Equation after equation (5): the square outside the $\exp(\gamma_k)$ term should be inside the bracket. Same applies to equation after equation (6) Thanks to: Pei Gao and David Luengo

Equation after equation (5): there is a missing $t$ on the second line of the equation after $D_j$. Thanks to: Pei Gao

Equation (10): There is a missing log on the left hand side of the equation. Thanks to: Pei Gao

Equation (10): The sign before log(\sigma_{ji}^2) should be positive, not negative. Thanks to: Pei Gao

Equation (7): We missed the mean function which should be subtracted from the genes observations, $\mathbf{x}$, to get the posterior mean prediction. It was also misimplemented in the original code, but since everything needs to be offset to fit the earlier results we didn't notice. It is correct in the later journal paper \cite{Gao:latent08} Thanks to: Pei Gao and James Anderson

Abstract

Modelling the dynamics of transcriptional processes in the cell requires the knowledge of a number of key biological quantities. While some of them are relatively easy to measure, such as mRNA decay rates and mRNA abundance levels, it is still very hard to measure the active concentration levels of the transcription factor proteins that drive the process and the sensitivity of target genes to these concentrations. In this paper we show how these quantities for a given transcription factor can be inferred from gene expression levels of a set of known target genes. We treat the protein concentration as a latent function with a Gaussian Process prior, and include the sensitivities, mRNA decay rates and baseline expression levels as hyperparameters. We apply this procedure to a human leukemia dataset, focusing on the tumour repressor p53 and obtaining results in good accordance with recent biological studies.

@InProceedings{lawrence-transcriptionalgp06,
title = {Modelling transcriptional regulation using Gaussian Processes},
author = {Neil D. Lawrence and Guido Sanguinetti and Magnus Rattray},
booktitle = {Advances in Neural Information Processing Systems},
pages = {785},
year = {2007},
editor = {Bernhard Schölkopf and John C. Platt and Thomas Hofmann},
volume = {19},
address = {Cambridge, MA},
month = {00},
publisher = {MIT Press},
edit = {https://github.com/lawrennd//publications/edit/gh-pages/_posts/2007-01-01-lawrence-transcriptionalgp06.md},
url = {http://inverseprobability.com/publications/lawrence-transcriptionalgp06.html},
abstract = {Modelling the dynamics of transcriptional processes in the cell requires the knowledge of a number of key biological quantities. While some of them are relatively easy to measure, such as mRNA decay rates and mRNA abundance levels, it is still very hard to measure the active concentration levels of the transcription factor proteins that drive the process and the sensitivity of target genes to these concentrations. In this paper we show how these quantities for a given transcription factor can be inferred from gene expression levels of a set of known target genes. We treat the protein concentration as a latent function with a Gaussian Process prior, and include the sensitivities, mRNA decay rates and baseline expression levels as hyperparameters. We apply this procedure to a human leukemia dataset, focusing on the tumour repressor p53 and obtaining results in good accordance with recent biological studies.},
crossref = {Schoelkopf:nips06},
key = {Lawrence:transcriptionalGP06},
linkpdf = {ftp://ftp.dcs.shef.ac.uk/home/neil/gpsim.pdf},
linkpsgz = {ftp://ftp.dcs.shef.ac.uk/home/neil/gpsim.ps.gz},
linksoftware = {http://inverseprobability.com/gpsim/},
group = {gene networks,shefml,puma}
}

%T Modelling transcriptional regulation using Gaussian Processes
%A Neil D. Lawrence and Guido Sanguinetti and Magnus Rattray
%B
%C Advances in Neural Information Processing Systems
%D
%E Bernhard Schölkopf and John C. Platt and Thomas Hofmann
%F lawrence-transcriptionalgp06
%I MIT Press
%P 785--792
%R
%U http://inverseprobability.com/publications/lawrence-transcriptionalgp06.html
%V 19
%X Modelling the dynamics of transcriptional processes in the cell requires the knowledge of a number of key biological quantities. While some of them are relatively easy to measure, such as mRNA decay rates and mRNA abundance levels, it is still very hard to measure the active concentration levels of the transcription factor proteins that drive the process and the sensitivity of target genes to these concentrations. In this paper we show how these quantities for a given transcription factor can be inferred from gene expression levels of a set of known target genes. We treat the protein concentration as a latent function with a Gaussian Process prior, and include the sensitivities, mRNA decay rates and baseline expression levels as hyperparameters. We apply this procedure to a human leukemia dataset, focusing on the tumour repressor p53 and obtaining results in good accordance with recent biological studies.

TY - CPAPER
TI - Modelling transcriptional regulation using Gaussian Processes
AU - Neil D. Lawrence
AU - Guido Sanguinetti
AU - Magnus Rattray
BT - Advances in Neural Information Processing Systems
PY - 2007/01/01
DA - 2007/01/01
ED - Bernhard Schölkopf
ED - John C. Platt
ED - Thomas Hofmann
ID - lawrence-transcriptionalgp06
PB - MIT Press
SP - 785
EP - 792
L1 - ftp://ftp.dcs.shef.ac.uk/home/neil/gpsim.pdf
UR - http://inverseprobability.com/publications/lawrence-transcriptionalgp06.html
AB - Modelling the dynamics of transcriptional processes in the cell requires the knowledge of a number of key biological quantities. While some of them are relatively easy to measure, such as mRNA decay rates and mRNA abundance levels, it is still very hard to measure the active concentration levels of the transcription factor proteins that drive the process and the sensitivity of target genes to these concentrations. In this paper we show how these quantities for a given transcription factor can be inferred from gene expression levels of a set of known target genes. We treat the protein concentration as a latent function with a Gaussian Process prior, and include the sensitivities, mRNA decay rates and baseline expression levels as hyperparameters. We apply this procedure to a human leukemia dataset, focusing on the tumour repressor p53 and obtaining results in good accordance with recent biological studies.
ER -

Lawrence, N.D., Sanguinetti, G. & Rattray, M.. (2007). Modelling transcriptional regulation using Gaussian Processes. Advances in Neural Information Processing Systems 19:785-792