$)$ Write all steps of the LIME algorithm for providing explainability for a black box model. Specify SHRherever applicable. equation

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b$)$ Assume a non$-$interpretable black box model F$($x$1,$x$2).$ For the purpose of computation assume F$($x$1,$x$2)$ sigmoid $($x$1-2"$x$2).$ Use LIME to explain the model's prediction for a test data point $(4\mathrm{.}5).$ Generate random perturbations by changing only the first variable with $+/-1$: Ignore the weights of perturbations. Find coefficients of the surrogate model $($linear regression, assume co $0)$ that can explain the test data point