Table 1 

The kinetic ODE and both the conjugate gradient and LARS optimization algorithms obtain the best fit to the 0 to 15 minutes data, with good leaveoutlast predictions 

Best hyperparameters (with respect to SNR on leave1 training dataset) 
Performed on training set: 
Performed on test set: 

Dynamics 
Normalization 
Optimization 
Gamma (statespace coefficient) 
Tau (kinetic time constant) 
Lambda (regularization parameter) 
SNR (in dB) on leave1 training dataset 
percentage of correct signs on leave1 test dataset 


Kinetic 
MAS5 
Gradient 
1 
3 
0.0001 
32.4 
68% 
Kinetic 
MAS5 
LARS 
0.1 
3 
0.1 
32.4 
74% 
Kinetic 
MAS5 
Elastic Nets 
0.1 
7 
0.05 
32.2 
71% 
Brownian 
MAS5 
Gradient 
0.1 
NA 
0.0001 
32.1 
65% 
Brownian 
MAS5 
LARS 
0 
NA 
0.05 
32.1 
63% 
Brownian 
MAS5 
Elastic Nets 
0 
NA 
0.05 
32.1 
63% 
Naïve trend prediction 
MAS5 
NA 
NA 
NA 
NA 
52% 



Each line in the table represents the type of ODE for the dynamical model of transcription factorgene regulation (either kinetic, with mRNA degradation, or 'Brownian motion', without mRNA degradation), the type of microarray data normalization, and the optimization algorithm for learning the parameters of the dynamical model. For each of these, we selected the best hyperparameters, namely the statespace coefficient gamma, the kinetic time constant (in minutes) and the parameter regularization coefficient lambda, based on the quality of fit to the training data (from 0 to 15 minutes), as measured by the signaltonoise ratio (SNR), in dB. We then performed a leaveoutlast (leave1) prediction and counted the number of times the sign of the mRNA change between 15 minutes and 20 minutes was correct. We compared these results to a naïve extrapolation (based on the trend between 12 and 15 minutes) and obtained statistically significant results at P = 0.0145. 

Krouk et al. Genome Biology 2010 11:R123 doi:10.1186/gb20101112r123 