Explainable AI with Shapley Values (Part 3: KernelSHAP)

Key Takeaways

there are multiple ways to calculate and estimate sharply values in this video I would like to briefly go through kernelship again let's use the same example we used last time we have four house features predicting housing prices and would like to explain how this certain instance predicted and what are the contributions of each feature to this prediction with kernel shop there are six steps step one is to generate a coalition Z we randomly generate 0 or 1 for each feature with a zero representing the feature being absent and one representing the feature present so in this case only the number of bedrooms and the age features are present Step 2 is to convert Z to the original feature space what does this mean let's call this new instance HZ and let's copy the values from X whenever Z is 0 we replace the corresponding HZ values with a randomly sampled value from the data here we replace one with two and replace the second one with three step three is to input this HZ into our machine learning model the function f and to get an input which is fhz for example it could be 400k following the same steps we could sample the Collision Z many many times and we will get the values of fhz many many times our goal is to approximate the sharply values from those values somehow since sharply values are additive it is natural to think that we can fit the sharply values into a regression model but each Coalition of z may need to be weighted differently we'll need to compute the weight for each Z here's the equation for the weight where m is the number of features and one Norm of Z Prime is the number of present features in Z Prime features with less present features or more present features have more weight because they might be providing more information for a specific feature in this case Z2 and Z3 will have more weight than Z1 Z2 and Z3 actually have the same weight in this case step 5 is to build this weighted regression model let's create a new function G which is the sum of shapley values for present features in a given collagen C in this example of z g z is 5 0 plus 5 2 plus 5 4. we want to approximate the sum of the shapely values to the model output fhz that's why the first half of the loss function is trying to minimize the difference between fhc and GZ and then additionally there is a weight function here to provide the weight for each Z and then we can optimize this loss function and calculate Phi which are the chapter values to recap here's the algorithm for kernel shap hope you have a better understanding of this algorithm now thank you