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 leave-out-last predictions

Best hyperparameters (with respect to SNR on leave-1 training dataset)

Performed on training set:

Performed on test set:

Dynamics

Normalization

Optimization

Gamma (state-space coefficient)

Tau (kinetic time constant)

Lambda (regularization parameter)

SNR (in dB) on leave-1 training dataset

percentage of correct signs on leave-1 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 factor-gene 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 state-space 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 signal-to-noise ratio (SNR), in dB. We then performed a leave-out-last (leave-1) 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/gb-2010-11-12-r123

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