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This paper is primarily about machine learning: it proposes a new training loss (BOLT) derived from a Bayes-error upper bound and benchmarks it against cross-entropy. The reported advantage is modest and limited to specific settings, so readers should treat the empirical gains as preliminary until independent replication on broader tasks and architectures appears. The theoretical contribution, a bound that is tight in the binary case, is the piece most worth evaluating for anyone working on classifier training objectives.
BOLT: Universal Classifier Training via a Bayes-Error Upper Bound
arXiv:2501.07754v2 Announce Type: replace Abstract: 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.
Abstract: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.
Machine Learning (cs.LG); Computer Vision and Pattern Recognition (cs.CV); Information Theory (cs.IT); Image and Video Processing (eess.IV); Signal Processing (eess.SP)
arXiv:2501.07754 [cs.LG]
(or arXiv:2501.07754v2 [cs.LG] for this version)
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