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## Figure 5.
Gaussian process fit on expression profile of gene Cyp1b1 in the experimental mouse
data. Figure 5: A GP fitted on the centred profile of the gene Cyp1b1 (probeID 1416612_at in the GSE10562 dataset) with different settings of the lengthscale hyperparameter ℓ^{2}. The blue crosses represent zero-mean hybridised gene expression in time (log2 ratios
between treatment and control) and the shaded area indicates the point-wise mean plus/minus
two times the standard deviation (95% confidence region). (a) Mean function is constant as ℓ^{2 }→ ∞ (0 inverse lengthscale in eq. (14)) and all of the observed data variance is attributed
to noise (). (b) The lengthscale is manually set to a local-optimum large value (ℓ^{2 }= 30) and thus the mean function roughly fits the data-points. The observed data variance
is equally attributed to signal () and noise (). Consequently, the GP features high uncertainty in its predictive curve. (c) The lengthscale is manually set to a local-optimum small value (ℓ^{2 }= 15.6) and thus the mean function tighly fits the data-points with high certainty.
The interpretation from the covariance function in this case is that the profile contains
a minimal amount of noise and that most of the observed data variance is attributed
to the underlying signal (). (d) The contour of the corresponding LML function plotted by an exhaustive search of ℓ^{2 }and SNR values. The two main local-optima are indicated by the green dots and a third
optimum that corresponds to the 1st panel appears almost as flat in the contour and
its vicinity encompasses the whole lengthscale axis for very small values of SNR (i.e.
given that SNR ≈ 0, the lengthscale is trivial).
Kalaitzis and Lawrence |