SCFGP is a proposed improvement of Sparse Spectrum Gaussian Process (SPGP), which is a new branch of method to speed up Gaussian process model taking advantage of Fourier features. Recall that using Gaussian processes for machine learning is a state-of-the-art technique that is originated from and popularized by Carl Edward Rasmussen and Christopher K. I. Williams.

Based on minimization of the marginal likelihood, SCFGP selects a set of vectors to obtain a Gramian matrix, which is treated as the frequency matrix for later computation of Fourier features. This procedure indeed can be viewed as constructing sparsely correlated Fourier features.

Note that the Fourier features are identically and independently distributed in SPGP, therefore the size of optimization parameters is proportional to the number of Fourier features times the number of dimension. This is undoubtedly an unfavorable property, since the model is likely to stick in local minima and becomes very unstable when dealing with very high dimensional data, such as images, speech signals, text, etc.

The formulation of SCFGP is briefly described in this sheet: (Derivation will be included in the future)

SCFGP is implemented in python using Theano by Max W. Y. Lam ([email protected]).

To install SCFGP, use pip:

$ pip install SCFGP

Or clone this repo:

$ git clone https://github.com/MaxInGaussian/SCFGP.git
$ python setup.py install

Theano is used due to its nice and simple syntax to set up the tedious formulas in SCFGP, and
its capability of computing automatic differentiation.

To install Theano, see this page:

http://deeplearning.net/software/theano/install.html

To install scikit-learn, see this page:

https://github.com/scikit-learn/scikit-learn

from SCFGP import *
# <>: necessary inputs, {}: optional inputs
model = SCFGP(rank=<rank_of_frequency_matrix>,
              feature_size=<number_of_Fourier_features>,
              fftype={feature_type},
              msg={print_message_or_not})
model.fit(X_train, y_train, {X_test}, {y_test})
predict_mean, predict_std = model.predict(X_test, {y_test})

Copyright (c) 2016, Max W. Y. Lam All rights reserved.

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