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arXiv Statistics ML

Robust Bayesian Inference for Unnormalized Models with Mixed-Domain Data

The paper introduces SME-BETEL, a semiparametric Bayesian method that merges score matching estimating equations with Bayesian exponentially tilted empirical likelihood to perform inference on models with intractable normalizing constants. SME-BETEL avoids evaluating these constants and eliminates the need for learning-rate calibration, while providing consistency, asymptotic normality, and a Bernstein‑von Mises theorem that guarantees asymptotically calibrated credible sets even under model misspecification. The authors extend the framework to mixed‑domain data, enabling robust inference for doubly‑intractable models such as spatial preferential sampling, and demonstrate its effectiveness through simulations and an ozone‑monitoring application.

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arXiv Machine Learning
Sep 11

Generalized Score Matching for Parameter Estimation on Convex Domains

The paper introduces a generalized score matching objective for parameter estimation on convex subsets of ρ^d, derived from Minimum Probability Flow learning. It shows that this objective is a proper local scoring rule of second order, ensuring recovery of the true density when minimized, and proves convexity and consistency for exponential family models under standard conditions. Experiments demonstrate the method’s effectiveness on constrained domains where the partition function is intractable, including a generative modeling use‑case.

By Nishanth Shetty, Saisuchith Mahajan, Chandra Sekhar Seelamantula
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arXiv Statistics ML
Oct 22

Generalised Robust Bayes for Joint Inference of Model and Contamination

The paper introduces H"older--Bayes, a robust generalised Bayesian framework that jointly infers model parameters and the proportion of contamination without specifying an outlier distribution. By applying the H"older divergence to a scaled model, each posterior draw identifies observations least compatible with the fitted model, and averaging these selections propagates uncertainty to outlier‑detection scores. The authors provide theoretical guarantees—including uniform boundedness of the posterior influence function, an $n^{-1/2}$ bound on posterior‑averaged excess risk, and a Bernstein–von Mises theorem—while also demonstrating practical performance through simulations and real‑data experiments.

By Masahiro Fujisawa, Masaki Adachi, Takuo Matsubara
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arXiv Machine Learning
Oct 19

ENFR: Evidence Networks with Flow-Matched References for Amortized Simulation-Based Model Inference

The paper introduces ENFR, a method for estimating the absolute evidence ζ of a data‑generating model in Bayesian inference. It learns Bayes factors relative to a flow‑matched reference and then recovers the absolute evidence, improving over existing flow‑based baselines across multiple applications. The authors also provide a joint architecture for estimating evidences of multiple models and demonstrate its performance and scalability on diverse scientific datasets.

By Kai Lehman, Jameson Dong, Carolina Cuesta-Lazaro, Niall Jeffrey, Benjamin D. Wandelt, Francisco Villaescusa-Navarro, Sven Krippendorf, Jochen Weller
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arXiv Machine Learning
Oct 7

ProximalFM: Amortized Proximal Causal Inference under Hidden Confounding

ProximalFM is a transformer‑based model that uses prior‑data fitted networks (PFNs) to perform Bayesian proximal causal inference under hidden confounding. By training on synthetic data generated from structural causal models with oracle counterfactuals, it amortizes the Bayesian operator inversion into a single forward pass, producing posterior estimates of the conditional average treatment effect (CATE). The approach consistently outperforms prior methods across various proximal regimes, especially when latent confounding is strong and proxy variables are weakly informative, and it requires no dataset‑specific tuning.

By Christophe Muller, Ayub Kharel, Alex Luedtke, Chan Park, Eric Tchetgen Tchetgen, Juan L. Gamella, Rahul Krishnan, Ricardo Silva, Jakob Zeitler
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