Approximate Stein Classes for Truncated Density Estimation
This work addresses a specific challenge in statistical machine learning for researchers and practitioners dealing with truncated data, offering an incremental improvement by relaxing boundary constraints without needing explicit boundary forms.
The paper tackles the problem of estimating truncated density models, which is difficult due to intractable normalizing constants and boundary conditions, by proposing approximate Stein classes and a novel discrepancy measure called truncated kernelised Stein discrepancy (TKSD) that uses only boundary samples and does not require a predefined weighting function, with experiments showing improved accuracy over previous methods.
Estimating truncated density models is difficult, as these models have intractable normalising constants and hard to satisfy boundary conditions. Score matching can be adapted to solve the truncated density estimation problem, but requires a continuous weighting function which takes zero at the boundary and is positive elsewhere. Evaluation of such a weighting function (and its gradient) often requires a closed-form expression of the truncation boundary and finding a solution to a complicated optimisation problem. In this paper, we propose approximate Stein classes, which in turn leads to a relaxed Stein identity for truncated density estimation. We develop a novel discrepancy measure, truncated kernelised Stein discrepancy (TKSD), which does not require fixing a weighting function in advance, and can be evaluated using only samples on the boundary. We estimate a truncated density model by minimising the Lagrangian dual of TKSD. Finally, experiments show the accuracy of our method to be an improvement over previous works even without the explicit functional form of the boundary.