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Observations in data which are significantly different from its neighbouring points but cannot be classified as noise are known as anomalies or outliers. These anomalies are a cause of concern and a timely warning about their presence could…

We extend the recent sparse Fourier transform algorithm of (Lawlor, Christlieb, and Wang, 2013) to the noisy setting, in which a signal of bandwidth N is given as a superposition of k << N frequencies and additive noise. We present two such…

Many models for sparse regression typically assume that the covariates are known completely, and without noise. Particularly in high-dimensional applications, this is often not the case. This paper develops efficient OMP-like algorithms to…

Robust change-point detection for large-scale data streams has many real-world applications in industrial quality control, signal detection, biosurveillance. Unfortunately, it is highly non-trivial to develop efficient schemes due to three…

We present a novel approach for recovering a sparse signal from cross-correlated data. Cross-correlations naturally arise in many fields of imaging, such as optics, holography and seismic interferometry. Compared to the sparse signal…

The problem of denoising a one-dimensional signal possessing varying degrees of smoothness is ubiquitous in time-domain astronomy and astronomical spectroscopy. For example, in the time domain, an astronomical object may exhibit a smoothly…

Scientists aim to extract simplicity from observations of the complex world. An important component of this process is the exploration of data in search of trends. In practice, however, this tends to be more of an art than a science. Among…

This paper evaluates algorithms for classification and outlier detection accuracies in temporal data. We focus on algorithms that train and classify rapidly and can be used for systems that need to incorporate new data regularly. Hence, we…

In this work, we study the problem of common and unique feature extraction from noisy data. When we have N observation matrices from N different and associated sources corrupted by sparse and potentially gross noise, can we recover the…

We consider the problem of estimating the factors of a rank-$1$ matrix with i.i.d. Gaussian, rank-$1$ measurements that are nonlinearly transformed and corrupted by noise. Considering two prototypical choices for the nonlinearity, we study…

Tucker decomposition has been widely used in a variety of applications to obtain latent factors of tensor data. In these applications, a common need is to compute Tucker decomposition for a given time range. Furthermore, real-world tensor…

In this paper we consider the trace regression model. Assume that we observe a small set of entries or linear combinations of entries of an unknown matrix $A_0$ corrupted by noise. We propose a new rank penalized estimator of $A_0$. For…

Timely and accurate detection of anomalies in power electronics is becoming increasingly critical for maintaining complex production systems. Robust and explainable strategies help decrease system downtime and preempt or mitigate…

Often the challenge associated with tasks like fraud and spam detection[1] is the lack of all likely patterns needed to train suitable supervised learning models. In order to overcome this limitation, such tasks are attempted as outlier or…

Nonnegative matrix factorization (NMF) is a powerful technique for dimension reduction, extracting latent factors and learning part-based representation. For large datasets, NMF performance depends on some major issues: fast algorithms,…

Permutation patterns and pattern avoidance have been intensively studied in combinatorics and computer science, going back at least to the seminal work of Knuth on stack-sorting (1968). Perhaps the most natural algorithmic question in this…

Detecting anomalies in temporal data has gained significant attention across various real-world applications, aiming to identify unusual events and mitigate potential hazards. In practice, situations often involve a mix of segment-level…

This paper establishes theoretical bonafides for implicit concurrent multivariate effect evaluation--implicit concurrency for short---a broad and versatile computational learning efficiency thought to underlie general-purpose, non-local,…

In many problems in Computational Physics and Chemistry, one finds a special kind of sparse matrices, termed "banded matrices". These matrices, which are defined as having non-zero entries only within a given distance from the main…

We present a matrix-factorization algorithm that scales to input matrices with both huge number of rows and columns. Learned factors may be sparse or dense and/or non-negative, which makes our algorithm suitable for dictionary learning,…