相关论文: Manifold-regularised Large-Margin $\ell_p$-SVDD fo…

Semi-supervised graph anomaly detection (GAD) has recently received increasing attention, which aims to distinguish anomalous patterns from graphs under the guidance of a moderate amount of labeled data and a large volume of unlabeled data.…

Many measurements in computer vision and machine learning manifest as non-Euclidean data samples. Several researchers recently extended a number of deep neural network architectures for manifold valued data samples. Researchers have…

The problem of sampling a target probability distribution on a constrained domain arises in many applications including machine learning. For constrained sampling, various Langevin algorithms such as projected Langevin Monte Carlo (PLMC),…

Detecting anomalies in multivariate time-series data is essential in many real-world applications. Recently, various deep learning-based approaches have shown considerable improvements in time-series anomaly detection. However, existing…

We present a new method of training energy-based models (EBMs) for anomaly detection that leverages low-dimensional structures within data. The proposed algorithm, Manifold Projection-Diffusion Recovery (MPDR), first perturbs a data point…

In this paper, we investigate discrete regularity estimates for a broad class of temporal numerical schemes for parabolic stochastic evolution equations. We provide a characterization of discrete stochastic maximal $\ell^p$-regularity in…

Probabilistic Manifold Decomposition (PMD)\cite{doi:10.1137/25M1738863}, developed in our earlier work, provides a nonlinear model reduction by embedding high-dimensional dynamics onto low-dimensional probabilistic manifolds. The PMD has…

Regularization is essential for avoiding over-fitting to training data in network optimization, leading to better generalization of the trained networks. The label noise provides a strong implicit regularization by replacing the target…

Mirror Descent (MD) is a scalable first-order method widely used in large-scale optimization, with applications in image processing, policy optimization, and neural network training. This paper generalizes MD to optimization on Riemannian…

In large scale machine learning, random sampling is a popular way to approximate datasets by a small representative subset of examples. In particular, sensitivity sampling is an intensely studied technique which provides provable guarantees…

In this paper, we develop a new approach to learning high-dimensional Poisson directed acyclic graphical (DAG) models from only observational data without strong assumptions such as faithfulness and strong sparsity. A key component of our…

Manifold regularization model is a semi-supervised learning model that leverages the geometric structure of a dataset, comprising a small number of labeled samples and a large number of unlabeled samples, to generate classifiers. However,…

In this paper we present a novel algorithm and efficient data structure for anomaly detection based on temporal data. Time-series data are represented by a sequence of symbolic time intervals, describing increasing and decreasing trends, in…

Recently, there has been a significant amount of interest in satellite telemetry anomaly detection (AD) using neural networks (NN). For AD purposes, the current approaches focus on either forecasting or reconstruction of the time series,…

Despite many applications, dimensionality reduction in the $\ell_1$-norm is much less understood than in the Euclidean norm. We give two new oblivious dimensionality reduction techniques for the $\ell_1$-norm which improve exponentially…

Support Vector Data Description (SVDD) is a popular outlier detection technique which constructs a flexible description of the input data. SVDD computation time is high for large training datasets which limits its use in big-data…

For parabolic stochastic partial differential equations (SPDEs), we show that the numerical methods, including the spatial spectral Galerkin method and further the full discretization via the temporal accelerated exponential Euler method,…

The core challenge in unsupervised anomaly detection is identifying abnormal patterns without prior knowledge of their characteristics. While existing methods have addressed aspects of this problem, they often struggle to learn a robust…

This work aims to prove the small time large deviation principle (LDP) for a class of stochastic partial differential equations (SPDEs) with locally monotone coefficients in generalized variational framework. The main result could be…

This paper investigates the robust linear discriminant analysis (LDA) problem with elliptical distributions in high-dimensional data. We propose a robust classification method, named SSLDA, that is intended to withstand heavy-tailed…