Gaussian process modelling of multiple short time series
This addresses a common issue in bioinformatics for researchers analyzing gene expression time series, though it is incremental as it builds on existing GP methods.
The paper tackled the problem of over-fitting and under-fitting in Gaussian process models applied to multiple short time series, such as gene expression data with few time points, by constraining the GP length-scale and using informative priors on noise, enabling reliable automatic application to large datasets.
We present techniques for effective Gaussian process (GP) modelling of multiple short time series. These problems are common when applying GP models independently to each gene in a gene expression time series data set. Such sets typically contain very few time points. Naive application of common GP modelling techniques can lead to severe over-fitting or under-fitting in a significant fraction of the fitted models, depending on the details of the data set. We propose avoiding over-fitting by constraining the GP length-scale to values that focus most of the energy spectrum to frequencies below the Nyquist frequency corresponding to the sampling frequency in the data set. Under-fitting can be avoided by more informative priors on observation noise. Combining these methods allows applying GP methods reliably automatically to large numbers of independent instances of short time series. This is illustrated with experiments with both synthetic data and real gene expression data.