As the observations we can make from patients are limited compared to the complexity of the physiology, underdetermined inverse problems appear often in the parameter estimation problems of physiologically based pharmacokinetics (PBPK) models. We address this issues of not being able to identify the model parameter set uniquely by finding multiple sets of possible parameter sets that are consistent with the observations. As this approach requires multiple parameter estimations of a complex model, the computational cost can be a bottle neck. In this paper, we introduce a new computationally efficient algorithm called the Cluster Newton method to find multiple solutions of an underdetermined inverse problem.

View full abstract

Tensor decomposition methods are applied to wide variety of application areas such as signal processing, neuroimaging, bioinformatics, and relational data analysis. However, hampered by the non-convexity of these methods, their statistical performance for dealing with noise and missing entries has not been clearly understood. In this paper, we review the algorithm and statistical performance of a convex optimization based tensor decomposition algorithm. We also explain the limitation of the current approach and point to possible future directions.

View full abstract