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Gaussian-Bernoulli restricted Boltzmann machines (GBRBMs) are often used for semi-supervised anomaly detection, where they are trained using only normal data points. In GBRBM-based anomaly detection, normal and anomalous data are classified…
A linear Gaussian state-space smoothing algorithm is presented for estimation of derivatives from a sequence of noisy measurements. The algorithm uses numerically stable square-root formulas, can handle simultaneous independent measurements…
An analysis of high-dimensional data can offer a detailed description of a system but is often challenged by the curse of dimensionality. General dimensionality reduction techniques can alleviate such difficulty by extracting a few…
Anomaly detection is the process of finding data points that deviate from a baseline. In a real-life setting, anomalies are usually unknown or extremely rare. Moreover, the detection must be accomplished in a timely manner or the risk of…
In an era of ubiquitous large-scale streaming data, the availability of data far exceeds the capacity of expert human analysts. In many settings, such data is either discarded or stored unprocessed in datacenters. This paper proposes a…
This paper addresses the statistical estimation of Gaussian Mixture Models (GMMs) with unknown diagonal covariances from independent and identically distributed samples. We employ the Beurling-LASSO (BLASSO), a convex optimization framework…
Fine-grained anomaly detection has recently been dominated by segmentation based approaches. These approaches first classify each element of the sample (e.g., image patch) as normal or anomalous and then classify the entire sample as…
In this study, we focus on sampling from the latent space of generative models built upon autoencoders so as the reconstructed samples are lifelike images. To do to, we introduce a novel post-training sampling algorithm rooted in the…
Graphical model has been widely used to investigate the complex dependence structure of high-dimensional data, and it is common to assume that observed data follow a homogeneous graphical model. However, observations usually come from…
We describe a general technique that yields the first {\em Statistical Query lower bounds} for a range of fundamental high-dimensional learning problems involving Gaussian distributions. Our main results are for the problems of (1) learning…
Mixtures of Gaussian factors are powerful tools for modeling an unobserved heterogeneous population, offering - at the same time - dimension reduction and model-based clustering. Unfortunately, the high prevalence of spurious solutions and…
We present a method based on unsupervised machine learning to identify regions of interest using particle velocity distributions as a signature pattern. An automatic density estimation technique is applied to particle distributions provided…
Anomalies are those deviating from the norm. Unsupervised anomaly detection often translates to identifying low density regions. Major problems arise when data is high-dimensional and mixed of discrete and continuous attributes. We propose…
Modern distributed cyber-physical systems (CPSs) encounter a large variety of physical faults and cyber anomalies and in many cases, they are vulnerable to catastrophic fault propagation scenarios due to strong connectivity among the…
Detecting anomalous activity in human mobility data has a number of applications including road hazard sensing, telematic based insurance, and fraud detection in taxi services and ride sharing. In this paper we address two challenges that…
In medical imaging, obtaining large amounts of labeled data is often a hurdle, because annotations and pathologies are scarce. Anomaly detection is a method that is capable of detecting unseen abnormal data while only being trained on…
Recently developed techniques have made it possible to quickly learn accurate probability density functions from data in low-dimensional continuous space. In particular, mixtures of Gaussians can be fitted to data very quickly using an…
High-dimensional feature spaces in particle physics events pose a fundamental challenge to density-estimation-based weakly supervised anomaly detection, whose fidelity degrades rapidly with an increasing number of dimensions. We propose a…
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.…
In this paper, we outline the use of Mixture Models in density estimation of large astronomical databases. This method of density estimation has been known in Statistics for some time but has not been implemented because of the large…