Machine Learning and Approximate Explanations¶
For years, common sense has deemed the complex, intricate formulas created by training machine learning algorithms to be uninterpretable. While great advances have been made in recent years to make these often nonlinear, non-monotonic, and non-continuous machine-learned response functions more understandable (Hall et al, 2017), it is likely that such functions will never be as directly or universally interpretable as more traditional linear models.
Why consider machine learning approaches for inferential purposes? In general, linear models focus on understanding and predicting average behavior, whereas machine-learned response functions can often make accurate, but more difficult to explain, predictions for subtler aspects of modeled phenomenon. In a sense, linear models create very exact interpretations for approximate models. The approach here seeks to make approximate explanations for very exact models. It is quite possible that an approximate explanation of an exact model may have as much, or more, value and meaning than the exact interpretations of an approximate model. Moreover, the use of machine learning techniques for inferential or predictive purposes does not preclude using linear models for interpretation (Ribeiro et al, 2016).
The Multiplicity of Good Models in Machine Learning¶
It is well understood that for the same set of input variables and prediction targets, complex machine learning algorithms can produce multiple accurate models with very similar, but not exactly the same, internal architectures (Breiman, 2001). This alone is an obstacle to interpretation, but when using these types of algorithms as interpretation tools or with interpretation tools it is important to remember that details of explanations will change across multiple accurate models.
Expectations for Consistency Between Explanatory Techniques¶
The decision tree surrogate is a global, nonlinear description of the Driverless AI model behavior. Variables that appear in the tree should have a direct relationship with variables that appear in the global feature importance plot. For certain, more linear Driverless AI models, variables that appear in the decision tree surrogate model may also have large coefficients in the global K-LIME model.
K-LIME explanations are linear, do not consider interactions, and represent offsets from the local linear model intercept. LOCO importance values are nonlinear, do consider interactions, and do not explicitly consider a linear intercept or offset. LIME explanations and LOCO importance values are not expected to have a direct relationship but can align roughly as both are measures of a variable’s local impact on a model’s predictions, especially in more linear regions of the Driverless AI model’s learned response function.
ICE is a type of nonlinear sensitivity analysis which has a complex relationship to LOCO feature importance values. Comparing ICE to LOCO can only be done at the value of the selected variable that actually appears in the selected row of the training data. When comparing ICE to LOCO the total value of the prediction for the row, the value of the variable in the selected row, and the distance of the ICE value from the average prediction for the selected variable at the value in the selected row must all be considered.
ICE curves that are outside the standard deviation of partial dependence would be expected to fall into less populated decision paths of the decision tree surrogate; ICE curves that lie within the standard deviation of partial dependence would be expected to belong to more common decision paths.
Partial dependence takes into consideration nonlinear, but average, behavior of the complex Driverless AI model without considering interactions. Variables with consistently high partial dependence or partial dependence that swings widely across an input variable’s domain will likely also have high global importance values. Strong interactions between input variables can cause ICE values to diverge from partial dependence values.