Gaussian Process Regression with Time-shifts

Examples from the paper

GPR, fixed timesGPR with timeshift


Time-course gene expression data sets provide important insights into dynamic aspects of biological processes such as circadian rhythms, cell cycle, and organ development. A typical microarray time-course expression data set consists of measurements taken at a relatively small number of time-points (e.g., 5 to 10), where at each time-point microarray measurements are obtained on a few (say, 3) replicate samples. There has been considerable work in recent years in bioinformatics on the development of statistical techniques for accurately inferring expression profiles from such data, in the face of both measurement noise and biological variation across replicates.

However, a source of variation that has received little attention to date is uncertainty about the precise biological time at which measurements were taken. Specifically, replicates may be measured at the same chronological time, yet could be at different stages of development due to the replicate individuals having developed at different rates. Although the underlying true expression profiles for each gene may be noisy, we can infer time-shifts for each replicate by analyzing all genes simultaneously. In particular, we simultaneously estimate the profile shapes using a Gaussian process regression (GPR) model and estimate the time shifts by a maximum a-posteriori optimization.


This code implements a Gaussian process regression (GPR) model with uncertainty in the independent axis (in our case, time).

  • ZIP file (includes all code and the expression data used in our paper)

For more information on the model or its results, please see our publication

Copyright / license

The Gaussian Process with Time-Shifting code was written by Qiang Liu, and are copyrighted under the (lesser) GPL:

    Copyright (C) 2009 Qiang Liu

This program is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation; version 2.1 or later. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details. You should have received a copy of the GNU Lesser General Public License along with this program; if not, write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.

The authors may be contacted via email at: qliu1 (at) uci.edu


Last modified December 06, 2009, at 04:42 PM
Bren School of Information and Computer Science
University of California, Irvine