Tensor Neyman-Pearson Classification: Theory, Algorithms, and Error Control

TL;DR

This paper introduces a novel Tensor Neyman-Pearson classification framework that guarantees finite-sample control of type I error in tensor data, with applications to biochemical molecular structure classification.

Contribution

It develops the first Tensor-NP classification method with finite-sample error control, combining tensor geometry analysis, a new estimator, and deep learning techniques for multiway data.

Findings

Maintains type I error at preset levels across datasets

Achieves competitive type II error performance

Provides reliable asymmetric-risk decision tools in biochemistry

Abstract

Biochemical discovery increasingly relies on classifying molecular structures when the consequences of different errors are highly asymmetric. In mutagenicity and carcinogenicity, misclassifying a harmful compound as benign can trigger substantial scientific, regulatory, and health risks, whereas false alarms primarily increase laboratory workload. Modern representations transform molecular graphs into persistence image tensors that preserve multiscale geometric and topological structure, yet existing tensor classifiers and deep tensor neural networks provide no finite-sample guarantees on type I error and often exhibit severe error inflation in practice. We develop the first Tensor Neyman-Pearson (Tensor-NP) classification framework that achieves finite-sample control of type I error while exploiting the multi-mode structure of tensor data. Under a tensor-normal mixture model, we derive the oracle NP discriminant, characterize its Tucker low-rank manifold geometry, and establish tensor-specific margin and conditional detection conditions enabling high-probability bounds on excess type II error. We further propose a Discriminant Tensor Iterative Projection estimator and a Tensor-NP Neural Classifier combining deep learning with Tensor-NP umbrella calibration, yielding the first distribution-free NP-valid methods for multiway data. Across four biochemical datasets, Tensor-NP classifiers maintain type I errors at prespecified levels while delivering competitive type II error performance, providing reliable tools for asymmetric-risk decisions with complex molecular tensors.