Related papers: Parametrized tests of post-Newtonian theory using …

Gravitational waves enable tests of general relativity in the highly dynamical and strong-field regime. Using events detected by LIGO-Virgo up to 1 October 2019, we evaluate the consistency of the data with predictions from the theory. We…

A general asymptotic framework is developed for studying consis- tency properties of principal component analysis (PCA). Our frame- work includes several previously studied domains of asymptotics as special cases and allows one to…

One of the main tasks for present and future dark energy surveys is to determine whether the dark energy is dynamical or not. To illustrate this from data, it is commonly used to parameterize the dark energy equation of state w as several…

We study parameter estimation with post-Newtonian (PN) gravitational waveforms for the quasi-circular, adiabatic inspiral of spinning binary compact objects. The performance of amplitude-corrected waveforms is compared with that of the more…

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…

Principal component analysis (PCA) is a well-established tool in machine learning and data processing. The principal axes in PCA were shown to be equivalent to the maximum marginal likelihood estimator of the factor loading matrix in a…

Principal component analysis (PCA) is commonly used in genetics to infer and visualize population structure and admixture between populations. PCA is often interpreted in a way similar to inferred admixture proportions, where it is assumed…

We consider a family of vector dot products that can be implemented using sign changes and addition operations only. The dot products are energy-efficient as they avoid the multiplication operation entirely. Moreover, the dot products…

Tracing of the magnetic field with Velocity Gradient Technique (VGT) allows observers to probe magnetic field directions with spectroscopic data. In this paper, we employ the method of Principal Component Analysis (PCA) to extract the…

When the dimension of data is comparable to or larger than the number of data samples, Principal Components Analysis (PCA) may exhibit problematic high-dimensional noise. In this work, we propose an Empirical Bayes PCA method that reduces…

Recently, the robustification of principal component analysis has attracted lots of attention from statisticians, engineers and computer scientists. In this work we study the type of outliers that are not necessarily apparent in the…

In recent years, Artificial Intelligence techniques have proved to be very successful when applied to problems in physical sciences. Here we apply an unsupervised Machine Learning (ML) algorithm called Principal Component Analysis (PCA) as…

Probabilistic principal component analysis (PPCA) seeks a low dimensional representation of a data set in the presence of independent spherical Gaussian noise, Sigma = (sigma^2)*I. The maximum likelihood solution for the model is an…

Gravitational wave (GW) observations provide a unique opportunity to test Einstein's General Relativity (GR) in the strong-field regime. While GR predicts only two tensor polarization modes, generic metric theories allow up to six…

Machine Learning models are prone to fail when test data are different from training data, a situation often encountered in real applications known as distribution shift. While still valid, the training-time knowledge becomes less…

The Laser Interferometric Space Antenna (LISA) will observe supermassive black hole binary mergers with amplitude signal-to-noise ratio of several thousands. We investigate the extent to which such observations afford high-precision tests…

Principal component analysis (PCA) is one of the most popular dimension reduction techniques in statistics and is especially powerful when a multivariate distribution is concentrated near a lower-dimensional subspace. Multivariate extreme…

Sparse Principal Component Analysis (sparse PCA) is a fundamental dimension-reduction tool that enhances interpretability in various high-dimensional settings. An important variant of sparse PCA studies the scenario when samples are…

In this paper we develop a new approach to sparse principal component analysis (sparse PCA). We propose two single-unit and two block optimization formulations of the sparse PCA problem, aimed at extracting a single sparse dominant…

Principal component analysis (PCA) is widely used for feature extraction and dimensionality reduction, with documented merits in diverse tasks involving high-dimensional data. Standard PCA copes with one dataset at a time, but it is…