Quantized Prediction Models: Output-Space Regularization for Stable and Interpretable Regression

We introduce Quantized Prediction Models (QPMs), a regression framework
that constrains predictions to a finite set of output levels. Unlike
traditional parameter-based regularization, QPMs regularize directly in
the \emph{output space} through supervised quantization, creating a
functional bottleneck that suppresses noise, improves stability, and
produces discrete, monotone predictors suited for governance-sensitive
domains.

QPMs employ an optimizer-driven binning procedure that concentrates
resolution around high-stakes decision thresholds while maintaining a
globally coherent, interpretable score ladder. To address distributional
drift, we propose an Anchored Calibration update that adjusts bin
representatives while keeping bin edges fixed, thereby guaranteeing
zero rank-order churn.

Theoretically, QPMs reduce local sensitivity, decrease variance, and
preserve monotonicity under anchored updates. Empirically, they match the
predictive performance of standard gradient boosting models while
delivering dramatically improved stability, offering a practical,
governance-aligned alternative for applications in which stability is as
critical as accuracy. The methods described are fully specified in the
text.