Introduction

A MATLAB implementation of Probabilistic Least Squares Ordinal Regression [1]. Two covariance functions are provided, namely isotropic squared exponential and squared exponential with ARD. The implementation at hand is also compatible with GPML [2] covariances if GPML Toolbox is in path.

Usage

A simple example on random data:

% generate training samples
Xtr = linspace(0, 20, 21)';
Ytr = [ones(2, 1); 2*ones(3, 1); 3*ones(10,1); 4*ones(5,1); 5];

% train a PLSOR model with default settings
ordgp = OrdRegressionGP(Xtr, Ytr);

% make prediction
Xte = linspace(0, 20, 50)';
[Ypred, ~, mu] = ordgp.predict(Xte);

% plot results
plot(Xte, mu);          % latent GP mean
hold on;
plot(Xtr, Ytr, '+');    % training data
plot(Xte, Ypred, 'o');  % predicted ordinal labels

For more advanced examples on data from UCI Machine Learning Repository, see script benchmark.m.

MEX Files

The following functions for operations on a positive definite matrix are implemented also in C, using LAPACK and MATLAB C API:

• CHOLINV for inverting a positive definite matrix given its Cholesky factor
• CHOLSOLVE for solving a system of linear equations AX = B for X with positive definite A given by its Cholesky factor

Both functions can be compiled and linked against libraries in a MATLAB path by MEX. A Makefile is provided for convenience:

make cholinv cholsolve

MATLAB implementation is provided as well, so if any of the binaries is not present at call time, the corresponding MATLAB function will be called instead silently.

Dependencies

• MATLAB Optimization Toolbox
• MATLAB Statistics and Machine Learning Toolbox (for running tests)
• GPML Toolbox (optional)

References

[1] Srijith, P. K.; Shevade, S. & Sundararajan, S. A probabilistic least squares approach to ordinal regression Proceedings of the 25th Australasian Joint Conference on Advances in Artificial Intelligence, Springer-Verlag, 2012, 683-694

[2] Rasmussen, C. E. & Nickisch, H. Gaussian processes for machine learning (GPML) toolbox J. Mach. Learn. Res., JMLR.org, 2010, 11, 3011-3015