The paper investigates how well Prior-Data Fitted Networks (PFNs) approximate Bayesian posterior predictive distributions (PPDs). By decomposing deployment error into prior, context, and amortization components, the authors find that PFNs generally recover the target PPD accurately, but residual amortization errors remain in rare settings, leading to disagreement among independently pretrained models. They demonstrate that Bayesian model averaging can consistently reduce this uncertainty and improve predictions, even matching full-size TabICLv2 models.
arXiv:2601. 07944v2 Announce Type: replace-cross Abstract: Since the turn of the century, approximate Bayesian inference has steadily evolved as new computational techniques have been incorporated to handle increasingly complex, large-scale predictive problems.
SelectPFN is a prior‑data‑fitted network that jointly performs Bayesian variable selection and prediction for sparse nonlinear regression. In a single forward pass it outputs posterior inclusion probabilities for each variable and makes predictions using only sampled subsets, ensuring excluded variables cannot influence the result. The method achieves exact finite‑sample false discovery rate control via column‑permutation equivariance and knockoff statistics, and outperforms lasso, BART, DART, LassoNet, and other sparse neural networks on synthetic and real data with up to 500 predictors.
The paper introduces Amortized Factor Inference Networks (AFINs), a single inference network that can generalize across varying priors, likelihoods, latent dimensions, and observation counts. AFINs represent a model as a list of typed prior and likelihood factors and use an encode–merge–decode architecture to produce a Gaussian posterior approximation, with learned parameters independent of latent dimensionality or observation count. Experiments on synthetic and real datasets demonstrate that a single trained AFIN achieves competitive posterior approximations at significantly lower test‑time cost than NUTS and per‑task variational inference, with optional importance sampling further improving accuracy.
arXiv:2609.38902v1 Announce Type: cross Abstract: Augmenting small concurrent studies with external or historical cohorts is attractive in drug development, where enrollment is slow, follow-up is exp...
arXiv:2609.24422v1 Announce Type: new Abstract: Hierarchical data is ubiquitous in the empirical sciences and is most commonly analyzed with generalized linear mixed-effects models (GLMMs). Bayesian...
Hierarchical data is ubiquitous in the empirical sciences and is most commonly analyzed with generalized linear mixed-effects models (GLMMs). Bayesian inference for GLMMs yields calibrated uncertainty...
arXiv:2512. 22999v2 Announce Type: replace-cross Abstract: We consider problems of parameter estimation where design variables can be actively optimized to maximize information gain.
arXiv:2603. 12037v2 Announce Type: replace Abstract: Foundation models based on prior-data fitted networks (PFNs) have shown strong empirical performance in causal inference by framing the task as an in-context learning problem.
arXiv:2609.39525v1 Announce Type: new Abstract: Casting Bayesian inference as a neural network optimization problem targeting an amortized posterior is attractive, as it extends to otherwise intracta...
We develop a general method for amortized Bayesian inference on multilevel models of arbitrary structure. Given a generative model specified as a directed acyclic graph, our method automatically deriv...
arXiv:2610.18945v1 Announce Type: cross Abstract: Amortized Bayesian inference uses simulations to perform Bayesian estimation when likelihoods are expensive or analytically unavailable. However, lea...
arXiv:2609.40024v1 Announce Type: new Abstract: We develop a general method for amortized Bayesian inference on multilevel models of arbitrary structure. Given a generative model specified as a direc...