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CoLT The conditional localization test for assessing the accuracy of neural posterior estimates

T Chen, V Bansal, JG Scott - arXiv preprint arXiv:2507.17030, 2025 - arxiv.org
Computer Science paper stat.ML Suggest

… of this idea arises in validating conditional generative models for neural posterior estimation, or NPE, which is a rapidly growing area of simulation-based inference. Here θ …

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BibTeX

@article{2507.17030v1,
Author        = {Tianyu Chen and Vansh Bansal and James G. Scott},
Title         = {CoLT: The conditional localization test for assessing the accuracy of
  neural posterior estimates},
Eprint        = {2507.17030v1},
ArchivePrefix = {arXiv},
PrimaryClass  = {stat.ML},
Abstract      = {We consider the problem of validating whether a neural posterior estimate \(
q(\theta \mid x) \) is an accurate approximation to the true, unknown true
posterior \( p(\theta \mid x) \). Existing methods for evaluating the quality
of an NPE estimate are largely derived from classifier-based tests or
divergence measures, but these suffer from several practical drawbacks. As an
alternative, we introduce the \emph{Conditional Localization Test} (CoLT), a
principled method designed to detect discrepancies between \( p(\theta \mid x)
\) and \( q(\theta \mid x) \) across the full range of conditioning inputs.
Rather than relying on exhaustive comparisons or density estimation at every \(
x \), CoLT learns a localization function that adaptively selects points
$\theta_l(x)$ where the neural posterior $q$ deviates most strongly from the
true posterior $p$ for that $x$. This approach is particularly advantageous in
typical simulation-based inference settings, where only a single draw \( \theta
\sim p(\theta \mid x) \) from the true posterior is observed for each
conditioning input, but where the neural posterior \( q(\theta \mid x) \) can
be sampled an arbitrary number of times. Our theoretical results establish
necessary and sufficient conditions for assessing distributional equality
across all \( x \), offering both rigorous guarantees and practical
scalability. Empirically, we demonstrate that CoLT not only performs better
than existing methods at comparing $p$ and $q$, but also pinpoints regions of
significant divergence, providing actionable insights for model refinement.
These properties position CoLT as a state-of-the-art solution for validating
neural posterior estimates.},
Year          = {2025},
Month         = {Jul},
Url           = {http://arxiv.org/abs/2507.17030v1},
File          = {2507.17030v1.pdf}
}

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