Between Resolution Collapse and Variance Inflation: Weighted Conformal Anomaly Detection in Low-Data Regimes

TL;DR

This paper introduces a weighted conformal anomaly detection method that balances local adaptation and stability in low-data regimes, improving detection power under distribution shifts.

Contribution

It proposes a continuous weighted kernel density estimation approach that relaxes finite-sample guarantees for better anomaly detection in non-stationary data.

Findings

Restores detection capabilities where standard methods fail

Outperforms baseline methods in statistical power

Maintains valid marginal error control

Abstract

Standard conformal anomaly detection provides marginal finite-sample guarantees under the assumption of exchangeability . However, real-world data often exhibit distribution shifts, necessitating a weighted conformal approach to adapt to local non-stationarity. We show that this adaptation induces a critical trade-off between the minimum attainable p-value and its stability. As importance weights localize to relevant calibration instances, the effective sample size decreases. This can render standard conformal p-values overly conservative for effective error control, while the smoothing technique used to mitigate this issue introduces conditional variance, potentially masking anomalies. We propose a continuous inference relaxation that resolves this dilemma by decoupling local adaptation from tail resolution via continuous weighted kernel density estimation. While relaxing finite-sample exactness to asymptotic validity, our method eliminates Monte Carlo variability and recovers the statistical power lost to discretization. Empirical evaluations confirm that our approach not only restores detection capabilities where discrete baselines yield zero discoveries, but outperforms standard methods in statistical power while maintaining valid marginal error control in practice.