Research map / Label-efficient and robust learning / Recognition and long-tail

From Matrix Inversion to Constraints: Provably Tighter Confidence Regions for Importance Weights in Label Shift

NeurIPS 2026 · Label-efficient and robust learning › Recognition and long-tail · approach: Confidence calibration objectives · 0 citations (OpenAlex)

Read the paperCheck your idea against 108,967 papers

AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.

Proposes MaC-LP, a matrix-constraint plus linear-programming confidence region for label-shift importance weights that is provably tighter than interval Gaussian elimination while keeping finite-sample validity, and shows smaller weighted conformal prediction sets.

Problem

Finite-sample uncertainty quantification for importance weights under label shift; existing interval Gaussian elimination confidence regions are overly conservative, and asymptotic MLE-based intervals are unreliable in small samples.

Approach

Replace inversion of interval-valued confusion-matrix systems with a convex polytope defined by linear inequalities (overline C w >= underline q, underline C w <= overline q, w >= 0) obtained from elementwise binomial confidence intervals, and compute axis-aligned bounds per weight via 2K linear programs.

Key results

• On N24News, LP marginal intervals are consistently shorter than GE intervals across all 56 label-shift settings, with statistically significant log2 length ratios (t-test).
• The full MaC region Omega has volume only a small fraction of Omega_LP across shift intensities and sample sizes.
• Omega maintains empirical coverage above the nominal 90% in weighted conformal prediction and yields prediction sets closer to the oracle than Omega_LP and Omega_GE; on nuImages the point estimate undercovers.

Surprising findings

• The point estimate from BBSE can produce smaller prediction sets, but only because it undercovers under extreme shifts.

Limitations

• Region conservativeness: the full MaC region Omega is only valid with union-bound-based elementwise intervals, and Omega_LP and Omega_GE can be overly conservative.
• Scalability to large numbers of classes is not addressed; hierarchical decomposition is left to future work.
• On nuImages the label shift assumption may be violated, and even true weights undercover.

Experimental setup

Datasets: AGNews MNIST CIFAR-10 N24News nuImages

Benchmarks: AGNews MNIST CIFAR-10 N24News nuImages

Metrics: confidence interval length ratio (log2) volume ratio empirical coverage average prediction set size

Baselines: BBSE point estimate interval Gaussian elimination confidence region (Omega_GE) oracle importance weights

Builds on: black box shift estimation regularized learning under label shift weighted conformal prediction interval Gaussian elimination Clopper-Pearson interval

Closest papers by meaning

• Pseudo-Labeling for Unsupervised Domain Adaptation with Kernel GLMs (NeurIPS 2026 · similarity 0.86)
• Test-Time Domain Adaptation by Learning Domain-Aware Batch Normalization (AAAI 2024 · similarity 0.85)
• Theoretical Performance Guarantees for Partial Domain Adaptation via Partial Optimal Transport (ICML 2025 · similarity 0.85)
• Revisiting the Domain Shift and Sample Uncertainty in Multi-source Active Domain Transfer (CVPR 2024 · similarity 0.85)
• Pseudo-Calibration: Improving Predictive Uncertainty Estimation in Unsupervised Domain Adaptation (ICML 2024 · similarity 0.85)
• Importance Sampling for Nonlinear Models (ICML 2025 · similarity 0.84)