A Kernelized Stein Discrepancy for Goodness-of-fit Tests and Model Evaluation
This work addresses the challenge of model evaluation and goodness-of-fit testing for researchers and practitioners dealing with complex probabilistic models, though it appears incremental as it builds on existing Stein and kernel methods.
The authors tackled the problem of measuring differences between probability distributions and evaluating model fit by deriving a new discrepancy statistic based on Stein's identity and reproducing kernel Hilbert space theory, resulting in a class of goodness-of-fit tests applicable to complex, high-dimensional distributions with intractable normalization constants.
We derive a new discrepancy statistic for measuring differences between two probability distributions based on combining Stein's identity with the reproducing kernel Hilbert space theory. We apply our result to test how well a probabilistic model fits a set of observations, and derive a new class of powerful goodness-of-fit tests that are widely applicable for complex and high dimensional distributions, even for those with computationally intractable normalization constants. Both theoretical and empirical properties of our methods are studied thoroughly.