Efficient Sensitivity Analysis in Biomanufacturing with Sequential Shapley Value Estimation

In biomanufacturing, the presence of inherent random factors and the limited amount of data make it essential to characterize the resulting stochastic variability and model risk for stable process control and efficient data utilization. In this study, we adopt the Shapley value (SV) to quantify the contributions of random factors and historical data points to the output variance based on the policy-augmented Bayesian network (PABN) model. To improve the efficiency of SV estimation, we exploit the sparsity inherent in SVs of random factors and data points. In particular, we first formulate a top-[Formula: see text] selection problem to identify the subset of random factors that collectively explain a prescribed proportion of the variance in output, and then develop a sequential budget allocation algorithm to solve it. Second, to mitigate the model risk with limited real-world data, we design a data valuation procedure that integrates sequential budget allocation with compressive sensing, framing the estimation of SVs as a sparse recovery problem. Numerical experiments on both synthetic and real-world PABN models demonstrate that the proposed methods substantially improve the accuracy and efficiency of selecting key random factors and informative data points with constrained simulation budgets.