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

2025-12-04

AI Summary

In biochemical molecular structure classification, high asymmetry in misclassification costs and limited sample sizes pose significant challenges. Method: This paper proposes the first tensor-based Neyman–Pearson (NP) classification framework with rigorous finite-sample control of Type I error. It extends the NP paradigm to high-dimensional tensor data by integrating tensor discriminant analysis with deep learning, grounded in a tensor normal mixture model. Key innovations include discriminative iterative projection estimation, Tucker low-rank manifold modeling, and an NP umbrella calibration technique. Contribution/Results: The framework guarantees exact Type I error control at the prespecified level—without inflation—while substantially suppressing Type II error. Experiments on four biochemical datasets demonstrate stable adherence to the target Type I error bound and significantly lower Type II error compared to state-of-the-art baselines, thereby enhancing reliability in high-stakes decision-making.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Natural Language Processing: Learning & Optimization for NLP
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems

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.

Problem

• Control type I error in tensor classification
• Handle asymmetric error consequences in biochemical discovery
• Develop reliable classifiers for complex molecular tensors

Innovation

• Tensor Neyman-Pearson classification for error control
• Discriminant Tensor Iterative Projection estimator
• Tensor-NP Neural Classifier with deep learning calibration