Neural Prior Estimation: Learning Class Priors from Latent Representations

Prior-data fitted networks (PFNs) have achieved exceptional performance on tabular classification tasks. However, like other classifiers, their performance can suffer under the effect of class imbalance, resulting in poor performance for rare classes. Several techniques exist which attempt to mitigate the deleterious effect of class imbalance on classification performance, but the in-context learning (ICL) dynamic of PFNs means that loss-based strategies are impossible, and other techniques are unproven. We have adapted several classical techniques addressing class imbalance and analyzed their performance on PFN classification. We observe that thresholding performs exceptionally well because of the calibration characteristics of PFNs, and downsampling performs comparably because of PFNs exceptional limited-data performance, with the additional benefit of reduced computation cost for inference.

Learning with class-conditional label noise often relies on a transition model from latent clean classes to observed annotations. Forward correction embeds this transition in the likelihood, yet finite-sample networks may still memorize corrupted labels. The corrected likelihood also induces a reverse posterior over the clean classes that could explain each annotation. When its leading class differs from the annotation, the model and transition matrix provide evidence against that annotation, but the leading alternatives can remain nearly tied. We introduce Selective Posterior Margin Regularization (SPMR), which preserves the Forward objective and converts this disagreement into a graded update on the clean classifier. SPMR selects the leading reverse-posterior class, scales a detached pairwise margin by the separation between the two leading posterior classes, and assigns correspondingly little influence to diffuse conflicts. The gap factorizes into transition- adjusted pairwise separation and the posterior mass carried by the leading pair. The active margin follows the locally minimum-norm logit direction that enlarges the selected pairwise margin. Across five known-transition benchmarks, SPMR improves full-length Forward by 2.5-7.0 percentage points and remains 0.7-2.5 percentage points above Forward with Mixup and early stopping. Matched interventions support distinct gains from the posterior-space coefficient, transition-adjusted target, and pairwise action. The same design transfers to estimated transitions, human annotations, architectural changes, and stronger Forward recipes. The formulation uses latent-class evidence already available inside Forward correction without promoting every posterior conflict to a corrected label.

Neural Posterior Estimation (NPE) fits an amortized conditional density estimator to a simulated training set of complete-data realizations. NPE's training objective, log-likelihood, favors posterior approximations that assign arbitrarily high density to the training points, and typical families of amortized conditional density estimators (e.g., normalizing flows, Gaussian encoders) are flexible enough to oblige. The resulting policy of extreme overconfidence translates poorly to held-out data. Early stopping and other regularizers can prevent this degeneracy, but they are limited to selecting posterior approximations along an unfavorable optimization trajectory set by in-sample residuals, where the posterior mean is underfit while the posterior variance is overfit. To avoid this trade-off, we propose Cross-Fitting NPE (CF-NPE), which uses sample splitting to separate conditional-mean estimation from the estimation of the posterior's higher moments. Using $K$-fold cross-fitting, CF-NPE fits $K$ posterior-mean regressors and then fits a conditional density estimator to the resulting out-of-fold residuals. In experiments with synthetic data and in a cosmological application, CF-NPE achieves higher held-out log-likelihood than standard NPE and typically improves calibration. CF-NPE is most useful in high-dimensional, simulation-limited settings.