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Principal Component Analysis (PCA) has wide applications in machine learning, text mining and computer vision. Classical PCA based on a Gaussian noise model is fragile to noise of large magnitude. Laplace noise assumption based PCA methods…

Functional data typically contains amplitude and phase variation. In many data situations, phase variation is treated as a nuisance effect and is removed during preprocessing, although it may contain valuable information. In this note, we…

High-dimensional data often exhibit dependencies among variables that violate the isotropic-noise assumption under which principal component analysis (PCA) is optimal. For cases where the noise is not independent and identically distributed…

The Laser Interferometer Space Antenna (LISA) will explore the source-rich milli-Hertz band of the gravitational wave spectrum. In contrast to ground based detectors, where typical signals are short-lived and discrete, LISA signals are…

Despite the rapid development of computational hardware, the treatment of large and high dimensional data sets is still a challenging problem. This paper provides a twofold contribution to the topic. First, we propose a Gaussian Mixture…

Searching for a modified dispersion relation is one of the general relativity tests performed by the LIGO-Virgo-KAGRA collaboration with each new cumulative Gravitational Wave Transient Catalog (GWTC). It considers classes of theories that…

The worldwide LIGO-Virgo-KAGRA network of gravitational-wave (GW) detectors continues to increase in sensitivity, thus increasing the quantity and quality of the detected GW signals from compact binary coalescences. These signals allow us…

We develop a new principal components analysis (PCA) type dimension reduction method for binary data. Different from the standard PCA which is defined on the observed data, the proposed PCA is defined on the logit transform of the success…

Extracting gravitational wave (GW) signals from individual Galactic binaries (GBs) against their self-generated confusion noise is a key data analysis challenge for space-borne detectors operating in the $\approx 0.1$ mHz to $\approx 10$…

We explore the use of principal component analysis (PCA) to characterize high-fidelity simulations and interferometric observations of the millimeter emission that originates near the horizons of accreting black holes. We show…

Our current understanding is that an environment - mainly consisting of gas or stars - is required to bring massive black hole binaries (MBHBs) with total redshifted mass $M_z\sim[10^{4},10^7]~{\rm M}_\odot$ to the LISA band from parsec…

Previous versions of sparse principal component analysis (PCA) have presumed that the eigen-basis (a $p \times k$ matrix) is approximately sparse. We propose a method that presumes the $p \times k$ matrix becomes approximately sparse after…

Upcoming space-based gravitational-wave detectors will be sensitive to millions and resolve tens of thousands of stellar-mass binary systems at mHz frequencies. The vast majority of these will be double white dwarfs in our Galaxy. The…

With strong evidence of a common-spectrum stochastic process in the most recent datasets from the NANOGrav Collaboration, the European Pulsar Timing Array (PTA), Parkes PTA, and the International PTA, it is crucial to assess the effects of…

We apply state-of-the-art, likelihood-free statistical inference (machine-learning-based) techniques for reconstructing the spectral shape of a gravitational wave background (GWB). We focus on the reconstruction of an arbitrarily shaped…

The space-based gravitational wave detector LISA will observe mergers of massive black hole binary systems (MBHBs) to cosmological distances, as well as inspiralling stellar-origin (or stellar-mass) binaries (SBHBs) years before they enter…

Alternative theories of gravity predict modifications in the propagation of gravitational waves (GW) through space-time. One of the smoking-gun predictions of such theories is the change in the GW luminosity distance to GW sources as a…

Principal component analysis (PCA) is a classical feature extraction method, but it may be adversely affected by outliers, resulting in inaccurate learning of the projection matrix. This paper proposes a robust method to estimate both the…

In the realm of statistical learning, the increasing volume of accessible data and increasing model complexity necessitate robust methodologies. This paper explores two branches of robust Bayesian methods in response to this trend. The…

Principal component analysis (PCA) is recognised as a quintessential data analysis technique when it comes to describing linear relationships between the features of a dataset. However, the well-known sensitivity of PCA to non-Gaussian…