We are interested in assessing the order of a finite-state Hidden Markov Model (HMM) with the only two assumptions that the transition matrix of the latent Markov chain has full rank and that the density functions of the emission distributions are linearly independent. We introduce a new procedure for estimating this order by investigating the rank of some well-chosen integral operator which relies on the distribution of a pair of consecutive observations. This method circumvents the usual limits of the spectral method when it is used for estimating the order of an HMM: it avoids the choice of the basis functions; it does not require any knowledge of an upper-bound on the order of the HMM (for the spectral method, such an upper-bound is defined by the number of basis functions); it permits to easily handle different types of data (including continuous data, circular data or multivariate continuous data) with a suitable choice of kernel. The method relies on the fact that the order of the HMM can be identified from the distribution of a pair of consecutive observations and that this order is equal to the rank of some integral operator (\emph{i.e.} the number of its singular values that are non-zero). Since only the empirical counter-part of the singular values of the operator can be obtained, we propose a data-driven thresholding procedure. An upper-bound on the probability of overestimating the order of the HMM is established. Moreover, sufficient conditions on the bandwidth used for kernel density estimation and on the threshold are stated to obtain the consistency of the estimator of the order of the HMM. The procedure is easily implemented since the values of all the tuning parameters are determined by the sample size.
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We systematically analyze the accuracy of Physics-Informed Neural Networks (PINNs) in approximating solutions to the critical Surface Quasi-Geostrophic (SQG) equation on two-dimensional periodic boxes. The critical SQG equation involves advection and diffusion described by nonlocal periodic operators, posing challenges for neural network-based methods that do not commonly exhibit periodic boundary conditions. In this paper, we present a novel approximation of these operators using their nonperiodic analogs based on singular integral representation formulas and use it to perform error estimates. This idea can be generalized to a larger class of nonlocal partial differential equations whose solutions satisfy prescribed boundary conditions, thereby initiating a new PINNs theory for equations with nonlocalities.
Software vulnerabilities are a major cyber threat and it is important to detect them. One important approach to detecting vulnerabilities is to use deep learning while treating a program function as a whole, known as function-level vulnerability detectors. However, the limitation of this approach is not understood. In this paper, we investigate its limitation in detecting one class of vulnerabilities known as inter-procedural vulnerabilities, where the to-be-patched statements and the vulnerability-triggering statements belong to different functions. For this purpose, we create the first Inter-Procedural Vulnerability Dataset (InterPVD) based on C/C++ open-source software, and we propose a tool dubbed VulTrigger for identifying vulnerability-triggering statements across functions. Experimental results show that VulTrigger can effectively identify vulnerability-triggering statements and inter-procedural vulnerabilities. Our findings include: (i) inter-procedural vulnerabilities are prevalent with an average of 2.8 inter-procedural layers; and (ii) function-level vulnerability detectors are much less effective in detecting to-be-patched functions of inter-procedural vulnerabilities than detecting their counterparts of intra-procedural vulnerabilities.
We describe a new construction of Boolean functions. A specific instance of our construction provides a 30-variable Boolean function having min-entropy/influence ratio to be $128/45 \approx 2.8444$ which is presently the highest known value of this ratio that is achieved by any Boolean function. Correspondingly, $128/45$ is also presently the best known lower bound on the universal constant of the Fourier min-entropy/influence conjecture.
Sensory substitution or enhancement techniques have been proposed to enable deaf or hard of hearing (DHH) people to listen to and even compose music. However, little is known about how such techniques enhance DHH people's music experience. Since deafness is a spectrum -- as are DHH people's preferences and perceptions of music -- a more situated understanding of their interaction with music is needed. To understand the music experience of this population, we conducted social media analyses, both qualitatively and quantitatively, in the deaf and hard of hearing Reddit communities. Our content analysis revealed that DHH people leveraged sign language and visual/haptic cues to feel the music and preferred familiar, non-lyrical, instrument-heavy, and loud music. In addition, hearing aids were not customized for music, and the visual/haptic techniques developed were not widely adopted by DHH people, leading to their suboptimal music experiences. The DHH community embodied mutual support among music lovers, evidenced by active information sharing and Q&A around music and hearing loss. We reflect on design justice for DHH people's music experience and propose practical design implications to create a more accessible music experience for them.
This paper proposes two methods for causal additive models with unobserved variables (CAM-UV). CAM-UV assumes that the causal functions take the form of generalized additive models and that latent confounders are present. First, we propose a method that leverages prior knowledge for efficient causal discovery. Then, we propose an extension of this method for inferring causality in time series data. The original CAM-UV algorithm differs from other existing causal function models in that it does not seek the causal order between observed variables, but rather aims to identify the causes for each observed variable. Therefore, the first proposed method in this paper utilizes prior knowledge, such as understanding that certain variables cannot be causes of specific others. Moreover, by incorporating the prior knowledge that causes precedes their effects in time, we extend the first algorithm to the second method for causal discovery in time series data. We validate the first proposed method by using simulated data to demonstrate that the accuracy of causal discovery increases as more prior knowledge is accumulated. Additionally, we test the second proposed method by comparing it with existing time series causal discovery methods, using both simulated data and real-world data.
Quasiperiodic systems are important space-filling ordered structures, without decay and translational invariance. How to solve quasiperiodic systems accurately and efficiently is of great challenge. A useful approach, the projection method (PM) [J. Comput. Phys., 256: 428, 2014], has been proposed to compute quasiperiodic systems. Various studies have demonstrated that the PM is an accurate and efficient method to solve quasiperiodic systems. However, there is a lack of theoretical analysis of PM. In this paper, we present a rigorous convergence analysis of the PM by establishing a mathematical framework of quasiperiodic functions and their high-dimensional periodic functions. We also give a theoretical analysis of quasiperiodic spectral method (QSM) based on this framework. Results demonstrate that PM and QSM both have exponential decay, and the QSM (PM) is a generalization of the periodic Fourier spectral (pseudo-spectral) method. Then we analyze the computational complexity of PM and QSM in calculating quasiperiodic systems. The PM can use fast Fourier transform, while the QSM cannot. Moreover, we investigate the accuracy and efficiency of PM, QSM and periodic approximation method in solving the linear time-dependent quasiperiodic Schr\"{o}dinger equation.
Networks, threat models, and malicious actors are advancing quickly. With the increased deployment of the 5G networks, the security issues of the attached 5G physical devices have also increased. Therefore, artificial intelligence based autonomous end-to-end security design is needed that can deal with incoming threats by detecting network traffic anomalies. To address this requirement, in this research, we used a recently published 5G traffic dataset, 5G-NIDD, to detect network traffic anomalies using machine and deep learning approaches. First, we analyzed the dataset using three visualization techniques: t-Distributed Stochastic Neighbor Embedding (t-SNE), Uniform Manifold Approximation and Projection (UMAP), and Principal Component Analysis (PCA). Second, we reduced the data dimensionality using mutual information and PCA techniques. Third, we solve the class imbalance issue by inserting synthetic records of minority classes. Last, we performed classification using six different classifiers and presented the evaluation metrics. We received the best results when K-Nearest Neighbors classifier was used: accuracy (97.2%), detection rate (96.7%), and false positive rate (2.2%).
Explainable Artificial Intelligence (XAI) is transforming the field of Artificial Intelligence (AI) by enhancing the trust of end-users in machines. As the number of connected devices keeps on growing, the Internet of Things (IoT) market needs to be trustworthy for the end-users. However, existing literature still lacks a systematic and comprehensive survey work on the use of XAI for IoT. To bridge this lacking, in this paper, we address the XAI frameworks with a focus on their characteristics and support for IoT. We illustrate the widely-used XAI services for IoT applications, such as security enhancement, Internet of Medical Things (IoMT), Industrial IoT (IIoT), and Internet of City Things (IoCT). We also suggest the implementation choice of XAI models over IoT systems in these applications with appropriate examples and summarize the key inferences for future works. Moreover, we present the cutting-edge development in edge XAI structures and the support of sixth-generation (6G) communication services for IoT applications, along with key inferences. In a nutshell, this paper constitutes the first holistic compilation on the development of XAI-based frameworks tailored for the demands of future IoT use cases.
Graph Neural Networks (GNNs) have recently become increasingly popular due to their ability to learn complex systems of relations or interactions arising in a broad spectrum of problems ranging from biology and particle physics to social networks and recommendation systems. Despite the plethora of different models for deep learning on graphs, few approaches have been proposed thus far for dealing with graphs that present some sort of dynamic nature (e.g. evolving features or connectivity over time). In this paper, we present Temporal Graph Networks (TGNs), a generic, efficient framework for deep learning on dynamic graphs represented as sequences of timed events. Thanks to a novel combination of memory modules and graph-based operators, TGNs are able to significantly outperform previous approaches being at the same time more computationally efficient. We furthermore show that several previous models for learning on dynamic graphs can be cast as specific instances of our framework. We perform a detailed ablation study of different components of our framework and devise the best configuration that achieves state-of-the-art performance on several transductive and inductive prediction tasks for dynamic graphs.
Deep Convolutional Neural Networks (CNNs) are a special type of Neural Networks, which have shown state-of-the-art results on various competitive benchmarks. The powerful learning ability of deep CNN is largely achieved with the use of multiple non-linear feature extraction stages that can automatically learn hierarchical representation from the data. Availability of a large amount of data and improvements in the hardware processing units have accelerated the research in CNNs and recently very interesting deep CNN architectures are reported. The recent race in deep CNN architectures for achieving high performance on the challenging benchmarks has shown that the innovative architectural ideas, as well as parameter optimization, can improve the CNN performance on various vision-related tasks. In this regard, different ideas in the CNN design have been explored such as use of different activation and loss functions, parameter optimization, regularization, and restructuring of processing units. However, the major improvement in representational capacity is achieved by the restructuring of the processing units. Especially, the idea of using a block as a structural unit instead of a layer is gaining substantial appreciation. This survey thus focuses on the intrinsic taxonomy present in the recently reported CNN architectures and consequently, classifies the recent innovations in CNN architectures into seven different categories. These seven categories are based on spatial exploitation, depth, multi-path, width, feature map exploitation, channel boosting and attention. Additionally, it covers the elementary understanding of the CNN components and sheds light on the current challenges and applications of CNNs.
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