Fig. 6: Closed-form models for mobility flows.
From: Human mobility is well described by closed-form gravity-like models learned automatically from data
We ran the Bayesian machine scientist (BMS) with a training set of 1000 points and three features: origin and destination populations and the distance between them. We used 5 independent Markov chains of 12,000 Monte Carlo steps each. A Minimum description length model (Methods) for the logarithm of the data, where d is the inter-municipality distance, mo is the origin population, and md is the destination population. In the table, we show the fitting parameters for each state of the training data. B Median predictive model (Methods) for the logarithm of the data. As before, d is the inter-municipality distance, mo is the origin population, and md is the destination population. In the table, we show the fitting parameters for each state of the training data. C Ratio between the distance exponent and the population exponent. Round-filled points are obtained from the most plausible model, and empty square points are obtained from the median predictive model. D Relative improvement of each model and metric for the out-of-sample states. We average the relative improvement across the out-of-sample-states. As in Fig. 3I–L, higher values of the performance ratio are always better (also for CPC). BMS models perform significantly better than all other algorithms in three out of four metrics. E We fit the BMS Plausible and BMS Predictive model parameters for the out-of-sample states. We compute the metric using the observed values from the test set and the predicted values of the model using the corresponding set of fitted parameters for each state. Filled bars show the training states and empty bars show the out-of-sample states. Performance in out-of-sample states is similar to training states, confirming that BMS models generalize well.
