ASNPE brings an active learning scheme into the inference loop to estimate the utility of simulation parameter candidates to the underlying probabilistic model.

ASNPE brings an active learning scheme into the inference loop to estimate the utility of simulation parameter candidates to the underlying probabilistic model.

We consider the problem of validating whether a neural posterior estimate \( q(θ\mid x) \) is an accurate approximation to the true, unknown true posterior \( p(θ\mid x) \). 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 \( p(θ\mid x) \) and \( q(θ\mid x) \) 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 $θ_l(x)$ 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 \( θ\sim p(θ\mid x) \) from the true posterior is observed for each conditioning input, but where the neural posterior \( q(θ\mid x) \) 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.

Across many domains of science, stochastic models are an essential tool to understand the mechanisms underlying empirically observed data. Models can be of different levels of detail and accuracy, with models of high-fidelity (i.e., high accuracy) to the phenomena under study being often preferable. However, inferring parameters of high-fidelity models via simulation-based inference is challenging, especially when the simulator is computationally expensive. We introduce MF-NPE, a multifidelity approach to neural posterior estimation that leverages inexpensive low-fidelity simulations to infer parameters of high-fidelity simulators within a limited simulation budget. MF-NPE performs neural posterior estimation with limited high-fidelity resources by virtue of transfer learning, with the ability to prioritize individual observations using active learning. On one statistical task with analytical ground-truth and two real-world tasks, MF-NPE shows comparable performance to current approaches while requiring up to two orders of magnitude fewer high-fidelity simulations. Overall, MF-NPE opens new opportunities to perform efficient Bayesian inference on computationally expensive simulators.

Are these based on a parametric estimate of the distribution, where the parameter samples are aggregated with an average? My overall takeaway from the toy examples (which exhibit skewness and/or multiple modes) is that, with averaging techniques such as mean, the resulting aggregated posterior is a poor representation of the true posterior. However, I have questions about whether such comparisons are fair, since (at least in the case of a known bimodal distribution) averaging techniques are clearly a poor choice. Therefore it feels that the comparison is a bit unfair.

The primary originality of this paper derives from dealing with active-learning regime with little or no data. This is an extremely important problem for ML, especially as ML is applied to more real-world domains where data is minimal and collection is expensive. The significance of this problem is therefore of high significance. I will discuss the significance their approach to the problem below. Related to this first point, the authors do a fantastic job of situating themselves in the wider active-learning literature, highlighting where there "ice-problem" sits and specifying its unique differences to alternative active learning scenarios.