We introduce Conformal Interquantile Regression (CIR), a conformal regression method that efficiently constructs near-minimal prediction intervals with guaranteed coverage. CIR leverages black-box machine learning models to estimate outcome distributions through interquantile ranges, transforming these estimates into compact prediction intervals while achieving approximate conditional coverage. We further propose CIR+ (Conditional Interquantile Regression with More Comparison), which enhances CIR by incorporating a width-based selection rule for interquantile intervals. This refinement yields narrower prediction intervals while maintaining comparable coverage, though at the cost of slightly increased computational time. Both methods address key limitations of existing distributional conformal prediction approaches: they handle skewed distributions more effectively than Conformalized Quantile Regression, and they achieve substantially higher computational efficiency than Conformal Histogram Regression by eliminating the need for histogram construction. Extensive experiments on synthetic and real-world datasets demonstrate that our methods optimally balance predictive accuracy and computational efficiency compared to existing approaches.

We introduce Density-Sorted Prediction Set ( DSPS ), a novel method for uncertainty quantification in multi-target regression that uses conditional normalizing flows with conformal calibration. This approach constructs flexible, non-convex predictive regions with guaranteed coverage probabilities, overcoming limitations of traditional methods. By learning a transformation where the conditional distribution of responses follows a known form, DSPS identifies dense regions in the original space using the conditional probability density, which is computed via the Jacobian determinant and the latent density. This enables the creation of prediction regions that adapt to the true underlying distribution, focusing on areas of high probability density. Experimental results demonstrate that DSPS produces smaller, more informative prediction regions while maintaining robust coverage guarantees, enhancing uncertainty modeling in complex, high-dimensional settings.

Cybersecurity in safety-critical data communication infrastructures presents a significant and open challenge for cyber-physical systems (CPS). While extensive research exists on wireless jamming, effectively detecting attacks in noisy wireless environments remains difficult. This article introduces a novel framework for detecting mobile jamming attacks in LoRaWAN-based CPS, designed to operate robustly in the presence of communication faults. Unlike traditional methods that rely on physical-layer metrics like RSSI from end devices, our strategy uses only data upload statistics available at the backend network server. We propose a multi-stage filtering approach that first identifies anomalous upload failures and then distinguishes jamming attacks from communication faults by analyzing their distinct spatio-temporal signatures. Furthermore, the framework can reconstruct the attacker’s trajectory from the identified attack events. We evaluate the proposed strategy via extensive discrete-time simulations under various network densities and attacker speeds. Results demonstrate high efficacy, achieving an F1-score of up to 1.00 for event detection and a trajectory reconstruction mean absolute error (MAE) as low as 7.07 meters in dense networks, even in the presence of faults. This work’s primary contribution is a backend-centric, fault-tolerant detection methodology that enhances situational awareness without imposing additional overhead on resource-constrained end devices.

This article designs a blockchain protocol to mitigate the spread of misinformation in online social networks. The blockchain protocol processes social media postings as transactions, with misinformation being treated as double-spend attacks. The probability and duration for a double-spend attack to succeed within the blockchain protocol are used to compute the misinformation propagation time distribution. Our findings indicate that the rate of misinformation propagation in blockchain-based online social networks is inversely correlated with the fraction of honest miners who reject double-spend attacks. To further analyze the dynamics of misinformation propagation, we employ a susceptible–infectious–recovered (SIR) model combined with preferential attachment in a multicommunity network, which accounts for homophily and community structure in social networks. Numerical experiments using parameters estimated from real-world Twitter hashtag datasets show that the proposed blockchain protocol can reduce the number of users exposed to misinformation by delaying its propagation.

Traffic prediction is a cornerstone of intelligent transportation systems (ITSs). The effectiveness of existing spatiotemporal graph neural networks (STGNNs) heavily relies on the independent identically distributed (i.i.d.) assumption of traffic data, which is frequently violated in practice because of distribution shifts owing to exogenous factors. While learning features that remain stable across all environments is promising for modeling robust frameworks, the fundamental challenge involves the decomposition of invariant features from the dynamic nature of spatiotemporal dependencies. In this article, we propose the disentangled spatiotemporal (DIST) graph neural networks, a novel framework for robust traffic forecasting considering distribution shifts. In DIST, latent invariant variables are explicitly decoupled from dynamically evolving spatiotemporal dependencies, enabling the learning of topology-agnostic representations resilient to distribution shifts. Specifically, we formulate a causality-driven learning objective that guides the separation of invariant variables from various exogenous factors. We then propose a spatiotemporal graph modeling module that can adaptively capture spatiotemporal dependencies in evolving traffic systems. Furthermore, we present a graph perturbation module to simulate topology variations during training, thereby encouraging the model to identify perturbation-sensitive dependencies and infer invariant and variant features for prediction and intervention tasks. The prediction risk and its variance on multiple interventional distributions are minimized in our learning strategy, allowing the model to identify invariant features, thus improving its robustness. The results of comprehensive real-world experiments demonstrate the superiority of our approach. The source code is available: https://github.com/tingwang25/DIST.

Uncertainty quantification is essential in decision-making, especially when joint distributions of random variables are involved. While conformal prediction provides distribution-free prediction sets with valid coverage guarantees, it traditionally focuses on single predictions. This paper introduces novel conformal prediction methods for estimating the sum or average of unknown labels over specific index sets. We develop conformal prediction intervals for single target to the prediction interval for sum of multiple targets. Under permutation invariant assumptions, we prove the validity of our proposed method. We also apply our algorithms on class average estimation and path cost prediction tasks, and we show that our method outperforms existing conformalized approaches as well as non-conformal approaches.

This paper introduces Conformal Thresholded Intervals (CTI), a novel conformal regression method that aims to produce the smallest possible prediction set with guaranteed coverage. Unlike existing methods that rely on nested conformal frameworks and full conditional distribution estimation, CTI estimates the conditional probability density for a new response to fall into each interquantile interval using off-the-shelf multi-output quantile regression. By leveraging the inverse relationship between interval length and probability density, CTI constructs prediction sets by thresholding the estimated conditional interquantile intervals based on their length. The optimal threshold is determined using a calibration set to ensure marginal coverage, effectively balancing the trade-off between prediction set size and coverage. CTI's approach is computationally efficient and avoids the complexity of estimating the full conditional distribution. The method is theoretically grounded, with provable guarantees for marginal coverage and achieving the smallest prediction size given by Neyman-Pearson . Extensive experimental results demonstrate that CTI achieves superior performance compared to state-of-the-art conformal regression methods across various datasets, consistently producing smaller prediction sets while maintaining the desired coverage level. The proposed method offers a simple yet effective solution for reliable uncertainty quantification in regression tasks, making it an attractive choice for practitioners seeking accurate and efficient conformal prediction.

Graph Neural Networks (GNNs) has been widely used in a variety of fields because of their great potential in representing graph-structured data. However, lacking of rigorous uncertainty estimations limits their application in high-stakes. Conformal Prediction (CP) can produce statistically guaranteed uncertainty estimates by using the classifier's probability estimates to obtain prediction sets, which contains the true class with a user-specified probability. In this paper, we propose a Rank-based CP during training framework to GNNs (RCP-GNN) for reliable uncertainty estimates to enhance the trustworthiness of GNNs in the node classification scenario. By exploiting rank information of the classifier's outcome, prediction sets with desired coverage rate can be efficiently constructed. The strategy of CP during training with differentiable rank-based conformity loss function is further explored to adapt prediction sets according to network topology information. In this way, the composition of prediction sets can be guided by the goal of jointly reducing inefficiency and probability estimation errors. Extensive experiments on several real-world datasets show that our model achieves any pre-defined target marginal coverage while significantly reducing the inefficiency compared with state-of-the-art methods.

Predicting unknown transcription factor-target gene (TF-target gene) interactions based on gene regulatory networks (GRNs) is critical for understanding cellular functions and biological discovery. Existing computational methods focus on the statistic corelation and neglect the semantic information of biomedical knowledge. To address this, we propose BioLinkGPT, a novel framework that integrates the robust textual comprehension capabilities of Large Language Models (LLMs) with graph neural networks (GNNs) to capture structural information of GRN. BioLinkGPT leverages gene information and the known TF-target gene relationships from literature to predict unknown TF-target gene interactions and improve its performance via a two-stage instruction fine-tuning strategy. We construct a comprehensive GRN dataset focused on human infectious diseases, and experimental results show that BioLinkGPT significantly outperforms existing baselines in link prediction metrics. We validate the model's accurate identification of known regulatory relationships and find that BioLinkGPT successfully uncover potential regulatory interactions with high confidence and biological relevance. BioLinkGPT offers an efficient and precise computational tool to infer TF-target gene interactions, accelerating research on infectious disease mechanisms and drug target development.

Predicting gene regulatory relationship is crucial to reveal cancer mechanism and develop targeted therapies. However, current computational methods typically estimate gene-gene associations without regulatory directions and only based on statistical significance, often lacking accuracy after validation by biological experiments. Therefore, we introduce a pipeline named LiGRNet that constructs gene regulatory networks as signed directed graphs using large language models (LLMs) from the literature and predicts potential gene regulatory relationship with magnetic signed graph neural networks (MSGNNs). First, we teach LLM to extract the known gene regulatory relationships proved by biological experiments through prompt. Then, a signed directed graph was constructed and learnt by MSGNN with a link prediction framework based on complex-valued gene embeddings. The potential regulatory relationships were predicted with direction and sign. We apply our pipeline in colorectal cancer, liver cancer, and colorectal liver metastasis including$11,000,19,000$, and 1,300 literature, respectively. The pipeline achieve$84.5 \%, 80.7 \%, 93.3 \%$accuracy in predicting unknown gene regulatory relationship. External cell line data also provide evidence for the predicted gene regulation in these cancers.

Conformal prediction provides a robust framework for generating prediction sets with finite-sample coverage guarantees, independent of the underlying data distribution. However, existing methods typically rely on a single conformity score function, which can limit the efficiency and informativeness of the prediction sets. In this paper, we present a novel approach that enhances conformal prediction for multi-class classification by optimally averaging multiple conformity score functions. Our method involves assigning weights to different score functions and employing various data splitting strategies. Additionally, our approach bridges concepts from conformal prediction and model averaging, offering a more flexible and efficient tool for uncertainty quantification in classification tasks. We provide a comprehensive theoretical analysis grounded in Vapnik–Chervonenkis (VC) theory, establishing finite-sample coverage guarantees and demonstrating the efficiency of our method. Empirical evaluations on benchmark datasets show that our weighted averaging approach consistently outperforms single-score methods by producing smaller prediction sets without sacrificing coverage.

As deep learning models are increasingly deployed in high-risk applications, robust defenses against adversarial attacks and reliable performance guarantees become paramount. Moreover, accuracy alone does not provide sufficient assurance or reliable uncertainty estimates for these models. This study advances adversarial training by leveraging principles from Conformal Prediction. Specifically, we develop an adversarial attack method, termed OPSA (OPtimal Size Attack), designed to reduce the efficiency of conformal prediction at any significance level by maximizing model uncertainty without requiring coverage guarantees. Correspondingly, we introduce OPSA-AT (Adversarial Training), a defense strategy that integrates OPSA within a novel conformal training paradigm. Experimental evaluations demonstrate that our OPSA attack method induces greater uncertainty compared to baseline approaches for various defenses. Conversely, our OPSA-AT defensive model significantly enhances robustness not only against OPSA but also other adversarial attacks, and maintains reliable prediction. Our findings highlight the effectiveness of this integrated approach for developing trustworthy and resilient deep learning models for safety-critical domains. Our code is available at https://github.com/bjbbbb/Enhancing-Adversarial-Robustness-with-Conformal-Prediction.

Graph Neural Networks (GNNs) excel at modeling relational data but face significant challenges in high-stakes domains due to unquantified uncertainty. Conformal prediction (CP) offers statistical coverage guarantees, but existing methods often produce overly conservative prediction intervals that fail to account for graph heteroscedasticity and structural biases. While residual reweighting CP variants address some of these limitations, they neglect graph topology, cluster-specific uncertainties, and risk data leakage by reusing training sets. To address these issues, we propose Residual Reweighted GNN (RR-GNN), a framework designed to generate minimal prediction sets with provable marginal coverage guarantees. RR-GNN introduces three major innovations to enhance prediction performance. First, it employs Graph-Structured Mondrian CP to partition nodes or edges into communities based on topological features, ensuring cluster-conditional coverage that reflects heterogeneity. Second, it uses Residual-Adaptive Nonconformity Scores by training a secondary GNN on a held-out calibration set to estimate task-specific residuals, dynamically adjusting prediction intervals according to node or edge uncertainty. Third, it adopts a Cross-Training Protocol, which alternates the optimization of the primary GNN and the residual predictor to prevent information leakage while maintaining graph dependencies. We validate RR-GNN on 15 real-world graphs across diverse tasks, including node classification, regression, and edge weight prediction. Compared to CP baselines, RR-GNN achieves improved efficiency over state-of-the-art methods, with no loss of coverage.

Abstract This paper investigates the application of probabilistic prediction methodologies in route planning within a road network context. Specifically, we introduce the Conformalized Quantile Regression for Graph Autoencoders (CQR-GAE), which leverages the conformal prediction technique to offer a coverage guarantee, thus improving the reliability and robustness of our predictions. By incorporating uncertainty sets derived from CQR-GAE, we substantially improve the decision-making process in route planning under a robust optimization framework. We demonstrate the effectiveness of our approach by applying the CQR-GAE model to a real-world traffic scenario. The results indicate that our model significantly outperforms baseline methods, offering a promising avenue for advancing intelligent transportation systems.

This article proposes a method to detect change points in dynamic social networks using Fréchet statistics. We address two main questions: 1) what metric can quantify the distances between graph Laplacians in a dynamic network and enable efficient computation, and 2) how can the Fréchet statistics be extended to detect multiple change points while maintaining the significance level of the hypothesis test? Our solution defines a metric space for graph Laplacians using the log-Euclidean metric, enabling a closed-form formula for Fréchet mean and variance. We present a framework for change point detection using Fréchet statistics and extend it to multiple change points with binary segmentation. The proposed algorithm uses incremental computation for Fréchet mean and variance to improve efficiency and is validated on simulated and four real-world datasets, namely, the UCI message dataset, the SFHH interaction dataset, the stack overflow Q&A dataset, and the Enron email dataset.

This article introduces a novel mutual information-based measure to assess the glass ceiling effect in preferential attachment networks, which advances the analysis of inequalities in attributed networks. Using Shannon entropy and generalizing to Rényi entropy, our measure evaluates the conditional probability distributions of node attributes given the node degrees of adjacent nodes, which offers a more nuanced understanding of inequality compared to traditional methods that emphasize node degree distributions and degree assortativity alone. To evaluate the efficacy of the proposed measure, we evaluate it using an analytical structural inequality model as well as historical publication data. Results show that our mutual information measure aligns well with both the theoretical model and empirical data, underscoring its reliability as a robust approach for capturing inequalities in attributed networks. Moreover, we introduce a novel stochastic optimization algorithm that utilizes a parameterized conditional logit model for edge addition. Our algorithm is shown to outperform the baseline uniform distribution based approach in mitigating the glass ceiling effect. By strategically recommending links based on this algorithm, we can effectively hinder the glass ceiling effect within networks.

This article deals with the modeling and estimation of the sociological phenomena called echo chambers and segregation in social networks. Specifically, we present a novel community-based graph model that represents the emergence of segregated echo chambers as a Markov bridge (MB) process. An MB is a 1-D Markov random field that facilitates modeling the formation and disassociation of communities at deterministic times, which is important in social networks with known timed events. We justify the proposed model with real-world examples and examine its performance on a recent Twitter dataset. We provide a model parameter estimation algorithm based on maximum likelihood and a Bayesian filtering algorithm for recursively estimating the level of segregation using noisy samples obtained from the network. Numerical results indicate that the proposed filtering algorithm outperforms the conventional hidden Markov modeling in terms of the mean-squared error. The proposed filtering method is useful in computational social science where data-driven estimation of the level of segregation from noisy data is required.

This paper deals with the modeling and estimation of the sociological phenomena called segregation in social networks. Specifically, we present a novel community-based graph model that represent segregation as a Markov bridge process. A Markov bridge is a one-dimensional Markov random field that facilitates modeling the formation and disassociation of communities at deterministic times which is important in social networks with known timed events. Based on the proposed model, we provide Bayesian filtering algorithms for recursively estimating the level of segregation using noisy samples obtained from the graph. Numerical results indicate that the proposed filtering algorithm outperforms the conventional hidden Markov modeling in terms of the mean-squared error. The proposed filtering method is useful in computational social science where data-driven estimation of the level of segregation from noisy data is required.