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6. Sensitivity Analysis
At this point, we've inferred equations that sufficiently estimate the unknown parameters that provide solutions that accurately model our ABM. We got them via sparse regression techniques, however, it would benefit to do a further analysis on these equations to figure out which components of the equation are highly explanatory of the parameter. Even though sparse regression hopefully provides us a parsimonious equation, coefficients may remain non-zero since the penalty is on the magnitude of coefficients and is a multi-objective optimization problem. Therefore, even after obtaining the best possible inferred equation from a sparse regression method (we use LASSO), further reduction of non-zero coefficients and thus relevant components of our inferred equation remains possible. This is done via sensitivity analysis.
Local normalized sensitivity analysis on the solutions with respect to the components in the parameter equations.
Global sensitivity analysis on the parameters with respect to their components.