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Anomaly detection (AD) plays a pivotal role across diverse domains, including cybersecurity, finance, healthcare, and industrial manufacturing, by identifying unexpected patterns that deviate from established norms in real-world data.…
Most of the existing methods for anomaly detection use only positive data to learn the data distribution, thus they usually need a pre-defined threshold at the detection stage to determine whether a test instance is an outlier.…
In this paper, we propose a test for the equality of multiple distributions based on kernel mean embeddings. Our framework provides a flexible way to handle multivariate or even high-dimensional data by virtue of kernel methods and allows…
In this paper, we propose CKGAN, a novel generative adversarial network (GAN) variant based on an integral probability metrics framework with characteristic kernel (CKIPM). CKIPM, as a distance between two probability distributions, is…
Selecting an appropriate kernel is a central challenge in kernel-based spectral methods. In \emph{Kernelized Diffusion Maps} (KDM), the kernel determines the accuracy of the RKHS estimator of a diffusion-type operator and hence the quality…
This paper addresses the problem of seeking a common fixed point for a collection of nonexpansive operators over time-varying multi-agent networks in real Hilbert spaces, where each operator is only privately and approximately known to each…
Kernel-based tests provide a simple yet effective framework that use the theory of reproducing kernel Hilbert spaces to design non-parametric testing procedures. In this paper we propose new theoretical tools that can be used to study the…
We establish the limiting spectral distribution of Kendall's correlation matrices in the moderate high-dimensional regime where the dimension grows slower than the sample size. Our framework allows observations to be independent but not…
For data-driven iterative learning control (ILC) methods, both the model estimation and controller design problems are converted to parameter estimation problems for some chosen model structures. It is well-known that if the model order is…
As cyber threats continue to evolve in sophistication and scale, the ability to detect anomalous network behavior has become critical for maintaining robust cybersecurity defenses. Modern cybersecurity systems face the overwhelming…
When formulated as an unsupervised learning problem, anomaly detection often requires a model to learn the distribution of normal data. Previous works apply Generative Adversarial Networks (GANs) to anomaly detection tasks and show good…
Tabular anomaly detection under the one-class classification setting poses a significant challenge, as it involves accurately conceptualizing "normal" derived exclusively from a single category to discern anomalies from normal data…
The importance of wild video based image set recognition is becoming monotonically increasing. However, the contents of these collected videos are often complicated, and how to efficiently perform set modeling and feature extraction is a…
Motivated by multi-distribution divergences, which originate in information theory, we propose a notion of `multi-point' kernels, and study their applications. We study a class of kernels based on Jensen type divergences and show that these…
Hacking and false data injection from adversaries can threaten power grids' everyday operations and cause significant economic loss. Anomaly detection in power grids aims to detect and discriminate anomalies caused by cyber attacks against…
The goal of anomaly detection is to identify anomalous samples from normal ones. In this paper, a small number of anomalies are assumed to be available at the training stage, but they are assumed to be collected only from several anomaly…
This paper studies Kernel Density Estimation for a high-dimensional distribution $\rho(x)$. Traditional approaches have focused on the limit of large number of data points $n$ and fixed dimension $d$. We analyze instead the regime where…
Fisher's linear discriminant analysis is a classical method for classification, yet it is limited to capturing linear features only. Kernel discriminant analysis as an extension is known to successfully alleviate the limitation through a…
Do two data samples come from different distributions? Recent studies of this fundamental problem focused on embedding probability distributions into sufficiently rich characteristic Reproducing Kernel Hilbert Spaces (RKHSs), to compare…
In many applications one is interested to detect certain (known) patterns in the mean of a process with smallest delay. Using an asymptotic framework which allows to capture that feature, we study a class of appropriate sequential…