Calibration Is Grouping: VR-SAG with Intra-Group Variance Control and Logit-Cluster Evaluation

Accurate click-through and conversion-rate estimates are pivotal for bid optimization in large-scale advertising, yet modern deep CTR/CVR models are often miscalibrated. Classical global calibrators (Platt scaling, isotonic regression) and feature-based binning struggle to capture latent user-item heterogeneity. We approach calibration through the lens of latent, calibration-aware groupings and propose Variance-Reduced Semantic-Aware Grouping (VR-SAG), a lightweight post-hoc layer over a frozen backbone that (i) learns calibration-aware groups in embedding space, (ii) fits per-group temperature+bias calibrators, and (iii) explicitly penalizes intra-group variance to tighten probability spreads. A group-wise decomposition of the Brier score guides our design. It separates within-group variance from score–label covariance and motivates a grouping regularizer. To decouple evaluation from training, we introduce Logit-Cluster Calibration Error (LCCE), an unsupervised fixed-partition metric obtained via $K$-means in logit space; LCCE aligns with the reliability term of proper scores while avoiding pitfalls of trainable grouping heads used as metrics. Across offline CTR logs and AdAuction (an ad-auction dataset with simulator-defined oracle CTRs), VR-SAG improves the reported calibration metrics over the corresponding SAG variants. Its additional computation scales linearly with the number of grouping heads and groups.