Data Perturbation Research Articles

Structural Stability of Pseudo-Parabolic Equations for Basic Data

This article investigates the spatial decay properties and continuous dependence on the basic geometric structure. Assuming that the total potential energy is bounded and the homogeneous Dirichlet condition is satisfied on the side of the solution within the cylindrical domain, we establish an auxiliary function related to the solution. By extending the data at the finite end forward, we can establish the continuous dependence on the perturbation of base data.

Embedded feature selection for robust probability learning machines

Methods:Feature selection is essential for building effective machine learning models in binary classification. Eliminating unnecessary features can reduce the risk of overfitting and improve classification performance. Moreover, the data we handle typically contains a stochastic component, making it important to develop robust models that are insensitive to data perturbations. Although there are numerous methods and tools for feature selection, relatively few studies address embedded feature selection within robust classification models using penalization techniques. Objective:In this work, we introduce robust classifiers with integrated feature selection capabilities, utilizing probability machines based on different penalization techniques, such as the ℓ1-norm or the elastic-net, combined with a novel Direct Feature Elimination process to improve model resilience and efficiency. Findings:Numerical experiments on standard datasets demonstrate the effectiveness and robustness of the proposed models in classification tasks even when using a reduced number of features. These experiments were evaluated using original performance indicators, highlighting the models’ ability to maintain high performance with fewer features. Novelty:The study discusses the trade-offs involved in combining different penalties to select the most relevant features while minimizing empirical risk. In particular, the integration of elastic-net and ℓ1-norm penalties within a unified framework, combined with the original Direct Feature Elimination approach, presents a novel method for improving both model accuracy and robustness.

A spatial hierarchical network learning framework for drug repositioning allowing interpretation from macro to micro scale

Biomedical network learning offers fresh prospects for expediting drug repositioning. However, traditional network architectures struggle to quantify the relationship between micro-scale drug spatial structures and corresponding macro-scale biomedical networks, limiting their ability to capture key pharmacological properties and complex biomedical information crucial for drug screening and therapeutic discovery. Moreover, challenges such as difficulty in capturing long-range dependencies hinder current network-based approaches. To address these limitations, we introduce the Spatial Hierarchical Network, modeling molecular 3D structures and biological associations into a unified network. We propose an end-to-end framework, SpHN-VDA, integrating spatial hierarchical information through triple attention mechanisms to enhance machine understanding of molecular functionality and improve the accuracy of virus-drug association identification. SpHN-VDA outperforms leading models across three datasets, particularly excelling in out-of-distribution and cold-start scenarios. It also exhibits enhanced robustness against data perturbation, ranging from 20% to 40%. It accurately identifies critical motifs for binding sites, even without protein residue annotations. Leveraging reliability of SpHN-VDA, we have identified 25 potential candidate drugs through gene expression analysis and CMap. Molecular docking experiments with the SARS-CoV-2 spike protein further corroborate the predictions. This research highlights the broad potential of SpHN-VDA to enhance drug repositioning and identify effective treatments for various diseases.

DMHANT: DropMessage Hypergraph Attention Network for Information Propagation Prediction.

Predicting propagation cascades is crucial for understanding information propagation in social networks. Existing methods always focus on structure or order of infected users in a single cascade sequence, ignoring the global dependencies of cascades and users, which is insufficient to characterize their dynamic interaction preferences. Moreover, existing methods are poor at addressing the problem of model robustness. To address these issues, we propose a predication model named DropMessage Hypergraph Attention Networks, which constructs a hypergraph based on the cascade sequence. Specifically, to dynamically obtain user preferences, we divide the diffusion hypergraph into multiple subgraphs according to the time stamps, develop hypergraph attention networks to explicitly learn complete interactions, and adopt a gated fusion strategy to connect them for user cascade prediction. In addition, a new drop immediately method DropMessage is added to increase the robustness of the model. Experimental results on three real-world datasets indicate that proposed model significantly outperforms the most advanced information propagation prediction model in both MAP@k and Hits@K metrics, and the experiment also proves that the model achieves more significant prediction performance than the existing model under data perturbation.

Data augmentation in human-centric vision

AbstractThis survey presents a comprehensive analysis of data augmentation techniques in human-centric vision tasks, a first of its kind in the field. It delves into a wide range of research areas including person ReID, human parsing, human pose estimation, and pedestrian detection, addressing the significant challenges posed by overfitting and limited training data in these domains. Our work categorizes data augmentation methods into two main types: data generation and data perturbation. Data generation covers techniques like graphic engine-based generation, generative model-based generation, and data recombination, while data perturbation is divided into image-level and human-level perturbations. Each method is tailored to the unique requirements of human-centric tasks, with some applicable across multiple areas. Our contributions include an extensive literature review, providing deep insights into the influence of these augmentation techniques in human-centric vision and highlighting the nuances of each method. We also discuss open issues and future directions, such as the integration of advanced generative models like Latent Diffusion Models, for creating more realistic and diverse training data. This survey not only encapsulates the current state of data augmentation in human-centric vision but also charts a course for future research, aiming to develop more robust, accurate, and efficient human-centric vision systems.

Primal characterizations of stability of error bounds for semi-infinite convex constraint systems in Banach spaces

This article focuses on the stability of error bounds, both local and global, for semi-infinite convex constraint systems in Banach spaces. We present primal characterizations of the stability of these error bounds under small perturbations. These characterizations are expressed through the directional derivatives of the functions that define the systems. It is shown that ensuring stability of the error bounds is closely tied to verifying that the optimal values of several minimax problems, formulated using the directional derivatives, remain outside a certain neighbourhood of zero. Furthermore, this stability condition only requires that all component functions of the system share the same linear perturbation. When applied to the sensitivity analysis of Hoffman's constants for semi-infinite linear systems, these stability results yield primal criteria that guarantee the uniform boundedness of Hoffman's constants under perturbations in the problem data.

Perturbational duality in optimization under evenly convex assumptions

In this paper, we consider an optimization problem which is embedded into a family of perturbed problems. We associate with it the classical conjugate dual problem and a surrogate dual problem called quasi-dual. For these two pairs of primal–dual problems, we provide necessary and sufficient conditions for zero duality gap, strong duality and converse duality, under evenly convex assumptions involving appropriate sets associated to the data perturbation function. To this aim, we firstly establish some new results for evenly convex and evenly quasiconvex functions. We conclude by applying our results to two remarkable instances of optimization problems.

Diagnostic analystics in the Bayesian vector autoregressive model

The vector autoregressive model is extensively employed in macroeconomics, finance, and the natural sciences. However, it often encounters the issue of over-parametrization, resulting in undesirable behavior within the model. In this paper, we utilize the Bayesian vector autoregressive model as a tool to tackle this problem. Additionally, we employ the Bayesian local influence method to detect possible extreme observations under the model. We use posterior inference to estimate related parameters and construct Bayesian perturbation schemes for priors, variance, and data perturbations. Bayesian local influence is conducted based on three objective functions: Bayes factor, ϕ divergence, and posterior mean. To demonstrate the effectiveness of the diagnostics, we conduct numerical simulations. In the real data example, we use US inflation, unemployment, and interest rate data to verify this method's effectiveness.

FINEST: Stabilizing Recommendations by Rank-Preserving Fine-Tuning

Modern recommender systems may output considerably different recommendations due to small perturbations in the training data. Changes in the data from a single user will alter the recommendations as well as the recommendations of other users. In applications like healthcare, housing, and finance, this sensitivity can have adverse effects on user experience. We propose a method to stabilize a given recommender system against such perturbations. This is a challenging task due to (1) the lack of a “reference” rank list that can be used to anchor the outputs; and (2) the computational challenges in ensuring the stability of rank lists with respect to all possible perturbations of training data. Our method, FINEST, overcomes these challenges by obtaining reference rank lists from a given recommendation model and then fine-tuning the model under simulated perturbation scenarios with rank-preserving regularization on sampled items. Our experiments on real-world datasets demonstrate that FINEST can ensure that recommender models output stable recommendations under a wide range of different perturbations without compromising next-item prediction accuracy.

Rational Polynomial Coefficient Estimation via Adaptive Sparse PCA-Based Method

The Rational Function Model (RFM) is composed of numerous highly correlated Rational Polynomial Coefficients (RPCs), establishing a mathematical relationship between two-dimensional images and three-dimensional spatial coordinates. Due to the existence of ill-posedness and overparameterization, the estimated RPCs are sensitive to any slight perturbations in the observation data, particularly when handling a limited number of Ground Control Points (GCPs). Recently, Principal Component Analysis (PCA) has demonstrated significant performance improvements in the RFM optimization problem. In the PCA-based RFM, each Principal Component (PC) is a linear combination of all variables in the design matrix. However, some original variables are noise related and have very small or almost zero contributions to the construction of PCs, which leads to the overparameterization problem and makes the RPC estimation process ill posed. To address this problem, in this paper, we propose an Adaptive Sparse Principal Component Analysis-based RFM method (ASPCA-RFM) for RPC estimation. In this method, the Elastic Net sparsity constraint is introduced to ensure that each PC contains only a small number of original variables, which automatically eliminates unnecessary variables during PC computation. Since the optimal regularization parameters of the Elastic Net vary significantly in different scenarios, an adaptive regularization parameter approach is proposed to dynamically adjust the regularization parameters according to the explained variance of PCs and degrees of freedom. By adopting the proposed method, the noise and error in the design matrix can be reduced, and the ill-posedness and overparameterization of the RPC estimation can be significantly mitigated. Additionally, we conduct extensive experiments to validate the effectiveness of our method. Compared to existing state-of-the-art methods, the proposed method yields markedly improved or competitive performance.

A physical layer security enhancement scheme for CO-OFDM systems based on 3D Brownian motion and TZBN Joint Scramble

In this paper, we propose a scheme for enhancing the physical layer security and transmission performance of coherent optical orthogonal frequency division multiplexing (CO-OFDM) systems. The scheme for OFDM data first after 3-dimensional (3D) Brownian motion rotational permutation, and then according to the time zone and band number (TZBN) scrambling to achieve the effect of further data perturbation, which through the SHA-256 algorithm and 6-dimensional (6D) hyperchaotic processing to obtain the chaotic keys to enhance the security. After simulation experiment of 16QAM CO-OFDM security system transmitting over 80 km standard single-mode fiber (SSMF) at the symbol rate of 30 Gbaud, it is shown that the encryption scheme can guarantee that the authorized user receives valid data and the eavesdropper obtains the information with the BER of about 0.5. The key space of the scheme is about 2.88×10194, which can effectively resist attacks such as violent attacks and chosen plaintext attacks. And the peak-to-average power ratio (PAPR) can be reduced by about 1.09 dB while the encryption process.

Diversity matters: Cross-head mutual mean-teaching for semi-supervised medical image segmentation

Semi-supervised medical image segmentation (SSMIS) has witnessed substantial advancements by leveraging limited labeled data and abundant unlabeled data. Nevertheless, existing state-of-the-art (SOTA) methods encounter challenges in accurately predicting labels for the unlabeled data, giving rise to disruptive noise during training and susceptibility to erroneous information overfitting. Moreover, applying perturbations to inaccurate predictions further impedes consistent learning. To address these concerns, we propose a novel cross-head mutual mean-teaching network (CMMT-Net) incorporated weak-strong data augmentations, thereby benefiting both co-training and consistency learning. More concretely, our CMMT-Net extends the cross-head co-training paradigm by introducing two auxiliary mean teacher models, which yield more accurate predictions and provide supplementary supervision. The predictions derived from weakly augmented samples generated by one mean teacher are leveraged to guide the training of another student with strongly augmented samples. Furthermore, two distinct yet synergistic data perturbations at the pixel and region levels are introduced. We propose mutual virtual adversarial training (MVAT) to smooth the decision boundary and enhance feature representations, and a cross-set CutMix strategy to generate more diverse training samples for capturing inherent structural data information. Notably, CMMT-Net simultaneously implements data, feature, and network perturbations, amplifying model diversity and generalization performance. Experimental results on three publicly available datasets indicate that our approach yields remarkable improvements over previous SOTA methods across various semi-supervised scenarios. The code is available at https://github.com/Leesoon1984/CMMT-Net.

Uniqueness, regularity, continuity, and stability of solutions of integral equations in irregular domains

This study explores the uniqueness, regularity, continuity, and stability of solutions to integral equations related to elliptical boundary value problems in irregular domains. Traditional methods usually consider soft boundaries, but this work extends these results to include domains with rough boundaries. By employing Sobolev spaces, especially fractional Sobolev spaces, we develop a comprehensive theoretical framework. Under appropriate conditions, the studied integral equation has a unique solution in fractional Sobolev spaces, maintaining the regularity properties of the input function. Two new theorems are introduced to strengthen the findings. The first theorem establishes that solutions are continuous with respect to perturbations in the input data. This means small changes in the input do not cause significant deviations in the solution, ensuring robustness in practical applications. The second theorem demonstrates the stability of the solutions when the domain geometry undergoes small changes. This stability is crucial for real-world scenarios where the exact shapes of domains may not be perfectly known or may vary slightly. These results significantly improve the mathematical understanding of boundary value problems in non-smooth domains. The proposed extended framework allows for more generalized applications, addressing challenges in various fields of physics and engineering. The ability to handle irregular domains with rough boundaries opens up new possibilities for modeling and solving complex problems where traditional soft boundary assumptions are not valid. This research provides a robust basis for future studies and applications, highlighting the importance of considering fractional Sobolev spaces in the analysis of integral equations.

An Empirical Study on the Effect of Training Data Perturbations on Neural Network Robustness.

The vulnerability of modern neural networks to random noise and deliberate attacks has raised concerns about their robustness, particularly as they are increasingly utilized in safety- and security-critical applications. Although recent research efforts were made to enhance robustness through retraining with adversarial examples or employing data augmentation techniques, a comprehensive investigation into the effects of training data perturbations on model robustness remains lacking. This paper presents the first extensive empirical study investigating the influence of data perturbations during model retraining. The experimental analysis focuses on both random and adversarial robustness, following established practices in the field of robustness analysis. Various types of perturbations in different aspects of the dataset are explored, including input, label, and sampling distribution. Single-factor and multi-factor experiments are conducted to assess individual perturbations and their combinations. The findings provide insights into constructing high-quality training datasets for optimizing robustness and recommend the appropriate degree of training set perturbations that balance robustness and correctness, and contribute to understanding model robustness in deep learning and offer practical guidance for enhancing model performance through perturbed retraining, promoting the development of more reliable and trustworthy deep learning systems for safety-critical applications.

Meta-analysis of RNA-seq studies with an adaptive weight and truncation p-value combination test

For RNA-seq studies, an important task is to identify genes that are differentially expressed between groups. Nevertheless, the identification of differentially expressed (DE) genes from a single study can be challenging as the small number of samples and the high sensitivity of data perturbations. Combining p-values from multiple RNA-seq studies can increase the statistical power and the accuracy in detecting DE genes. In this paper, we propose a weight and truncation p-value combination test for meta-analyzing RNA-seq studies. We show that with proper weight and truncation parameters, our new test has a higher statistical power over the existing tests, when the genes are weakly expressed in most studies and the sample size is unbalanced. We then present simulations and apply to two real data analysis. Finally, we provide some practical guidance for our new test and some existing p-value combination tests.

Physical layer security enhanced scheme based on joint encryption of DNA and RNA data perturbation in CO-OFDM system

—In the work, we propose a new chaotic encryption algorithm for optical physical layer security enhanced in coherent optical orthogonal frequency division multiplexing (CO-OFDM) systems. The proposed algorithm adopts the six-dimensional (6D) hyperchaotic to achieve the generation of key sequences, which can effectively improve the unpredictability and security of the system. The encryption scheme includes two steps, first, the binary sequence is disturbed by DNA and RNA two-stage encoding and RNA mutation, and then the initial encrypted data is injected into the algorithm module with two-dimensional continuous chaotic mapping (2D-SCL) and Brownian motion to scramble successively. Simulations in a 16QAM CO-OFDM system at a symbol rate of 30 Gbaud over 80 km of standard single-mode fiber (SSMF) show that a legitimate user is able to successfully decrypt the received signals, and an illegal eavesdropper obtains a useless signal with a bit error rate (BER) of about 0.5. The scheme can tolerate very small deviations and has a key space of approximately 10294, which can effectively withstand illegal attacks. And the peak-to-average power ratio (PAPR) can be reduced by about 1.01 dB.

English Network Teaching Model and Design of Evaluation System Based on Association Rule Algorithm

This study innovates English network teaching by applying a refined Association Rule Mining (ARM) algorithm. It integrates an “interest” parameter into ARM, dynamically adapting content to individual learners' profiles, improving engagement and outcomes. Controlled experiments, spanning diverse online platforms, validate the ARM model's efficacy by correlating learning content with academic performance, specifically CET-4 and CET-6 scores. Comprehensive preprocessing ensures data quality and privacy, employing techniques like de-identification, data perturbation, and aggregation. Advanced data analysis, including cross-validation and multivariate techniques, bolsters findings' reliability. Results highlight the ARM model's capacity to generate personalized learning paths, transcending conventional methods, and its potential as a cornerstone for data-driven education reforms. Future research will explore machine learning refinements and cultural adaptability to broaden its impact, fostering equitable, high-quality digital English education worldwide.

PathGPS: discover shared genetic architecture using GWAS summary data.

The increasing availability and scale of biobanks and "omic" datasets bring new horizons for understanding biological mechanisms. PathGPS is an exploratory data analysis tool to discover genetic architectures using Genome Wide Association Studies (GWAS) summary data. PathGPS is based on a linear structural equation model where traits are regulated by both genetic and environmental pathways. PathGPS decouples the genetic and environmental components by contrasting the GWAS associations of "signal" genes with those of "noise" genes. From the estimated genetic component, PathGPS then extracts genetic pathways via principal component and factor analysis, leveraging the low-rank and sparse properties. In addition, we provide a bootstrap aggregating ("bagging") algorithm to improve stability under data perturbation and hyperparameter tuning. When applied to a metabolomics dataset and the UK Biobank, PathGPS confirms several known gene-trait clusters and suggests multiple new hypotheses for future investigations.

Robust explainer recommendation for time series classification

Time series classification is a task which deals with temporal sequences, a prevalent data type common in domains such as human activity recognition, sports analytics and general sensing. In this area, interest in explanability has been growing as explanation is key to understand the data and the model better. Recently, a great variety of techniques (e.g., LIME, SHAP, CAM) have been proposed and adapted for time series to provide explanation in the form of saliency maps, where the importance of each data point in the time series is quantified with a numerical value. However, the saliency maps can and often disagree, so it is unclear which one to use. This paper provides a novel framework to quantitatively evaluate and rank explanation methods for time series classification. We show how to robustly evaluate the informativeness of a given explanation method (i.e., relevance for the classification task), and how to compare explanations side-by-side. The goal is to recommend the best explainer for a given time series classification dataset. We propose AMEE, a Model-Agnostic Explanation Evaluation framework, for recommending saliency-based explanations for time series classification. In this approach, data perturbation is added to the input time series guided by each explanation. Our results show that perturbing discriminative parts of the time series leads to significant changes in classification accuracy, which can be used to evaluate each explanation. To be robust to different types of perturbations and different types of classifiers, we aggregate the accuracy loss across perturbations and classifiers. This novel approach allows us to recommend the best explainer among a set of different explainers, including random and oracle explainers. We provide a quantitative and qualitative analysis for synthetic datasets, a variety of time-series datasets, as well as a real-world case study with known expert ground truth.

Insensitizing controls for the micropolar fluids

In this paper, we investigate the existence of insensitizing controls for the micropolar fluids in a bounded domain with homogeneous Dirichlet boundary conditions and arbitrarily located internal controller. The study of insensitizing controls is essential to solve a stability problem, which means that we look for controls such that some functionals of the velocity fields (the so‐called sentinels) are insensitive to the small perturbations of initial data. The problem of insensitizing controls is transformed into a suitable controllability problem for a cascade system. Our proof relies on a new global Carleman inequality and the inverse mapping theorem.