An Entropy-Based Approach to Model Selection with Application to Single-Cell Time-Stamped Snapshot Data

Recent single-cell experiments that measure copy numbers of over 40 proteins in individual cells at different time points [time-stamped snapshot (TSS) data] exhibit cell-to-cell variability. Because the same cells cannot be tracked over time, TSS data provide key information about the time-evolution of protein abundances that could yield mechanisms that underlie signaling kinetics. We recently developed a generalized method of moments (GMM) based approach that estimates parameters of mechanistic models using TSS data. However, when multiple mechanistic models potentially explain the same TSS data, selecting the best model (i.e., model selection) is often challenging. Popular approaches like Kullback-Leibler divergence and Akaikes Information Criterion are difficult to implement because the distribution that gave rise to the "noisy" data is only known numerically and approximately. To perform model selection in this situation, we introduce an entropy-based approach that incorporates our GMM based parameter estimation and commonly used estimators in kernel density estimation. Using simulated TSS data, we show that our approach can select the "ground truth" from a set of competing mechanistic models. Furthermore, we use a bootstrap procedure to compute model selection probabilities, which can be useful when measuring the relative support of a candidate model.