Addressing misclassification costs in machine learning through asymmetric loss functions

Abstract

Patterning defect metrology requires data interpretation with classification, each well-suited to machine learning (ML). Defect classification however has notable misclassification costs; mislabeling a defect as nominal has greater impact than the converse. Though quantified costs are not publicly available, total economic misclassification cost (total cost) is optimized across orders-of-magnitude variation in cost ratio C and classification threshold 0.01 &lt; <i>τ</i> &lt; 0.99. Convolutional neural networks are trained using the intrinsically weighted and scaled asymmetric focal losses (AFL, sAFL) with hyperparameter γ with weighted and unweighted binary cross-entropy (wBCE, BCE) functions trained for comparisons. Optimal functions and conditions are identified for reducing total cost. For reproducibility, publicly available ML data sets are surrogates for industrial imaging data. For these data the sAFL mimimizes total cost at <i>τ</i> = 0.5, <i>C</i> ≥ 16. The AFL reduces total cost at 0.1 ≤ <i>τ</i> &lt; 0.5, <i>C</i> > 128. Asymmetric loss functions lower total cost versus wBCE by 15 % to 40 % for 0.2 &lt; <i>τ</i> &lt; 0.5, <i>C</i> &lt; 64. Total economic misclassification cost can be tailored using asymmetric focal losses. Estimations are presented to allow the extension of reported trends to industrial applications with strong class imbalances between defect-indicative and nominal-indicative data.