aiqbench analysis
This paper is theoretical machine learning work on prior-data fitted networks (PFNs), a method for amortized Bayesian inference. It shows that an idealized PFN can converge slowly for semi-parametric targets, such as causal effects, and proposes label and prior corrections based on efficient influence functions to speed that up. Readers should note that the guarantees (Bernstein-von Mises and minimax optimality) hold only under additional assumptions, and the work has not been validated empirically in the abstract.
Debiased Prior-Data Fitted Networks for Amortized Bayesian Semi-Parametric Inference
arXiv:2610.28314v1 Announce Type: cross Abstract: Prior-data fitted networks (PFNs) have recently gained popularity as an end-to-end approach to amortized Bayesian inference. Yet, their statistical behavior for semi-parametric targets, such as means under missingness or causal effects, remains poorly understood. In this work, we develop theoretical foundations for debiased PFNs to perform inference on finite-dimensional targets in general semi-parametric settings. First, we show that, despite being Bayes-optimal with respect to the target, an idealized PFN can exhibit a posterior concentration rate that implicitly depends on the concentration rates of (latent) nuisance functions and can become slower as the prior becomes more diverse. Then, to speed up the target posterior concentration rates, we introduce two generic debiasing strategies based on efficient influence functions: (i) a label correction and (ii) a prior correction. Finally, we show that the debiased PFNs (i) & (ii) possess concentration rates that asymptotically match a convergence rate given by traditional frequentist bias-corrected estimators. In this way, we establish a novel connection between amortized Bayesian inference with PFNs and frequentist semi-parametric efficiency theory. Under additional assumptions, this allows us to guarantee local and global optimality of PFN-based estimators (namely, the Bernstein-von Mises property and minimax optimality, respectively). Therefore, our work provides guidelines for designing debiased PFNs for semi-parametric inference with principled and provable asymptotic guarantees.
Abstract:Prior-data fitted networks (PFNs) have recently gained popularity as an end-to-end approach to amortized Bayesian inference. Yet, their statistical behavior for semi-parametric targets, such as means under missingness or causal effects, remains poorly understood. In this work, we develop theoretical foundations for debiased PFNs to perform inference on finite-dimensional targets in general semi-parametric settings. First, we show that, despite being Bayes-optimal with respect to the target, an idealized PFN can exhibit a posterior concentration rate that implicitly depends on the concentration rates of (latent) nuisance functions and can become slower as the prior becomes more diverse. Then, to speed up the target posterior concentration rates, we introduce two generic debiasing strategies based on efficient influence functions: (i) a label correction and (ii) a prior correction. Finally, we show that the debiased PFNs (i) & (ii) possess concentration rates that asymptotically match a convergence rate given by traditional frequentist bias-corrected estimators. In this way, we establish a novel connection between amortized Bayesian inference with PFNs and frequentist semi-parametric efficiency theory. Under additional assumptions, this allows us to guarantee local and global optimality of PFN-based estimators (namely, the Bernstein-von Mises property and minimax optimality, respectively). Therefore, our work provides guidelines for designing debiased PFNs for semi-parametric inference with principled and provable asymptotic guarantees.
Machine Learning (stat.ML); Machine Learning (cs.LG)
arXiv:2610.28314 [stat.ML]
(or arXiv:2610.28314v1 [stat.ML] for this version)
https://doi.org/10.48550/arXiv.2610.28314 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 308 words