Mohammadreza Tavasoli Naeini

arXiv2026

BOLT: Universal Classifier Training via a Bayes-Error Upper Bound

This work introduces a novel approach to compute a universal upper bound on the Bayes error rate (BER) from classifier-output samples, which serves as a Bayes-error-related performance criterion for the underlying classification task. We show that the bound is tight in the binary case and characterize the max-sum gap that appears in the aggregate multiclass formulation. Based on this bound, we define a new loss function, called Bayes optimal learning threshold (BOLT), for training parameterized classifiers. For each data sample, the BOLT loss computes a term whose expectation upper-bounds the Bayes error, so that during training the model parameters can be updated toward minimizing this bound. Numerical experiments with both synthetic and real-world datasets show that, in the reported settings, BOLT training often attains lower held-out classification error than cross-entropy training.

cs.LG↗

arXiv2026

Revisiting GAN with Bayes-Optimal Discrimination

We propose an alternative to the standard GAN training approach, in which the discriminator is a binary classifier trained by cross-entropy to distinguish real samples from generated ones. Instead, we directly target the discrimination Bayes error rate (BER). To this end, we use the recently proposed Bayes optimal learning threshold (BOLT) loss and train the generator to maximize a surrogate of the discrimination BER. This viewpoint gives a unified perspective on GAN training: different objectives can be interpreted as parameterized bounds on the discrimination BER that describe a trade-off between smoothness and tightness. We show that, under balanced class priors, maximizing the surrogate BER with an unconstrained discriminator minimizes the total variation between the data and generator distributions. By constraining the discriminator to be $1$-Lipschitz, the proposed maximization objective defines a discrepancy that is upper-bounded by the Wasserstein-1 distance, thereby linking it to Wasserstein GAN. Experiments on several image-generation datasets under matched architectures and optimization settings show that GAN training using the surrogate BER improves sample quality and coverage over standard baselines. This analysis suggests that the proposed Bayesian viewpoint can achieve a better trade-off between training stability and convergence of the generator to the data distribution.

cs.LG↗