A Comparative Study of Methods for Estimating Conditional Shapley Values
  and When to Use Them
Lars Henry Berge Olsen Ingrid Kristine Glad Martin Jullum Kjersti Aas
Shapley values originated in cooperative game theory but are extensively used
today as a model-agnostic explanation framework to explain predictions made by
complex machine learning models in the industry and academia. There are several
algorithmic approaches for computing different versions of Shapley value
explanations. Here, we focus on conditional Shapley values for predictive
models fitted to tabular data. Estimating precise conditional Shapley values is
difficult as they require the estimation of non-trivial conditional
expectations. In this article, we develop new methods, extend earlier proposed
approaches, and systematize the new refined and existing methods into different
method classes for comparison and evaluation. The method classes use either
Monte Carlo integration or regression to model the conditional expectations. We
conduct extensive simulation studies to evaluate how precisely the different
method classes estimate the conditional expectations, and thereby the
conditional Shapley values, for different setups. We also apply the methods to
several real-world data experiments and provide recommendations for when to use
the different method classes and approaches. Roughly speaking, we recommend
using parametric methods when we can specify the data distribution almost
correctly, as they generally produce the most accurate Shapley value
explanations. When the distribution is unknown, both generative methods and
regression models with a similar form as the underlying predictive model are
good and stable options. Regression-based methods are often slow to train but
produce the Shapley value explanations quickly once trained. The vice versa is
true for Monte Carlo-based methods, making the different methods appropriate in
different practical situations.