In the last post in the series, we defined what interpretability is and looked at a few interpretable models and the quirks and'gotchas' in it. Now let's dig deeper into the post-hoc interpretation techniques which is useful when you model itself is not transparent. This resonates with most real world use cases, because whether we like it or not, we get better performance with a black box model. For this exercise, I have chosen the Adult dataset a.k.a Census Income dataset. Census Income is a pretty popular dataset which has demographic information like age, occupation, along with a column which tells us if the income of the particular person 50k or not. We are using this column to run a binary classification using Random Forest.
Recently, a number of techniques have been proposed to explain a machine learning (ML) model's prediction by attributing it to the corresponding input features. Popular among these are techniques that apply the Shapley value method from cooperative game theory. While existing papers focus on the axiomatic motivation of Shapley values, and efficient techniques for computing them, they do not justify the game formulations used. For instance, we find that the SHAP algorithm's formulation (Lundberg and Lee 2017) may give substantial attributions to features that play no role in a model. In this work, we study the game formulations underpinning several existing methods. Using a series of simple models, we illustrate how their subtle differences can yield large differences in attribution for the same prediction. We then present a general game formulation that unifies existing methods. After discussing the primitive of single-reference games, we decompose the Shapley values of the general game formulation into Shapley values of single-reference games. This is instructive in several ways. First, it enables confidence intervals on estimated attributions, which are not offered by previous works. Second, it enables different contrastive explanations of a prediction through comparison with different groups of reference inputs. We tie this idea to classic work on Norm Theory (Kahneman and Miller 1986) in cognitive psychology, and propose a general framework for generating explanations for ML models, called formulate, approximate, and explain (FAE). We apply this framework to explaining black-box models trained on two UCI datasets and a Lending Club dataset.
Game-theoretic formulations of feature importance have become popular as a way to "explain" machine learning models. These methods define a cooperative game between the features of a model and distribute influence among these input elements using some form of the game's unique Shapley values. Justification for these methods rests on two pillars: their desirable mathematical properties, and their applicability to specific motivations for explanations. We show that mathematical problems arise when Shapley values are used for feature importance and that the solutions to mitigate these necessarily induce further complexity, such as the need for causal reasoning. We also draw on additional literature to argue that Shapley values do not provide explanations which suit human-centric goals of explainability.
Explaining AI systems is fundamental both to the development of high performing models and to the trust placed in them by their users. A general framework for explaining any AI model is provided by the Shapley values that attribute the prediction output to the various model inputs ("features") in a principled and model-agnostic way. The outstanding strength of Shapley values is their combined generality and rigorous foundation: they can be used to explain any AI system, and one always understands their values as the unique attribution method satisfying a set of mathematical axioms. However, as a framework, Shapley values are too restrictive in one significant regard: they ignore all causal structure in the data. We introduce a less-restrictive framework for model-agnostic explainability: "Asymmetric" Shapley values. Asymmetric Shapley values (ASVs) are rigorously founded on a set of axioms, applicable to any AI system, and can flexibly incorporate any causal knowledge known a-priori to be respected by the data. We show through explicit, realistic examples that the ASV framework can be used to (i) improve model explanations by incorporating causal information, (ii) provide an unambiguous test for unfair discrimination based on simple policy articulations, (iii) enable sequentially incremental explanations in time-series models, and (iv) support feature-selection studies without the need for model retraining.