arXiv subjects

Zheshi Zheng

Publications and source records attributed to Zheshi Zheng.

6 recordsLinked to original sources

arXiv2026

Dual-Channel Tensor Neural Networks: Finite-Sample Theory and Conformal Structure Selection

Tensor-valued data arise naturally in neuroimaging, genomics, climate science, and spatiotemporal networks, where multilinear dependencies across modes carry information that is destroyed under vectorization. Existing approaches either impose a single low-rank structure, which can miss localized signal, or treat the tensor as a long vector, which discards its multiway geometry. We propose a *Dual-Channel Tensor Neural Network* (DC-TNN) that decomposes each tensor input into a low-rank core and a sparse refinement, and processes the two components through coupled neural channels. The framework is structure-agnostic and accommodates CP, Tucker, and tensor-train cores within a single architecture. For estimation, we establish non-asymptotic risk bounds for the DC-TNN estimator that decompose into network approximation, core estimation, and refinement-selection terms, and show that the effective dimension is determined jointly by the core rank and refinement sparsity rather than by the ambient tensor size. For inference, we develop a *structure-aware conformal ROC* procedure that calibrates within the core-refinement latent space and produces ROC and AUC confidence bands with finite-sample, distribution-free coverage. Building on this, we propose a *conformal structure selector* that, to our knowledge, is the *first distribution-free procedure* for choosing among candidate tensor decompositions with finite-sample validity. Simulations and an analysis of a protein dataset demonstrate competitive predictive accuracy, reliable uncertainty quantification, and consistent recovery of the tensor structure.

stat.ML↗

arXiv2025

Post-2024 U.S. Presidential Election Analysis of Election and Poll Data: Real-life Validation of Prediction via Small Area Estimation and Uncertainty Quantification

We carry out a post-election analysis of the 2024 U.S. Presidential Election (USPE) using a prediction model derived from the Small Area Estimation (SAE) methodology. With pollster data obtained one week prior to the election day, retrospectively, our SAE-based prediction model can perfectly predict the Electoral College election results in all 44 states where polling data were available. In addition to such desirable prediction accuracy, we introduce the probability of incorrect prediction (PoIP) to rigorously analyze prediction uncertainty. Since the standard bootstrap method appears inadequate for estimating PoIP, we propose a conformal inference method that yields reliable uncertainty quantification. We further investigate potential pollster biases by the means of sensitivity analyses and conclude that swing states are particularly vulnerable to polling bias in the prediction of the 2024 USPE.

stat.AP↗

arXiv2024

Conditional Prediction ROC Bands for Graph Classification

Graph classification in medical imaging and drug discovery requires accuracy and robust uncertainty quantification. To address this need, we introduce Conditional Prediction ROC (CP-ROC) bands, offering uncertainty quantification for ROC curves and robustness to distributional shifts in test data. Although developed for Tensorized Graph Neural Networks (TGNNs), CP-ROC is adaptable to general Graph Neural Networks (GNNs) and other machine learning models. We establish statistically guaranteed coverage for CP-ROC under a local exchangeability condition. This addresses uncertainty challenges for ROC curves under non-iid setting, ensuring reliability when test graph distributions differ from training data. Empirically, to establish local exchangeability for TGNNs, we introduce a data-driven approach to construct local calibration sets for graphs. Comprehensive evaluations show that CP-ROC significantly improves prediction reliability across diverse tasks. This method enhances uncertainty quantification efficiency and reliability for ROC curves, proving valuable for real-world applications with non-iid objects.

cs.LG↗

arXiv2024

Conditional Uncertainty Quantification for Tensorized Topological Neural Networks

Graph Neural Networks (GNNs) have become the de facto standard for analyzing graph-structured data, leveraging message-passing techniques to capture both structural and node feature information. However, recent studies have raised concerns about the statistical reliability of uncertainty estimates produced by GNNs. This paper addresses this crucial challenge by introducing a novel technique for quantifying uncertainty in non-exchangeable graph-structured data, while simultaneously reducing the size of label prediction sets in graph classification tasks. We propose Conformalized Tensor-based Topological Neural Networks (CF-T2NN), a new approach for rigorous prediction inference over graphs. CF-T2NN employs tensor decomposition and topological knowledge learning to navigate and interpret the inherent uncertainty in decision-making processes. This method enables a more nuanced understanding and handling of prediction uncertainties, enhancing the reliability and interpretability of neural network outcomes. Our empirical validation, conducted across 10 real-world datasets, demonstrates the superiority of CF-T2NN over a wide array of state-of-the-art methods on various graph benchmarks. This work not only enhances the GNN framework with robust uncertainty quantification capabilities but also sets a new standard for reliability and precision in graph-structured data analysis.

cs.LG↗

arXiv2024

Quantifying Uncertainty in Classification Performance: ROC Confidence Bands Using Conformal Prediction

To evaluate a classification algorithm, it is common practice to plot the ROC curve using test data. However, the inherent randomness in the test data can undermine our confidence in the conclusions drawn from the ROC curve, necessitating uncertainty quantification. In this article, we propose an algorithm to construct confidence bands for the ROC curve, quantifying the uncertainty of classification on the test data in terms of sensitivity and specificity. The algorithm is based on a procedure called conformal prediction, which constructs individualized confidence intervals for the test set and the confidence bands for the ROC curve can be obtained by combining the individualized intervals together. Furthermore, we address both scenarios where the test data are either iid or non-iid relative to the observed data set and propose distinct algorithms for each case with valid coverage probability. The proposed method is validated through both theoretical results and numerical experiments.

stat.ME↗

arXiv2020

Homeostasis phenomenon in predictive inference when using a wrong learning model: a tale of random split of data into training and test sets

This note uses a conformal prediction procedure to provide further support on several points discussed by Professor Efron (Efron, 2020) concerning prediction, estimation and IID assumption. It aims to convey the following messages: (1) Under the IID (e.g., random split of training and testing data sets) assumption, prediction is indeed an easier task than estimation, since prediction has a 'homeostasis property' in this case -- Even if the model used for learning is completely wrong, the prediction results maintain valid. (2) If the IID assumption is violated (e.g., a targeted prediction on specific individuals), the homeostasis property is often disrupted and the prediction results under a wrong model are usually invalid. (3) Better model estimation typically leads to more accurate prediction in both IID and non-IID cases. Good modeling and estimation practices are important and, in many times, crucial for obtaining good prediction results. The discussion also provides one explanation why the deep learning method works so well in academic exercises (with experiments set up by randomly splitting the entire data into training and testing data sets), but fails to deliver many `killer applications' in real world applications.

math.ST↗