We often need to adjust a fitted $E[Y|X]$ so that the aggregate $E[Y]$ (or class totals) matches known targets (see here). In binary classification, a single logit shift (or a global temperature) is a monotone transform of the model scores, so if person A had a higher

Textbook bias–variance intuition implies that worst‑case test error should eventually rise as model capacity overtakes the sample size because the variance term in the bound grows while the bias term has already bottomed out (see Vapnik and Chervonenkis, 1971; Bartlett and Mendelson, 2002). Those worst‑case guarantees shrink

Modern applications—from ad platforms calibrating click-through predictions to polling systems incorporating responses to ML algorithms adapting fairness thresholds—share a common challenge: maintaining calibrated weights on live data streams. To address streaming data, we recast raking as a streaming convex optimization problem: minimize the squared error between current weighted

Gradient descent commits to a single direction at each step based on the local gradient. This myopic approach can be suboptimal when gradients are noisy, local geometry is misleading, or the loss landscape has multiple competing descent directions. The algorithm makes irrevocable decisions based on local information, potentially missing better