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Weighted Conformal Clustering

NeurIPS 2026 · Label-efficient and robust learning › Recognition and long-tail · approach: Learning from unlabeled and positive-unlabeled data · 0 citations (OpenAlex)

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Proposes weighted conformal clustering that treats synthetic cluster labels as a conditional label-distribution shift, correcting it with likelihood-ratio weights and an augmented calibration set, yielding valid cluster-label confidence sets with estimated weights.

Problem

Cluster assignments are hard and lack rigorous uncertainty measures; calibration labels produced by a data-dependent clustering algorithm break exchangeability, so existing split conformal clustering can undercover.

Approach

Reframe conformal clustering as conditional label-distribution shift and apply weighted conformal prediction with likelihood-ratio weights. An augmented calibration set (clustering fit once on calibration plus test covariate) removes leave-one-out refits, and the conditional label density is estimated from the training split, giving a coverage loss bounded by the total-variation estimation error.

Key results

• On R^50 GMM with spectral clustering, the proposed method stays valid and informative at the largest variances (sigma^2 in {2.3, 2.5}) where split CC becomes oversized.
• On MNIST with deep clustering and alpha=0.1, 45.3% of test confidence sets are singletons, 30.4% size 2, and 24.3% size 3+.
• Nonlinear moons and circles: the proposed method keeps informative set sizes over a wider range of sigma^2 than split CC while maintaining valid coverage.

Surprising findings

• Split conformal clustering becomes oversized and uninformative in high-dimensional spectral clustering at large variance, where the augmented method remains informative.

Limitations

• Coverage with estimated weights holds only up to a total-variation estimation error term, which need not vanish under misspecification or with hard clustering such as k-means.
• Theory assumes i.i.d. covariates and a stochastic (soft) clustering algorithm; hard clustering cannot consistently recover the conditional label law.

Experimental setup

Datasets: MNIST synthetic Gaussian mixtures synthetic three moons synthetic concentric circles

Benchmarks: MNIST synthetic GMM (R^2, R^50) synthetic moons synthetic circles

Metrics: empirical coverage average confidence set size

Baselines: split conformal clustering (CC) naive cutoff method

Builds on: split conformal clustering weighted conformal prediction generalized inverse quantile conformity score full conformal prediction under arbitrary joint distributions

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