Parameter Estimation for the SEIR Model Using Recurrent Nets
This addresses the inefficiency and inaccuracy in parameter estimation for epidemiological models like SEIR, which is crucial for public health decision-making, though it is an incremental improvement over existing simulation-based methods.
The paper tackles the problem of estimating parameters for the SEIR model, which traditionally uses slow and inaccurate grid search, by proposing a method that trains a recurrent net to generalize simulations and transform the objective into a differentiable one, resulting in significantly better parameter estimations with fewer simulations on COVID-19 datasets.
The standard way to estimate the parameters $Θ_\text{SEIR}$ (e.g., the transmission rate $β$) of an SEIR model is to use grid search, where simulations are performed on each set of parameters, and the parameter set leading to the least $L_2$ distance between predicted number of infections and observed infections is selected. This brute-force strategy is not only time consuming, as simulations are slow when the population is large, but also inaccurate, since it is impossible to enumerate all parameter combinations. To address these issues, in this paper, we propose to transform the non-differentiable problem of finding optimal $Θ_\text{SEIR}$ to a differentiable one, where we first train a recurrent net to fit a small number of simulation data. Next, based on this recurrent net that is able to generalize SEIR simulations, we are able to transform the objective to a differentiable one with respect to $Θ_\text{SEIR}$, and straightforwardly obtain its optimal value. The proposed strategy is both time efficient as it only relies on a small number of SEIR simulations, and accurate as we are able to find the optimal $Θ_\text{SEIR}$ based on the differentiable objective. On two COVID-19 datasets, we observe that the proposed strategy leads to significantly better parameter estimations with a smaller number of simulations.