Explainable AI with Shapley Values (Part 2: Estimate Shapley Values)

Key Takeaways

We have a model predicting house prices based on several house features like house style, number of bedrooms, number of bathrooms, and house age. How do we calculate the Shapley values for each feature? Again, the setup is that we have a machine learning model F, which inputs a set of house features and outputs a house prices. Let's say we have an instance of four values X1, X2, X3, X4. For example, we have style one, three bedrooms, one bathroom, and the house is 5 years old. We want to understand how this instance predicted 390K in the housing price, and what are the contributions of each feature to this prediction. Here are five steps to do the calculation. Step one, we draw a random sample Z from our data. With four features, we get our four data points Z1, Z2, Z3, and Z4. Step two, let's permute the features, meaning that we change the order of the features. For example, here we get X2, X4, X3, X1, and Z2, Z4, Z3, Z1. To make it simpler, let's rewrite it into X (1, 2, 3, and so on). Step three is to construct two new instances X+J and X-J. For example, in this case, we're interested in the contribution of the number of bathrooms. So, we create new instances X+3 and X-3. X+3 means that the first three values stay the same, and everything afterwards we replace with the values we get from the sample Z. X-3 only has one value difference. For X-3, we also replace the X3 with Z3. Step four is to input X+3 and X-3 into the function F and calculate the difference between FX+3 and FX-3. This calculates the marginal contribution of the number of bathrooms in this specific combination of house feature values. Step five is to repeat this process for M iterations and take an average, and we will get the Shapley values of this feature. To recap, this is the algorithm of how Shapley value is calculated for a feature, and then we can repeat this process for all features. Shapley value for all features explain why the expected value or the average prediction of the model that might be 300K, and our output is 390K. For example, 5 years old contributes 50K, one bathroom contributes 40K, three bedrooms contributes 70K, and style one contributes 10K. Those four features contributed to the 90,000 difference. Now you know how to calculate Shapley values. Thank you.