Unsupervised Conformal Novelty Detection for Hierarchical Data

Thu, 01 Jan 2026 00:00:00 +0000

Abstract

Electric vehicle (EV) battery packs exhibit a natural pack–module–cell hierarchy, which induces dependence among measurements within the same module. Such hierarchical dependence poses challenges for the direct application of conventional novelty detection methods. To address these challenges, we develop conformal e-value procedures for hierarchical novelty detection, with the goal of controlling the false discovery rate (FDR) at both the group and unit levels. We combine hierarchical conformal score construction with eBH and U-eBH multiple testing procedures, and consider split conformal, full conformal, and group-wise conformal regimes. The proposed methods are evaluated through simulation studies and an analysis of EV battery pack data, where they provide empirical FDR control and detect localized module- and cell-level irregularities.

Type

Preprint

Publication

To be submitted to Journal of the Korean Statistical Society (JKSS, SCIE)

Keywords

novelty detection · hierarchical structure · conformal inference · false discovery rate · multiple testing

Motivation

Real-world industrial data — such as EV battery manufacturing — presents three compounding challenges that standard anomaly detection cannot handle jointly:

Hierarchical dependence: Cells within the same module share a common group effect, violating the IID assumption of most methods.
No anomaly labels: Ground-truth defect labels are expensive or infeasible to obtain in manufacturing, ruling out supervised approaches.
Multiple comparisons: Simultaneously testing hundreds of units inflates false discoveries without a principled error-control mechanism.

Method Overview

We frame hierarchical novelty detection as a multiple hypothesis testing problem at two levels simultaneously:

Group-level (HC-GND) — Does a test module contain any anomalous cells?
Unit-level (HC-UND) — Which specific cells within each module are anomalous?

Feature extraction: Charging voltage time series are treated as functional observations. Functional PCA (FPCA) projects each cell’s charging curve onto a low-dimensional score vector, placing cells from all packs on a common feature space.

Preprocessed charging voltage curves for all cells in the six test packs. Normal packs (blue) show regular charging behavior; Abnormal packs 4 and 5 (red) exhibit irregular patterns that are difficult to distinguish visually at the pack level.

Two-dimensional FPCA score vectors under the split conformal regime. Normal reference packs (black) form a tight cluster, while abnormal test packs (red) appear in a distinct region, validating FPCA as a discriminative feature extraction step.

Nonconformity score: For each cell, we compute a Mahalanobis-distance-based nonconformity score relative to a robust trimmed-mean group center. This naturally respects within-group dependence.

Multiple testing: Scores are converted to conformal e-values — non-negative statistics satisfying E[e] ≤ 1 under the null — and tested jointly via the eBH / U-eBH procedure, guaranteeing FDR control under minimal distributional assumptions.

We implement three conformal regimes with different data-efficiency / robustness trade-offs:

Regime	Training data	Contamination risk	Theoretical FDR guarantee
HSC (Split)	Reference only	None	✓ Both levels
HFC (Full)	Reference + all test	Higher	✓ Group level
HGC (Group-wise)	Reference + one test group	Moderate	✓ Group level

Results

Simulation Study

HC-GND simulation results. Empirical FDR (top) and power (bottom) under varying outlier proportions (left) and signal strengths (right). All three regimes maintain FDR below the target α = 0.1. HFC and HGC achieve higher power than HSC, especially at low outlier proportions, by exploiting more calibration data.

HC-UND vs. non-hierarchical baselines. The proposed hierarchical methods (HSC, HFC, HGC) consistently outperform non-hierarchical counterparts (SC, FC, AdaDetect) in power while maintaining empirical FDR control. Unit-level anomalies that are subtle in the pooled population become detectable within their own group context.

Key findings across 1,000 simulation replicates (α = 0.1):

Empirical FDR remains at or below the target level across all outlier proportions and signal strengths.
At weak signal, power reaches ~40%; as signal increases, power approaches 100%.
Hierarchical methods outperform non-hierarchical baselines by leveraging within-group structure.

EV Battery Pack Application

Pack-wise detection results (α = 0.1). Left three columns: hierarchical HC-GND/HC-UND results (yellow = module rejection, red = cell rejection). Right three columns: non-hierarchical baselines (SVM, Isolation Forest, AdaDetect). The proposed methods identify localized irregularities in Abnormal Pack 5 across multiple modules and cells that non-hierarchical methods largely miss.

The proposed procedures detect localized module- and cell-level irregularities not captured by pack-level labels.
Non-hierarchical baselines concentrate false detections on Normal Pack 0 and miss structured signals in Abnormal Pack 5.
Results provide an additional diagnostic layer when only coarse pack-level labels are available.