Background: Gene expression time series data are usually in the form of high-dimensional arrays. Unfortunately, the\ndata may sometimes contain missing values: for either the expression values of some genes at some time points or\nthe entire expression values of a single time point or some sets of consecutive time points. This significantly affects\nthe performance of many algorithms for gene expression analysis that take as an input, the complete matrix of gene\nexpression measurement. For instance, previous works have shown that gene regulatory interactions can be\nestimated from the complete matrix of gene expression measurement. Yet, till date, few algorithms have been\nproposed for the inference of gene regulatory network from gene expression data with missing values.\nResults: We describe a nonlinear dynamic stochastic model for the evolution of gene expression. The model\ncaptures the structural, dynamical, and the nonlinear natures of the underlying biomolecular systems. We present\npoint-based Gaussian approximation (PBGA) filters for joint state and parameter estimation of the system with\none-step or two-step missing measurements. The PBGA filters use Gaussian approximation and various quadrature rules,\nsuch as the unscented transform (UT), the third-degree cubature rule and the central difference rule for computing\nthe related posteriors. The proposed algorithm is evaluated with satisfying results for synthetic networks, in silico\nnetworks released as a part of the DREAM project, and the real biological network, the in vivo reverse engineering and\nmodeling assessment (IRMA) network of yeast Saccharomyces cerevisiae.\nConclusion: PBGA filters are proposed to elucidate the underlying gene regulatory network (GRN) from time series\ngene expression data that contain missing values. In our state-space model, we proposed a measurement model that\nincorporates the effect of the missing data points into the sequential algorithm. This approach produces a better\ninference of the model parameters and hence, more accurate prediction of the underlying GRN compared to when\nusing the conventional Gaussian approximation (GA) filters ignoring the missing data points.
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