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In this work, we present a novel approach to transform supervised classifiers into effective unsupervised anomaly detectors. The method we have developed, termed Discriminatory Detection of Distortions (DDD), enhances anomaly detection by…

In this paper we propose a novel augmentation technique that improves not only the performance of deep neural networks on clean test data, but also significantly increases their robustness to random transformations, both affine and…

This paper presents a rigorous numerical framework for computing multiple solutions of semilinear elliptic problems by spatiotemporal high-index saddle dynamics (HiSD), which extends the traditional HiSD to the continuous-in-space setting,…

Anomaly detection is a crucial machine-learning task with wide-ranging applications. Deep Support Vector Data Description (Deep SVDD) is a prominent deep one-class method, but it is vulnerable to hypersphere collapse, often relies on…

The task of image segmentation is inherently noisy due to ambiguities regarding the exact location of boundaries between anatomical structures. We argue that this information can be extracted from the expert annotations at no extra cost,…

High-dimensional datasets are frequently subject to contamination by outliers and heavy-tailed noise, which can severely bias standard regularized estimators like the Lasso. While Maximum Mean Discrepancy (MMD) has recently been introduced…

Multivariate time-series (MTS) anomaly detection is critical in domains such as service monitor, IoT, and network security. While multi-model methods based on selection or ensembling outperform single-model ones, they still face…

Timely detection of abrupt anomalies is crucial for real-time monitoring and security of modern systems producing high-dimensional data. With this goal, we propose effective and scalable algorithms. Proposed algorithms are nonparametric as…

We propose a new method for computing Dynamic Mode Decomposition (DMD) evolution matrices, which we use to analyze dynamical systems. Unlike the majority of existing methods, our approach is based on a variational formulation consisting of…

We present a convex approach to probabilistic segmentation and modeling of time series data. Our approach builds upon recent advances in multivariate total variation regularization, and seeks to learn a separate set of parameters for the…

Time series anomaly detection (TSAD) is of widespread interest across many industries, including finance, healthcare, and manufacturing. Despite the development of numerous automatic methods for detecting anomalies, human oversight remains…

Many econometric analyses involve spatio--temporal data. A considerable amount of literature has addressed spatio--temporal models, with Spatial Dynamic Panel Data (SDPD) being widely investigated and applied. In real data applications,…

Astronomical time series from large-scale surveys like LSST are often irregularly sampled and incomplete, posing challenges for classification and anomaly detection. We introduce a new framework based on Neural Stochastic Delay Differential…

We develop a practical approach to semidefinite programming (SDP) that includes the von Neumann entropy, or an appropriate variant, as a regularization term. In particular we solve the dual of the regularized program, demonstrating how a…

Unsupervised machine learning methods are well suited to searching for anomalies at scale but can struggle with the high-dimensional representation of many modern datasets, hence dimensionality reduction (DR) is often performed first. In…

We present a high-order spacetime numerical method for discretizing and solving linear initial-boundary value problems using wavelet-based techniques with user-prescribed error estimates. The spacetime wavelet discretization yields a system…

Spatial modulation (SM) is a promising multiple-input multiple-output system used to increase spectral efficiency. The maximum likelihood (ML) decoder jointly detects the transmitted SM symbol, which is of high complexity. In this paper, a…

In this paper, we consider the large deviations principles (LDPs) for the stochastic linear Schr\"odinger equation and its symplectic discretizations. These numerical discretizations are the spatial semi-discretization based on spectral…

The stability and persistence of web services are important to Internet companies to improve user experience and business performances. To keep eyes on numerous metrics and report abnormal situations, time series anomaly detection methods…

We study geometric stochastic differential equations (SDEs) and their approximations on Riemannian manifolds. In particular, we introduce a simple new construction of geometric SDEs, using which with bounded curvature. In particular, we…