possibly matlab code to use the same here

Add a time integrated process kernel if such a thing exists

Make code usable by others

Remove dependence on config
Add GPML
Make parallelism less location dependent (picloud?)
...

Add remaining citations

Reorganise results files

Move unused results files so that they can be nuked if necessary

np.nan always get sorted to the end of a list

Laplace bug

This kernel

ScoredKernel(k_opt=ProductKernel([ MaskKernel(ndim=8, active_dimension=0, base_kernel=CubicKernel(offset=1.757755, output_variance=7.084045)), MaskKernel(ndim=8, active_dimension=7, base_kernel=SqExpPeriodicKernel(lengthscale=-2.701080, period=-0.380918, output_variance=-0.071214)) ]), nll=6348.096611, laplace_nle=-184450132.068237, bic_nle=12720.630212, noise=[-1.77276072])

applied to data set r_concrete_500_fold_10_of_10.mat

has a clearly erroneous laplace_nle

Why?

Nyquist aliasing with periodic kernels - and defaults

Prevent periods smaller than smallest data distance to prevent trivial aliasing

In general, what are 'sensible' default values

Revisit parameter defaults and random restarts

Make them shift and scale with the data appropriately

Why do linear kernels get sprinkled into expressions?

Similarity != Distance

Question about running in windows

Hi,

I am trying to run this code base on windows 10 and I am running into a number of issues after fixing the file paths and similar benign issues I ran into the following MATLAB error when running demo.py:

For online documentation, see http://www.mathworks.com/support
For product information, visit www.mathworks.com.

Undefined function or variable 'tmpb0_jih'.

Could you please assist?

Thank you

Add a spectral kernel

Fix extreme parameters in periodic kernel

Why do they get sprinkled into expressions - seemingly changing very little?

figs2pdf does not work on sagarmatha

Produces weird noise in the pdfs - any guesses why?

Experimental parameters should all be stored in a struct that's saved with the results files.

Be more Bayesian

Kernel over kernels + active learning / Bayesian optimisation
Priors on expressions
...

Add standard errors to multi-dimensional results tables

or just shrink them into one table

Fix months->years on airline plot

Make figures 1, 2 and 8 smaller.

Shorten related work section

Regression is a super-developed field, but the related work section is currently a bit too long.

Get gravatars

reset: unknown terminal type unknown Terminal type?

Dear authors,

I am thankful that you share the code in the Github.

I am really like your paper and try to run your code on your demo.py.

However, when I go to the source directory and run demo.py. This is an error on my computer:
"reset: unknown terminal type unknown
Terminal type? "
Could you please give me some suggestion about that?

The below is all the information when I run the demo.py.

"
runfile('/home/chunchao/Desktop/gp-structure-search-master/source/demo.py', wdir='/home/chunchao/Desktop/gp-structure-search-master/source')
Backend TkAgg is interactive backend. Turning interactive mode on.
Running experiment:
description = An example experiment,
data_dir = ../data/1d_data/01-airline.mat,
max_depth = 2,
random_order = False,
k = 1,
debug = False,
local_computation = True,
n_rand = 2,
sd = 4,
max_jobs = 500,
verbose = True,
make_predictions = False,
skip_complete = False,
results_dir = ../examples/,
iters = 10,
base_kernels = SE,Per,Lin,
zero_mean = True,
verbose_results = False,
random_seed = 0,
use_min_period = True,
period_heuristic = 10,
use_constraints = False,
alpha_heuristic = -2,
lengthscale_heuristic = -4.5,
Experiment 01-airline
Output to: ../examples/01-airline_result.txt
Creating data file locally
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All new results:
1251.6857440777076 nan 2513.311114754567 M(0, SE(ell=-0.8, sf=5.7))
1181.7783896324722 nan 2373.4964058640962 M(0, LN(off=-2.0, ell=0.0, loc=0.0))
1180.6405321123773 nan 2371.2206908239064 M(0, SE(ell=3.0, sf=6.2))
1027.923777964088 nan 2065.787182527328 M(0, LN(off=-7.3, ell=7.0, loc=1944.7))
1027.903814739796 nan 2065.7472560787437 M(0, SE(ell=0.0, sf=0.0))
1027.8720632958796 nan 2065.683753190911 M(0, LN(off=-8.7, ell=0.1, loc=1955.4))
1023.5392001361355 nan 2061.987840170999 M(0, PE(ell=1.5, p=2.2, sf=5.2))
1023.3361754305673 nan 2061.5817907598625 M(0, PE(ell=3.4, p=1.8, sf=4.9))
All new results after duplicate removal:
1251.6857440777076 nan 2513.311114754567 M(0, SE(ell=-0.8, sf=5.7))
1181.7783896324722 nan 2373.4964058640962 M(0, LN(off=-2.0, ell=0.0, loc=0.0))
1180.6405321123773 nan 2371.2206908239064 M(0, SE(ell=3.0, sf=6.2))
1027.923777964088 nan 2065.787182527328 M(0, LN(off=-7.3, ell=7.0, loc=1944.7))
1027.903814739796 nan 2065.7472560787437 M(0, SE(ell=0.0, sf=0.0))
1027.8720632958796 nan 2065.683753190911 M(0, LN(off=-8.7, ell=0.1, loc=1955.4))
1023.5392001361355 nan 2061.987840170999 M(0, PE(ell=1.5, p=2.2, sf=5.2))
1023.3361754305673 nan 2061.5817907598625 M(0, PE(ell=3.4, p=1.8, sf=4.9))
Printing all results
1251.6857440777076 nan 2513.311114754567 M(0, SE(ell=-0.8, sf=5.7))
1181.7783896324722 nan 2373.4964058640962 M(0, LN(off=-2.0, ell=0.0, loc=0.0))
1180.6405321123773 nan 2371.2206908239064 M(0, SE(ell=3.0, sf=6.2))
1027.923777964088 nan 2065.787182527328 M(0, LN(off=-7.3, ell=7.0, loc=1944.7))
1027.903814739796 nan 2065.7472560787437 M(0, SE(ell=0.0, sf=0.0))
1027.8720632958796 nan 2065.683753190911 M(0, LN(off=-8.7, ell=0.1, loc=1955.4))
1023.5392001361355 nan 2061.987840170999 M(0, PE(ell=1.5, p=2.2, sf=5.2))
1023.3361754305673 nan 2061.5817907598625 M(0, PE(ell=3.4, p=1.8, sf=4.9))
Seed kernels :
M(0, PE(ell=3.4, p=1.8, sf=4.9))
Expanded kernels :
( M(0, LN(off=-2.0, ell=0.0, loc=0.0)) x M(0, PE(ell=3.4, p=1.8, sf=4.9)) )
( M(0, PE(ell=0.0, p=-2.0, sf=0.0)) x M(0, PE(ell=3.4, p=1.8, sf=4.9)) )
( M(0, PE(ell=3.4, p=1.8, sf=4.9)) x M(0, SE(ell=0.0, sf=0.0)) )
( M(0, LN(off=-2.0, ell=0.0, loc=0.0)) + M(0, PE(ell=3.4, p=1.8, sf=4.9)) )
( M(0, PE(ell=0.0, p=-2.0, sf=0.0)) + M(0, PE(ell=3.4, p=1.8, sf=4.9)) )
( M(0, PE(ell=3.4, p=1.8, sf=4.9)) + M(0, SE(ell=0.0, sf=0.0)) )
M(0, LN(off=-2.0, ell=0.0, loc=0.0))
M(0, PE(ell=0.0, p=-2.0, sf=0.0))
M(0, SE(ell=0.0, sf=0.0))
Creating data file locally
Creating scripts
Sending scripts to cblparallel
Submitting job 1 of 27
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All new results:
1231.2193188407873 nan 2482.3178908798786 ( M(0, PE(ell=3.4, p=1.8, sf=4.6)) x M(0, SE(ell=-0.0, sf=3.7)) )
1195.301552405626 nan 2410.482358009556 ( M(0, LN(off=-2.0, ell=0.1, loc=0.0)) x M(0, PE(ell=3.4, p=1.8, sf=4.9)) )
1180.5636329338015 nan 2390.946145665059 ( M(0, PE(ell=4.6, p=6.9, sf=-2.7)) + M(0, PE(ell=3.4, p=1.8, sf=5.0)) )
1180.5492496798781 nan 2390.917379157212 ( M(0, PE(ell=1.9, p=6.9, sf=3.3)) + M(0, PE(ell=3.4, p=1.8, sf=5.0)) )
1181.7816979119368 nan 2388.4124623217535 ( M(0, LN(off=-2.0, ell=0.0, loc=0.0)) + M(0, PE(ell=3.4, p=1.8, sf=4.9)) )
1180.563652648244 nan 2385.976371794368 ( M(0, PE(ell=3.4, p=1.8, sf=5.0)) + M(0, SE(ell=0.0, sf=-0.0)) )
1180.5636337552983 nan 2385.9763340084764 ( M(0, LN(off=-11.8, ell=3.4, loc=1960.9)) + M(0, PE(ell=3.4, p=1.8, sf=5.0)) )
1180.5636331360015 nan 2385.976332769883 ( M(0, PE(ell=3.4, p=1.8, sf=5.0)) + M(0, SE(ell=0.7, sf=-2.1)) )
1180.5636329755807 nan 2385.9763324490414 ( M(0, LN(off=-13.6, ell=5.1, loc=1970.5)) + M(0, PE(ell=3.4, p=1.8, sf=5.0)) )
1181.7125696761482 nan 2383.3043925506004 ( M(0, PE(ell=3.4, p=1.8, sf=4.9)) x M(0, SE(ell=0.0, sf=-0.0)) )
1180.663863187727 nan 2376.237166274182 M(0, PE(ell=2.9, p=1.0, sf=6.3))
1181.7783896324722 nan 2373.4964058640962 M(0, LN(off=-2.0, ell=0.0, loc=0.0))
1181.4844478710331 nan 2372.908522341218 M(0, SE(ell=4.4, sf=3.8))
1027.6078027525305 nan 2080.064672002941 ( M(0, PE(ell=3.6, p=6.3, sf=-4.3)) x M(0, PE(ell=3.4, p=1.8, sf=5.0)) )
1027.9237881880226 nan 2070.7570162747734 M(0, PE(ell=0.0, p=1.9, sf=-5.8))
1023.6929509234078 nan 2067.2651550451196 ( M(0, PE(ell=3.4, p=1.8, sf=6.1)) x M(0, SE(ell=-0.3, sf=-0.6)) )
1027.911635944512 nan 2065.762898488176 M(0, SE(ell=3.8, sf=-1.0))
1027.903814739796 nan 2065.7472560787437 M(0, SE(ell=0.0, sf=0.0))
1027.714691100425 nan 2065.3690088000017 M(0, LN(off=-8.4, ell=0.8, loc=1959.7))
1002.522711842176 nan 2024.924676882656 ( M(0, LN(off=-3.4, ell=1.0, loc=1965.1)) x M(0, PE(ell=3.3, p=0.7, sf=5.1)) )
974.4348088970949 nan 1958.8092443933417 M(0, LN(off=-15.0, ell=-1.1, loc=1967.5))
897.9109529202489 nan 1815.7011590388017 ( M(0, LN(off=-0.8, ell=-2.2, loc=1975.3)) x M(0, PE(ell=3.4, p=1.8, sf=5.0)) )
894.5560567068537 nan 1813.9611799115874 ( M(0, PE(ell=3.4, p=1.8, sf=5.0)) + M(0, SE(ell=-0.8, sf=2.0)) )
827.4239624014712 nan 1679.6969913008222 ( M(0, PE(ell=4.6, p=1.6, sf=7.2)) x M(0, PE(ell=3.5, p=2.2, sf=4.8)) )
All new results after duplicate removal:
1231.2193188407873 nan 2482.3178908798786 ( M(0, PE(ell=3.4, p=1.8, sf=4.6)) x M(0, SE(ell=-0.0, sf=3.7)) )
1195.301552405626 nan 2410.482358009556 ( M(0, LN(off=-2.0, ell=0.1, loc=0.0)) x M(0, PE(ell=3.4, p=1.8, sf=4.9)) )
1180.5636329338015 nan 2390.946145665059 ( M(0, PE(ell=4.6, p=6.9, sf=-2.7)) + M(0, PE(ell=3.4, p=1.8, sf=5.0)) )
1180.5492496798781 nan 2390.917379157212 ( M(0, PE(ell=1.9, p=6.9, sf=3.3)) + M(0, PE(ell=3.4, p=1.8, sf=5.0)) )
1181.7816979119368 nan 2388.4124623217535 ( M(0, LN(off=-2.0, ell=0.0, loc=0.0)) + M(0, PE(ell=3.4, p=1.8, sf=4.9)) )
1180.563652648244 nan 2385.976371794368 ( M(0, PE(ell=3.4, p=1.8, sf=5.0)) + M(0, SE(ell=0.0, sf=-0.0)) )
1180.5636337552983 nan 2385.9763340084764 ( M(0, LN(off=-11.8, ell=3.4, loc=1960.9)) + M(0, PE(ell=3.4, p=1.8, sf=5.0)) )
1180.5636331360015 nan 2385.976332769883 ( M(0, PE(ell=3.4, p=1.8, sf=5.0)) + M(0, SE(ell=0.7, sf=-2.1)) )
1180.5636329755807 nan 2385.9763324490414 ( M(0, LN(off=-13.6, ell=5.1, loc=1970.5)) + M(0, PE(ell=3.4, p=1.8, sf=5.0)) )
1181.7125696761482 nan 2383.3043925506004 ( M(0, PE(ell=3.4, p=1.8, sf=4.9)) x M(0, SE(ell=0.0, sf=-0.0)) )
1180.663863187727 nan 2376.237166274182 M(0, PE(ell=2.9, p=1.0, sf=6.3))
1181.7783896324722 nan 2373.4964058640962 M(0, LN(off=-2.0, ell=0.0, loc=0.0))
1181.4844478710331 nan 2372.908522341218 M(0, SE(ell=4.4, sf=3.8))
1027.6078027525305 nan 2080.064672002941 ( M(0, PE(ell=3.6, p=6.3, sf=-4.3)) x M(0, PE(ell=3.4, p=1.8, sf=5.0)) )
1027.9237881880226 nan 2070.7570162747734 M(0, PE(ell=0.0, p=1.9, sf=-5.8))
1023.6929509234078 nan 2067.2651550451196 ( M(0, PE(ell=3.4, p=1.8, sf=6.1)) x M(0, SE(ell=-0.3, sf=-0.6)) )
1027.911635944512 nan 2065.762898488176 M(0, SE(ell=3.8, sf=-1.0))
1027.903814739796 nan 2065.7472560787437 M(0, SE(ell=0.0, sf=0.0))
1027.714691100425 nan 2065.3690088000017 M(0, LN(off=-8.4, ell=0.8, loc=1959.7))
1002.522711842176 nan 2024.924676882656 ( M(0, LN(off=-3.4, ell=1.0, loc=1965.1)) x M(0, PE(ell=3.3, p=0.7, sf=5.1)) )
974.4348088970949 nan 1958.8092443933417 M(0, LN(off=-15.0, ell=-1.1, loc=1967.5))
897.9109529202489 nan 1815.7011590388017 ( M(0, LN(off=-0.8, ell=-2.2, loc=1975.3)) x M(0, PE(ell=3.4, p=1.8, sf=5.0)) )
894.5560567068537 nan 1813.9611799115874 ( M(0, PE(ell=3.4, p=1.8, sf=5.0)) + M(0, SE(ell=-0.8, sf=2.0)) )
827.4239624014712 nan 1679.6969913008222 ( M(0, PE(ell=4.6, p=1.6, sf=7.2)) x M(0, PE(ell=3.5, p=2.2, sf=4.8)) )
Printing all results
1251.6857440777076 nan 2513.311114754567 M(0, SE(ell=-0.8, sf=5.7))
1231.2193188407873 nan 2482.3178908798786 ( M(0, PE(ell=3.4, p=1.8, sf=4.6)) x M(0, SE(ell=-0.0, sf=3.7)) )
1195.301552405626 nan 2410.482358009556 ( M(0, LN(off=-2.0, ell=0.1, loc=0.0)) x M(0, PE(ell=3.4, p=1.8, sf=4.9)) )
1180.5636329338015 nan 2390.946145665059 ( M(0, PE(ell=4.6, p=6.9, sf=-2.7)) + M(0, PE(ell=3.4, p=1.8, sf=5.0)) )
1180.5492496798781 nan 2390.917379157212 ( M(0, PE(ell=1.9, p=6.9, sf=3.3)) + M(0, PE(ell=3.4, p=1.8, sf=5.0)) )
1181.7816979119368 nan 2388.4124623217535 ( M(0, LN(off=-2.0, ell=0.0, loc=0.0)) + M(0, PE(ell=3.4, p=1.8, sf=4.9)) )
1180.563652648244 nan 2385.976371794368 ( M(0, PE(ell=3.4, p=1.8, sf=5.0)) + M(0, SE(ell=0.0, sf=-0.0)) )
1180.5636337552983 nan 2385.9763340084764 ( M(0, LN(off=-11.8, ell=3.4, loc=1960.9)) + M(0, PE(ell=3.4, p=1.8, sf=5.0)) )
1180.5636331360015 nan 2385.976332769883 ( M(0, PE(ell=3.4, p=1.8, sf=5.0)) + M(0, SE(ell=0.7, sf=-2.1)) )
1180.5636329755807 nan 2385.9763324490414 ( M(0, LN(off=-13.6, ell=5.1, loc=1970.5)) + M(0, PE(ell=3.4, p=1.8, sf=5.0)) )
1181.7125696761482 nan 2383.3043925506004 ( M(0, PE(ell=3.4, p=1.8, sf=4.9)) x M(0, SE(ell=0.0, sf=-0.0)) )
1180.663863187727 nan 2376.237166274182 M(0, PE(ell=2.9, p=1.0, sf=6.3))
1181.7783896324722 nan 2373.4964058640962 M(0, LN(off=-2.0, ell=0.0, loc=0.0))
1181.7783896324722 nan 2373.4964058640962 M(0, LN(off=-2.0, ell=0.0, loc=0.0))
1181.4844478710331 nan 2372.908522341218 M(0, SE(ell=4.4, sf=3.8))
1180.6405321123773 nan 2371.2206908239064 M(0, SE(ell=3.0, sf=6.2))
1027.6078027525305 nan 2080.064672002941 ( M(0, PE(ell=3.6, p=6.3, sf=-4.3)) x M(0, PE(ell=3.4, p=1.8, sf=5.0)) )
1027.9237881880226 nan 2070.7570162747734 M(0, PE(ell=0.0, p=1.9, sf=-5.8))
1023.6929509234078 nan 2067.2651550451196 ( M(0, PE(ell=3.4, p=1.8, sf=6.1)) x M(0, SE(ell=-0.3, sf=-0.6)) )
1027.923777964088 nan 2065.787182527328 M(0, LN(off=-7.3, ell=7.0, loc=1944.7))
1027.911635944512 nan 2065.762898488176 M(0, SE(ell=3.8, sf=-1.0))
1027.903814739796 nan 2065.7472560787437 M(0, SE(ell=0.0, sf=0.0))
1027.903814739796 nan 2065.7472560787437 M(0, SE(ell=0.0, sf=0.0))
1027.8720632958796 nan 2065.683753190911 M(0, LN(off=-8.7, ell=0.1, loc=1955.4))
1027.714691100425 nan 2065.3690088000017 M(0, LN(off=-8.4, ell=0.8, loc=1959.7))
1023.5392001361355 nan 2061.987840170999 M(0, PE(ell=1.5, p=2.2, sf=5.2))
1023.3361754305673 nan 2061.5817907598625 M(0, PE(ell=3.4, p=1.8, sf=4.9))
1002.522711842176 nan 2024.924676882656 ( M(0, LN(off=-3.4, ell=1.0, loc=1965.1)) x M(0, PE(ell=3.3, p=0.7, sf=5.1)) )
974.4348088970949 nan 1958.8092443933417 M(0, LN(off=-15.0, ell=-1.1, loc=1967.5))
897.9109529202489 nan 1815.7011590388017 ( M(0, LN(off=-0.8, ell=-2.2, loc=1975.3)) x M(0, PE(ell=3.4, p=1.8, sf=5.0)) )
894.5560567068537 nan 1813.9611799115874 ( M(0, PE(ell=3.4, p=1.8, sf=5.0)) + M(0, SE(ell=-0.8, sf=2.0)) )
827.4239624014712 nan 1679.6969913008222 ( M(0, PE(ell=4.6, p=1.6, sf=7.2)) x M(0, PE(ell=3.5, p=2.2, sf=4.8)) )
Seed kernels :
( M(0, PE(ell=4.6, p=1.6, sf=7.2)) x M(0, PE(ell=3.5, p=2.2, sf=4.8)) )
Expanded kernels :
( ( M(0, LN(off=-2.0, ell=0.0, loc=0.0)) + M(0, PE(ell=3.5, p=2.2, sf=4.8)) ) x M(0, PE(ell=4.6, p=1.6, sf=7.2)) )
( ( M(0, LN(off=-2.0, ell=0.0, loc=0.0)) + M(0, PE(ell=4.6, p=1.6, sf=7.2)) ) x M(0, PE(ell=3.5, p=2.2, sf=4.8)) )
( ( M(0, PE(ell=0.0, p=-2.0, sf=0.0)) + M(0, PE(ell=3.5, p=2.2, sf=4.8)) ) x M(0, PE(ell=4.6, p=1.6, sf=7.2)) )
( ( M(0, PE(ell=0.0, p=-2.0, sf=0.0)) + M(0, PE(ell=4.6, p=1.6, sf=7.2)) ) x M(0, PE(ell=3.5, p=2.2, sf=4.8)) )
( ( M(0, PE(ell=3.5, p=2.2, sf=4.8)) + M(0, SE(ell=0.0, sf=0.0)) ) x M(0, PE(ell=4.6, p=1.6, sf=7.2)) )
( ( M(0, PE(ell=4.6, p=1.6, sf=7.2)) + M(0, SE(ell=0.0, sf=0.0)) ) x M(0, PE(ell=3.5, p=2.2, sf=4.8)) )
( M(0, LN(off=-2.0, ell=0.0, loc=0.0)) x M(0, PE(ell=3.5, p=2.2, sf=4.8)) )
( M(0, LN(off=-2.0, ell=0.0, loc=0.0)) x M(0, PE(ell=3.5, p=2.2, sf=4.8)) x M(0, PE(ell=4.6, p=1.6, sf=7.2)) )
( M(0, LN(off=-2.0, ell=0.0, loc=0.0)) x M(0, PE(ell=4.6, p=1.6, sf=7.2)) )
( M(0, PE(ell=0.0, p=-2.0, sf=0.0)) x M(0, PE(ell=3.5, p=2.2, sf=4.8)) )
( M(0, PE(ell=0.0, p=-2.0, sf=0.0)) x M(0, PE(ell=3.5, p=2.2, sf=4.8)) x M(0, PE(ell=4.6, p=1.6, sf=7.2)) )
( M(0, PE(ell=0.0, p=-2.0, sf=0.0)) x M(0, PE(ell=4.6, p=1.6, sf=7.2)) )
( M(0, PE(ell=3.5, p=2.2, sf=4.8)) x M(0, PE(ell=4.6, p=1.6, sf=7.2)) x M(0, SE(ell=0.0, sf=0.0)) )
( M(0, PE(ell=3.5, p=2.2, sf=4.8)) x M(0, SE(ell=0.0, sf=0.0)) )
( M(0, PE(ell=4.6, p=1.6, sf=7.2)) x M(0, SE(ell=0.0, sf=0.0)) )
( ( M(0, PE(ell=3.5, p=2.2, sf=4.8)) x M(0, PE(ell=4.6, p=1.6, sf=7.2)) ) + M(0, LN(off=-2.0, ell=0.0, loc=0.0)) )
( ( M(0, PE(ell=3.5, p=2.2, sf=4.8)) x M(0, PE(ell=4.6, p=1.6, sf=7.2)) ) + M(0, PE(ell=0.0, p=-2.0, sf=0.0)) )
( ( M(0, PE(ell=3.5, p=2.2, sf=4.8)) x M(0, PE(ell=4.6, p=1.6, sf=7.2)) ) + M(0, SE(ell=0.0, sf=0.0)) )
reset: unknown terminal type unknown
Terminal type? "

Best wishes,
Chunchao

Add GPML to repo - update paths / config etc

Add licence

Which licence? GPL, CRAPL, MIT?

Add constant kernel in general?

This might fix some bugs of extraneous kernels being discovered - the algorithm might be working round a stuck optimiser.

Create flag to reduce experiment output

Too much data!

Complete synthetic experiments table

Linear kernel doesn't have an offset

Move counter.py to utils

Add more 1D datasets

And Josh's examples. We might consider making nice 2D plots for the EEG data, as well.

Import matlab code from Dave's additive paper to automatically recreate latex results tables

Replace hard constraints

Either with priors + MAP (i.e. regularisation) or a more Bayesian treatment (Laplace, sampling...?)

Figures -> svg

Windows compatibility

See readme for details

• sh -> cmd
• string sanitization