Everyone wants to solve AI’s black box problem: the dilemma of understanding how a machine learning (ML) computer model arrives at its decisions. The hard part is figuring out the influence of each of the hundreds or thousands of variables interacting in nearly infinite combinations to derive an outcome in an ML model.
In 2017 two computer scientists from the University of Washington published a technique for generating fast and practical explanations of a particular kind of ML called tree-based models (specifically, a variant called XGBoost). The algorithm’s authors named their work SHAP, for Shapley additive explanations, and it’s been used hundreds of times for coding projects.
The Shapley name refers to American economist and Nobelist Lloyd Shapley, who in 1953 first published his formulas for assigning credit to “players” in a multi-dimensional game where no player acts alone. Shapley’s seminal game theory work has influenced voting systems, college admissions, and scouting in professional sports. Shapley Values work well in machine learning, too. The catch is that they’re expensive to compute. In a game or model with just 50 variables you’re already looking at considering more options than there are stars than there are in the universe.
That’s where SHAP comes in. SHAP approximates Shapley values quickly by cleverly using the tree structure of XGBoost models, speeding up the explanation time enough to make it practical to assign credit to each variable. Some banks and lenders eager to use machine learning in credit underwriting or other models are asking themselves, “Why not just use SHAP to power my explanation requirements?"
Fair question. The answer? Because that would be irresponsible for a bunch of reasons. For credit and finance applications, bridging from off-the-shelf SHAP to a safe application takes a lot of care and work, even if you just want to explain XGBoost models. Credit risk models must be treated particularly carefully because they highly regulated and significantly impact consumers’ lives. When a consumer is denied credit, the Fair Credit Reporting Act of 1970 requires accurate and actionable reasons for the decision so that consumers can repair their credit and re-apply successfully.
SHAP is a practical solution for some use cases of ML, but in credit underwriting, it just doesn’t hold water on its own. Here are a few reasons why we’ve faced serious challenges in our attempts to apply SHAP in credit risk -- and why we had to invent something new.
Score space vs margin space - these details really matter
Lending businesses want to be able to set a target and approve, say, 20% of applicants. That means the business wants a function that outputs numbers between 0 and 100, where 0 is the worst and 100 is the best, and for which exactly 20% of all scores lie above 80, 30% of all scores lie above 70%, and so on. This well-defined output is said to be in “score space."
The score space is very different mathematically from the credit model’s actual output, which is said to be in “margin space.” Margin space numbers fall in a narrow range from 0 to 1. In general, the relationship between the model’s actual output in margin space and the acceptance threshold in score space is extremely non-linear, and you have to transform the model’s output to generate the number the lending business wants. Don’t worry, you’re not the only one that struggles to keep track: we do too, and while technical, the margin space/score space transition really matters.
The problem with SHAP is that, because of the way it computes its Shapley values, it really only works in margin space. If you compute the set of weighted key factors in margin space, you'll get a very different set of factors and weights than if you compute them in score space, which is where banks derive their top five explanations for rejecting a borrower. Even if you are using the same populations and are only looking at the transformed values, you will not get the same importance weights. Worse, you likely won’t end up with the same factors in the top five.
The table below shows how this plays out for a real applicant for an auto loan. The reasons returned to the rejected borrower were dramatically different when translated from margin space to score space. If you skipped this important step, and just used SHAP out of the box, you would have thought the main reason for denial was the bankruptcy count. But the real top reason for denial, in score space, was the number of credit inquiries. A consumer relying on reasons generated by margin space attribution would be misled. Getting this wrong could have devastating consequences to consumers seeking to access financing for their first house or car, who rely on denial reasons to improve their ability to access credit. It could also cause a lender to run afoul of fair lending and fair credit rules.
Why does this happen? Because SHAP derives its values by looking at all the results of taking a path down each tree in the model, and it assumes that the sum of the values along a set of paths down a tree gives you the score -- basically, you can compute the score with only the data in the trees. That's not true when you transform into score space; the transformation destroys that structure. SHAP can also have trouble recovering even a simple model’s internal structure, as we’ll explain in the last point.
Explanation by reference
SHAP computes variable importance globally, which means it shows how the model behaves for every applicant (in margin space) with respect to the overall model itself. In credit risk modeling, it is often required to understand an applicant’s score in terms of another applicant or applicant population, that is, with respect to a reference population. For example, when lenders compute the reasons an applicant was rejected (for adverse action notices), they want to explain the applicant’s score in terms of the approved applicants. When they do disparate impact analysis lenders want to understand the drivers of approval rate disparity. This requires comparing the feature importance for the population of, say, white non-Hispanic male applicants to protected groups and performing a search for less discriminatory alternatives. These are illustrated in the diagrams below.
Left: Adverse action requires comparing the denied applicant to good borrowers.
Right: Fair lending analysis requires comparing minority applicants with non-minority applicants.
There are many details you need to get right in this process, including the appropriate application of sample weights, mapping to score space at the approval cut-off, sampling methods, and accompanying documentation. Out of the box, SHAP doesn’t allow you to easily do this.
You want to use modeling methods other than XGBoost
Using SHAP is hard enough because it outputs values in margin space that you have to correctly map into score space. But it has other important limitations. Although SHAP provides fast explanations for gradient-boosted tree models, there are many other mechanisms for building scoring functions, including many alternative forms of tree models such as random forests and extremely random forests, not to mention other implementations of gradient boosting such as LightGBM.
You may also want to use continuous modeling methods such as radial basis function networks, Gaussian mixture models, and, perhaps most commonly, deep neural networks. The current implementation of SHAP cannot explain any of the other types of tree models, and cannot explain any continuous model outside a small collection, and only by importing algorithms other than SHAP.
What’s more, SHAP cannot explain ensembles of continuous and tree-based models, such as stacked or deeply stacked models that combine xgboost and deep neural networks. In our experience (and the experience of others), these types of ensembled models are more accurate and stable over time. That’s why we built ZAML to explain a much wider variety of model types, enabling you to use world-beating ensembled models to drive your lending business.
Even on a simple XGBoost model, SHAP fails to uncover the underlying geometry
Machine learning models are effectively geometric entities: they embody the idea that things near to one another will tend to be mapped to the same place and then produce systems which reflect that structure. A good example of this is the ovals dataset, a two-dimensional dataset consisting of a set of points drawn uniformly from two overlapping ovals with the same number of points drawn from each. The ovals from which the points are drawn are arranged roughly vertically in the chart below, and the model is trained to predict membership in one or the other oval given the coordinates of a point. For convenience, the oval with a greater y value is arbitrarily assigned the target value 1 and the oval with the less y value is assigned the value 0.
When viewed geometrically, this dataset is inseparable: points in the overlapping region are equally likely to have been drawn from either of the two ovals and so no classifier can predict membership for any such point.
Intuitively, one would expect a classification function defined for the ovals dataset to correspond to three regions: a region of points belonging only to the upper oval, a region of points common to the two ovals, and a region of points belonging only to the lower oval. We trained an XGBoost model on a random sample of half of the ovals dataset, and looked at the model’s predictions on the other half.
The chart below shows the model’s predictions, and we can see the three regions we expected. The blue represents scores the model assigned to the bottom region, the green the middle, and the red, the top. As you can see the model produces nicely separated outputs.
We should see that same separation when we look at the explainer outputs. One would intuitively expect that items in the upper region will have average attributions which are relatively large and positive, items in the common area to have attributions which are relatively close to zero, and items in the lower region to have average attributions which are relatively large and negative. If the explainer doesn’t reflect this structure, it isn’t really explaining the model, and probably shouldn’t be trusted. To investigate that question, we compared SHAP attribution weights with the attribution weights generated by Zest’s ZAML software in the charts below.
Let’s walk through what we’re seeing. The left column shows the feature importance for each model prediction, as assigned by ZAML. The right column shows the feature importance for each model prediction as generated by SHAP. The top row is the feature importance for f0, the x coordinate in our ovals dataset. The bottom row is the feature importance for f1, the y coordinate. The blue, green and red colors correspond to the bottom, middle and top regions, respectively.
As you can see, ZAML readily separates the top, middle, and bottom regions -- notice how the blue green and red bars are all nicely separated in the charts in the left column -- while SHAP, shown on the right, gets them all jumbled up. The results suggest that SHAP may not be the right tool to use off the shelf for the rigorous and regulated requirements of credit underwriting.
We did not expect these results when we first saw them, and frankly we thought they were wrong. After careful review by multiple teams inside and outside the company, however, we’re confident they’re not. Look for a scientific paper describing our algorithm, a mathematical proof of its correctness and uniqueness, and other empirical results to be published soon. In the meantime, if you care about getting your model explanations right, feel free to reach out to us.
SHAP was a giant leap forward in model explainability. The use of a game-theoretic framework to explain models is powerful and creative. Nonetheless, as the above analyses show, you really need more than just the out-of-the-box SHAP to provide the kind of accurate explanations required for real-world credit decisioning applications. Even on a simple XGBoost model, SHAP can provide inaccurate explanations, and care must be taken to map into score space correctly and to mitigate numerical precision issues, when computing explanations by reference. Before diving head first into ML explainability with SHAP, it is important to understand its limitations and determine whether or how you will address those limitations in your ML application. Credit decisions make lasting impacts on people’s lives and getting the explanations right matters.
Jay Budzik is the CTO of ZestFinance.
Photo: Scott Robinson/flickr