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Graph neural network (GNN) models play a pivotal role in numerous tasks involving graph-related data analysis. Despite their efficacy, similar to other deep learning models, GNNs are susceptible to adversarial attacks. Even minor perturbations in graph data can induce substantial alterations in model predictions. While existing research has explored various adversarial defense techniques for GNNs, the challenge of defending against adversarial attacks on real-world scale graph data remains largely unresolved. On one hand, methods reliant on graph purification and preprocessing tend to excessively emphasize local graph information, leading to sub-optimal defensive outcomes. On the other hand, approaches rooted in graph structure learning entail significant time overheads, rendering them impractical for large-scale graphs. In this paper, we propose a new defense method named Talos, which enhances the global, rather than local, homophily of graphs as a defense. Experiments show that the proposed approach notably outperforms state-of-the-art defense approaches, while imposing little computational overhead.

We introduce a novel meta-analysis framework to combine dependent tests under a general setting, and utilize it to synthesize various microbiome association tests that are calculated from the same dataset. Our development builds upon the classical meta-analysis methods of aggregating $p$-values and also a more recent general method of combining confidence distributions, but makes generalizations to handle dependent tests. The proposed framework ensures rigorous statistical guarantees, and we provide a comprehensive study and compare it with various existing dependent combination methods. Notably, we demonstrate that the widely used Cauchy combination method for dependent tests, referred to as the vanilla Cauchy combination in this article, can be viewed as a special case within our framework. Moreover, the proposed framework provides a way to address the problem when the distributional assumptions underlying the vanilla Cauchy combination are violated. Our numerical results demonstrate that ignoring the dependence among the to-be-combined components may lead to a severe size distortion phenomenon. Compared to the existing $p$-value combination methods, including the vanilla Cauchy combination method, the proposed combination framework can handle the dependence accurately and utilizes the information efficiently to construct tests with accurate size and enhanced power. The development is applied to Microbiome Association Studies, where we aggregate information from multiple existing tests using the same dataset. The combined tests harness the strengths of each individual test across a wide range of alternative spaces, %resulting in a significant enhancement of testing power across a wide range of alternative spaces, enabling more efficient and meaningful discoveries of vital microbiome associations.

This paper presents a novel method to make statistical inferences for both the model support and regression coefficients in a high-dimensional logistic regression model. Our method is based on the repro samples framework, in which we conduct statistical inference by generating artificial samples mimicking the actual data-generating process. The proposed method has two major advantages. Firstly, for model support, we introduce the first method for constructing model confidence set in a high-dimensional setting and the proposed method only requires a weak signal strength assumption. Secondly, in terms of regression coefficients, we establish confidence sets for any group of linear combinations of regression coefficients. Our simulation results demonstrate that the proposed method produces valid and small model confidence sets and achieves better coverage for regression coefficients than the state-of-the-art debiasing methods. Additionally, we analyze single-cell RNA-seq data on the immune response. Besides identifying genes previously proved as relevant in the literature, our method also discovers a significant gene that has not been studied before, revealing a potential new direction in understanding cellular immune response mechanisms.

Vibrational resonance (VR) is a nonlinear phenomenon in which the system response to a weak signal can be resonantly enhanced by applying a high-frequency modulation signal with an appropriate amplitude. The majority of VR research has focused on amplifying the amplitude or intensity of the system response to a weak signal, whereas the study of the phase information of system responses in VR remains limited. Here, we investigate the VR phenomena in both amplitude and phase quadratures of an optical field in a Kerr nonlinear cavity driven by a near-resonant weak signal and a far-detuned modulation signal. Analytical and numerical results demonstrated that the resonant enhancement in the amplitude and phase quadratures of the system response to a weak signal simultaneously occurs as the amplitude of the modulation signal is varied. There is a linear relation between the amplitude and frequency of the modulation signal for achieving an optimal VR effect. Furthermore, we generalized our study to investigate the quadrature at an arbitrary phase and determined that the VR enhancement sensitively depends on the phase. Our findings not only broaden the scope of VR research by incorporating phase information but also introduces an approach for amplifying an optical field by manipulating another optical field.

Prognostics and health management (PHM) is essential for industrial operation and maintenance, focusing on predicting, diagnosing, and managing the health status of industrial systems. The emergence of the ChatGPT-Like large-scale language model (LLM) has begun to lead a new round of innovation in the AI field. It has extensively promoted the level of intelligence in various fields. Therefore, it is also expected further to change the application paradigm in industrial PHM and promote PHM to become intelligent. Although ChatGPT-Like LLMs have rich knowledge reserves and powerful language understanding and generation capabilities, they lack domain-specific expertise, significantly limiting their practicability in PHM applications. To this end, this study explores the ChatGPT-Like LLM empowered by the local knowledge base (LKB) in industrial PHM to solve the above limitations. In addition, we introduce the method and steps of combining the LKB with LLMs, including LKB preparation, LKB vectorization, prompt engineering, etc. Experimental analysis of real cases shows that combining the LKB with ChatGPT-Like LLM can significantly improve its performance and make ChatGPT-Like LLMs more accurate, relevant, and able to provide more insightful information. This can promote the development of ChatGPT-Like LLMs in industrial PHM and promote their efficiency and quality.

The mixed-size placement benchmarks described in this book chapter directly address several of the shortcomings in previously published suboptimality benchmarks. Two new sets of placement examples are constructed, one targeting the role of nonlocal nets in suboptimality, and another targeting the role of white space and large variations in module sizes. The first set, PEKO-MC, is a set of standard-cell circuits with nonlocal nets in known optimal placements. A given netlist is modified so as to render a given placement for it optimal for the new netlist. Cell dimensions and locations are not changed, net-degree statistics are matched exactly, and over 60% of the original netlist is left unchanged. The second set, PEKO-MS, incorporates a parametrized percentage of white space into a mixed-size placement which precisely matches given macro dimensions and locations as well as the net-degree distributions of the ISPD 2005 benchmark suite [21]. HPWL for the placements generated for the PEKO-MS circuits are proven to be less than 3% above optimal for most cases and within 8% of optimal on all cases., Comment: Version of Record: https://link.springer.com/book/10.1007/978-0-387-68739-1 Pre-print of Chapter 2 from the following work: Gi-Joon Nam and Jason Cong, Modern Circuit Placement Best Practices and Results, 2007, Springer, reproduced with permission of Springer Science+Business Media, LLC. The final authenticated version is available online at: http://dx.doi.org/10.1007/978-0-387-68739-1

In this paper, we present a new and effective simulation-based approach to conduct both finite- and large-sample inference for high-dimensional linear regression models. This approach is developed under the so-called repro samples framework, in which we conduct statistical inference by creating and studying the behavior of artificial samples that are obtained by mimicking the sampling mechanism of the data. We obtain confidence sets for (a) the true model corresponding to the nonzero coefficients, (b) a single or any collection of regression coefficients, and (c) both the model and regression coefficients jointly. We also extend our approaches to drawing inferences on functions of the regression coefficients. The proposed approach fills in two major gaps in the high-dimensional regression literature: (1) lack of effective approaches to address model selection uncertainty and provide valid inference for the underlying true model; (2) lack of effective inference approaches that guarantee finite-sample performances. We provide both finite-sample and asymptotic results to theoretically guarantee the performances of the proposed methods. In addition, our numerical results demonstrate that the proposed methods are valid and achieve better coverage with smaller confidence sets than the existing state-of-art approaches, such as debiasing and bootstrap approaches.

A class of nonparametric two-sample tests has been proposed in this article. As a generalization of the original \v{S}id\'aks' test, the proposed test statistic is developed as the sum of the maximal precedence and maximal exceedance statistics. Unlike the \v{S}id\'ak-type precedence-exceedance test and the maximal precedence test, the proposed test is suitable for a two-sided alternative while being free from any parametric assumption. Exact distribution of the test statistic is obtained under the null as well as under the Lehmann alternative. Power value comparison has been carried out that shows the competency of the proposed test as a useful alternative to a number of existing tests based on precedence-exceedance statistics. Real-life example is provided to illustrate the application of the proposed test.

This article presents a novel, general, and effective simulation-inspired approach, called {\it repro samples method}, to conduct statistical inference. The approach studies the performance of artificial samples, referred to as {\it repro samples}, obtained by mimicking the true observed sample to achieve uncertainty quantification and construct confidence sets for parameters of interest with guaranteed coverage rates. Both exact and asymptotic inferences are developed. An attractive feature of the general framework developed is that it does not rely on the large sample central limit theorem and is likelihood-free. As such, it is thus effective for complicated inference problems which we can not solve using the large sample central limit theorem. The proposed method is applicable to a wide range of problems, including many open questions where solutions were previously unavailable, for example, those involving discrete or non-numerical parameters. To reduce the large computational cost of such inference problems, we develop a unique matching scheme to obtain a data-driven candidate set. Moreover, we show the advantages of the proposed framework over the classical Neyman-Pearson framework. We demonstrate the effectiveness of the proposed approach on various models throughout the paper and provide a case study that addresses an open inference question on how to quantify the uncertainty for the unknown number of components in a normal mixture model. To evaluate the empirical performance of our repro samples method, we conduct simulations and study real data examples with comparisons to existing approaches. Although the development pertains to the settings where the large sample central limit theorem does not apply, it also has direct extensions to the cases where the central limit theorem does hold.

Linear transformation model provides a general framework for analyzing censored survival data with covariates. The proportional hazards and proportional odds models are special cases of the linear transformation model. In biomedical studies, covariates with measurement error may occur in survival data. In this work, we propose a method to obtain estimators of the regression coefficients in the linear transformation model when the covariates are subject to measurement error. In the proposed method, we assume that instrumental variables are available. We develop counting process based estimating equations for finding the estimators of regression coefficients. We prove the large sample properties of the estimators using the martingale representation of the regression estimators. The finite sample performance of the estimators are evaluated through an extensive Monte Carlo simulation study. Finally, we illustrate the proposed method using an AIDS clinical trial (ACTG 175) data., Comment: We proposed an instrumental variable approach to analyze the linear transformation model when covariates are measured with error

This paper introduces to readers the new concept and methodology of confidence distribution and the modern-day distributional inference in statistics. This discussion should be of interest to people who would like to go into the depth of the statistical inference methodology and to utilize distribution estimators in practice. We also include in the discussion the topic of generalized fiducial inference, a special type of modern distributional inference, and relate it to the concept of confidence distribution. Several real data examples are also provided for practitioners. We hope that the selected content covers the greater part of the developments on this subject., Comment: To appear as a chapter in Springer Handbook of Engineering Statistics, 2nd ed

In the context of big data analysis, the divide-and-conquer methodology refers to a multiple-step process: first splitting a data set into several smaller ones; then analyzing each set separately; finally combining results from each analysis together. This approach is effective in handling large data sets that are unsuitable to be analyzed entirely by a single computer due to limits either from memory storage or computational time. The combined results will provide a statistical inference which is similar to the one from analyzing the entire data set. This article reviews some recently developments of divide-and-conquer methods in a variety of settings, including combining based on parametric, semiparametric and nonparametric models, online sequential updating methods, among others. Theoretical development on the efficiency of the divide-and-conquer methods is also discussed.

Modern radar systems have high requirements in terms of accuracy, robustness and real-time capability when operating on increasingly complex electromagnetic environments. Traditional radar signal processing (RSP) methods have shown some limitations when meeting such requirements, particularly in matters of target classification. With the rapid development of machine learning (ML), especially deep learning, radar researchers have started integrating these new methods when solving RSP-related problems. This paper aims at helping researchers and practitioners to better understand the application of ML techniques to RSP-related problems by providing a comprehensive, structured and reasoned literature overview of ML-based RSP techniques. This work is amply introduced by providing general elements of ML-based RSP and by stating the motivations behind them. The main applications of ML-based RSP are then analysed and structured based on the application field. This paper then concludes with a series of open questions and proposed research directions, in order to indicate current gaps and potential future solutions and trends.

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.

The notion of p-value is a fundamental concept in statistical inference and has been widely used for reporting outcomes of hypothesis tests. However, p-value is often misinterpreted, misused or miscommunicated in practice. Part of the issue is that existing definitions of p-value are often derived from constructions under specific settings, and a general definition that directly reflects the evidence of the null hypothesis is not yet available. In this article, we first propose a general and rigorous definition of p-value that fulfills two performance-based characteristics. The performance-based definition subsumes all existing construction-based definitions of the p-value, and justifies their interpretations. The paper further presents a specific approach based on confidence distribution to formulate and calculate p-values. This specific way of computing p values has two main advantages. First, it is applicable for a wide range of hypothesis testing problems, including the standard one- and two-sided tests, tests with interval-type null, intersection-union tests, multivariate tests and so on. Second, it can naturally lead to a coherent interpretation of p-value as evidence in support of the null hypothesis, as well as a meaningful measure of degree of such support. In particular, it places a meaning of a large p-value, e.g. p-value of 0.8 has more support than 0.5. Numerical examples are used to illustrate the wide applicability and computational feasibility of our approach. We show that our proposal is effective and can be applied broadly, without further consideration of the form/size of the null space. As for existing testing methods, the solutions have not been available or cannot be easily obtained., Comment: 30 pages, 8 figures

The discrepant posterior phenomenon (DPP) is a counter-intuitive phenomenon that can frequently occur in a Bayesian analysis of multivariate parameters. It refers to the phenomenon that a parameter estimate based on a posterior is more extreme than both of those inferred based on either the prior or the likelihood alone. Inferential claims that exhibit DPP defy the common intuition that the posterior is a prior-data compromise, and the phenomenon can be surprisingly ubiquitous in well-behaved Bayesian models. In this paper we revisit this phenomenon and, using point estimation as an example, derive conditions under which the DPP occurs in Bayesian models with exponential quadratic likelihoods and conjugate multivariate Gaussian priors. The family of exponential quadratic likelihood models includes Gaussian models and those models with local asymptotic normality property. We provide an intuitive geometric interpretation of the phenomenon and show that there exists a nontrivial space of marginal directions such that the DPP occurs. We further relate the phenomenon to the Simpson's paradox and discover their deep-rooted connection that is associated with marginalization. We also draw connections with Bayesian computational algorithms when difficult geometry exists. Our discovery demonstrates that DPP is more prevalent than previously understood and anticipated. Theoretical results are complemented by numerical illustrations. Scenarios covered in this study have implications for parameterization, sensitivity analysis, and prior choice for Bayesian modeling.

We study the interaction between a quantum-dot and a bi-mode micro/nano-optical cavity composed of second-order nonlinear materials. Compared with the Jaynes-Cummings (J-C) model, except for a coherent weak driving field, a strong pump light illuminates the two-mode optical cavity. Analytical results indicate that the model exhibits abundant non-classical optical phenomena, such as conventional photon blockade induced by the nonlinear interaction between polaritons. It constitutes unconventional photon blockade induced by quantum interference due to parametric driving. We compare the photon statistical properties and average photon number of the proposed model, J-C model, and double-mode driven optical cavity under the same parameters and the proposed model can obtain stronger antibunching photons and higher average photon number.

Many massive data are assembled through collections of information of a large number of individuals in a population. The analysis of such data, especially in the aspect of individualized inferences and solutions, has the potential to create significant value for practical applications. Traditionally, inference for an individual in the data set is either solely relying on the information of the individual or from summarizing the information about the whole population. However, with the availability of big data, we have the opportunity, as well as a unique challenge, to make a more effective individualized inference that takes into consideration of both the population information and the individual discrepancy. To deal with the possible heterogeneity within the population while providing effective and credible inferences for individuals in a data set, this article develops a new approach called the individualized group learning (iGroup). The iGroup approach uses local nonparametric techniques to generate an individualized group by pooling other entities in the population which share similar characteristics with the target individual, even when individual estimates are biased due to limited number of observations. Three general cases of iGroup are discussed, and their asymptotic performances are investigated. Both theoretical results and empirical simulations reveal that, by applying iGroup, the performance of statistical inference on the individual level are ensured and can be substantially improved from inference based on either solely individual information or entire population information. The method has a broad range of applications. Two examples in financial statistics and maritime anomaly detection are presented.

End-to-end neural models for intelligent dialogue systems suffer from the problem of generating uninformative responses. Various methods were proposed to generate more informative responses by leveraging external knowledge. However, few previous work has focused on selecting appropriate knowledge in the learning process. The inappropriate selection of knowledge could prohibit the model from learning to make full use of the knowledge. Motivated by this, we propose an end-to-end neural model which employs a novel knowledge selection mechanism where both prior and posterior distributions over knowledge are used to facilitate knowledge selection. Specifically, a posterior distribution over knowledge is inferred from both utterances and responses, and it ensures the appropriate selection of knowledge during the training process. Meanwhile, a prior distribution, which is inferred from utterances only, is used to approximate the posterior distribution so that appropriate knowledge can be selected even without responses during the inference process. Compared with the previous work, our model can better incorporate appropriate knowledge in response generation. Experiments on both automatic and human evaluation verify the superiority of our model over previous baselines.

Noise usually has an unwelcome influence on system performance. For instance, noise inevitably affects the low-frequency mechanical freedom in optomechanical experiments. However, we investigate here the beneficial effects of thermal noise on a basic optomechanical system with parametric instability. In a regime near parametric instability, it is found that thermal noise in the mechanical freedom can sustain long-term quasi-coherent oscillations when the system would otherwise remain in the equilibrium state. In an overlapping regime of parametric instability and bistability, intermittent switching between a self-sustained oscillating state and an equilibrium can be induced by adding a certain amount of noise. When a subthreshold periodic signal is applied to the mechanics, the switching between the self-sustained oscillations and the equilibrium exhibits good periodicity at a rate that is synchronized to the signal frequency, resulting in a significant amplification of the signal. Our results deepen the understanding of the interplay between optomechanical nonlinearity and noise and provide theoretical guidance for experimental observation of noise-induced beneficial phenomena in optomechanics., Comment: 9 pages, 4 figures

In this paper, we study the stochastic resonance (SR) effect in an optomechanical system driven by a strong coupling field and two weak signals in both semiclassical and quantum frameworks. In the semiclassical description, the SR phenomena are found at the cooperation of input signals and system noises. When two signals co-act on our system, the interference effect between the optically induced SR and the mechanically induced SR can be generated. In particular, a unique beating effect, which makes the SR effect robust against the initial phase difference of two signals, appears in the SR synchronization process with unsynchronized signals. In addition, the quantum stochastic resonance effect is numerically observed in the full quantum framework induced by pure quantum fluctuations.

Model selection strategies have been routinely employed to determine a model for data analysis in statistics, and further study and inference then often proceed as though the selected model were the true model that were known a priori. This practice does not account for the uncertainty introduced by the selection process and the fact that the selected model can possibly be a wrong one. Model averaging approaches try to remedy this issue by combining estimators for a set of candidate models. Specifically, instead of deciding which model is the 'right' one, a model averaging approach suggests to fit a set of candidate models and average over the estimators using certain data adaptive weights. In this paper we establish a general frequentist model averaging framework that does not set any restrictions on the set of candidate models. It greatly broadens the scope of the existing methodologies under the frequentist model averaging development. Assuming the data is from an unknown model, we derive the model averaging estimator and study its limiting distributions and related predictions while taking possible modeling biases into account. We propose a set of optimal weights to combine the individual estimators so that the expected mean squared error of the average estimator is minimized. Simulation studies are conducted to compare the performance of the estimator with that of the existing methods. The results show the benefits of the proposed approach over traditional model selection approaches as well as existing model averaging methods.

In this work we study the stochastic resonance (SR) effect in a driven dissipative Jaynes-Cummings model. The SR effect is systematically studied in the semiclassical and full quantum frameworks and in both cases we find that SRs simultaneously occur for the optical and atomic freedoms. In particular, at zero temperature quantum SR can be induced merely by vacuum fluctuations. The qualitative features of semiclassical SR and quantum SR are similar, but the parameter region of quantum SR are shifted from the semiclassical region due to the widely-used factorization in obtaining semiclassical equations of motion. Our results provide a theoretical basis for experimentally observing and studying the SR phenomenon of the Jaynes-Cummings model in the quantum regime., Comment: 7 figures

Approximate Bayesian computing is a powerful likelihood-free method that has grown increasingly popular since early applications in population genetics. However, complications arise in the theoretical justification for Bayesian inference conducted from this method with a non-sufficient summary statistic. In this paper, we seek to re-frame approximate Bayesian computing within a frequentist context and justify its performance by standards set on the frequency coverage rate. In doing so, we develop a new computational technique called approximate confidence distribution computing, yielding theoretical support for the use of non-sufficient summary statistics in likelihood-free methods. Furthermore, we demonstrate that approximate confidence distribution computing extends the scope of approximate Bayesian computing to include data-dependent priors without damaging the inferential integrity. This data-dependent prior can be viewed as an initial `distribution estimate' of the target parameter which is updated with the results of the approximate confidence distribution computing method. A general strategy for constructing an appropriate data-dependent prior is also discussed and is shown to often increase the computing speed while maintaining statistical inferential guarantees. We supplement the theory with simulation studies illustrating the benefits of the proposed method, namely the potential for broader applications and the increased computing speed compared to the standard approximate Bayesian computing methods.

In this work we theoretically investigate the stochastic resonance (SR) effect in an optomechanical membrane system subject to two weak signals (one optical field and one mechanical force). The quadratic optomechanical coupling allows us to find a region with tristability where the noise activated stochastic switching among three stable states occurs and SR phenomena are observed at the cooperation of input signals and noises. We show that the mechanical force and the optical field respectively serve as an additive signal and a multiplicative signal to the membrane position and they induce completely different SR behaviors. Moreover, when two signals coexist the SR effect can be enhanced and the beating effect appears in the SR synchronization process with unsynchronized signals., Comment: 6 pages,7 figures

Stochastic network calculus is a newly developed theory for stochastic service guarantee analysis of computer networks. In the current stochastic network calculus literature, its fundamental models are based on the cumulative amount of traffic or cumulative amount of service. However, there are network scenarios where direct application of such models is difficult. This paper presents a temporal approach to stochastic network calculus. The key idea is to develop models and derive results from the time perspective. Particularly, we define traffic models and service models based on the cumulative packet inter-arrival time and the cumulative packet service time, respectively. Relations among these models as well as with the existing models in the literature are established. In addition, we prove the basic properties of the proposed models, such as delay bound and backlog bound, output characterization, concatenation property and superposition property. These results form a temporal stochastic network calculus and compliment the existing results., Comment: 45 pages. An early version of this paper has been presented at 17th Annual Meeting of the IEEE/ACM International Symposium on Modelling, Analysis and Simulation of Computer and Telecommunication Systems. This version has been submitted to a journal and is waiting for being reviewed