Anytime-Valid Confirmation of Covariate Balance for Prespecified Corrections

Many covariate-shift adaptation methods construct a correction $w(x)$, but users must still determine whether the corrected distribution is sufficiently balanced for the target stream.

We study anytime-valid confirmation of prespecified corrections from sequential unlabeled target inputs.

Our primary contribution is a procedure for confirming covariate balance.

For a prespecified class of balancing functions and tolerances, time-uniform confidence sequences permit continuous monitoring and data-dependent stopping once all plausible target moments lie within their tolerance bands.

If the correction is out of tolerance for at least one function, the probability of ever incorrectly confirming balance is at most the prescribed level.

Upon stopping, the procedure yields a certificate local to the chosen functions and tolerances, yet providing an absolute downstream-adequacy statement that ordinary shift diagnostics generally do not.

With finite source data, contracted bands preserve this guarantee while accounting for uncertainty in weighted source moments, whereas expanded bands support only compatibility diagnostics.

As complementary information, we study a source-calibrated likelihood-ratio e-process whose KL-drift identity characterizes correction directions relative to the source.

Under the source-reference distribution, the probability of ever crossing its evidence threshold is controlled, but crossing does not confirm balance.

We also give an exponential-tilt test for departures beyond an acceptable correction region and deploy balance-confirmed corrections in weighted conformal prediction.

Experiments illustrate false-confirmation control, locality to the balancing-function class, KL-drift diagnostics, acceptable-region monitoring, finite-source effects, and downstream conformal coverage under covariate shift.