Pathspace Kalman Filters with Dynamic Process Uncertainty for Analyzing Time-course Data
This method addresses uncertainty quantification and model-data deviation detection in time-course analysis, particularly for biological data, but it appears incremental as an extension of the Kalman Filter.
The paper tackles the problem of analyzing time-course data by developing a Pathspace Kalman Filter (PKF) that dynamically tracks uncertainties and detects deviations between models and data, resulting in a reduction of mean-squared-error by several orders of magnitude on synthetic data and application to a biological dataset with over 1.8 million gene expression measurements.
Kalman Filter (KF) is an optimal linear state prediction algorithm, with applications in fields as diverse as engineering, economics, robotics, and space exploration. Here, we develop an extension of the KF, called a Pathspace Kalman Filter (PKF) which allows us to a) dynamically track the uncertainties associated with the underlying data and prior knowledge, and b) take as input an entire trajectory and an underlying mechanistic model, and using a Bayesian methodology quantify the different sources of uncertainty. An application of this algorithm is to automatically detect temporal windows where the internal mechanistic model deviates from the data in a time-dependent manner. First, we provide theorems characterizing the convergence of the PKF algorithm. Then, we numerically demonstrate that the PKF outperforms conventional KF methods on a synthetic dataset lowering the mean-squared-error by several orders of magnitude. Finally, we apply this method to biological time-course dataset involving over 1.8 million gene expression measurements.