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Gaussian process regression (GPR) or kernel ridge regression is a widely used and powerful tool for nonlinear prediction. Therefore, active learning (AL) for GPR, which actively collects data labels to achieve an accurate prediction with…
In cluster tomography, we propose measuring the number of clusters $N$ intersected by a line segment of length $\ell$ across a finite sample. As expected, the leading order of $N(\ell)$ scales as $a\ell$, where $a$ depends on microscopic…
We assess the effect of magnification bias on the $E_G$ statistic for probing gravity. $E_G$, a statistic constructed from power spectrum estimates of both weak lensing and redshift space distortions (RSD), directly tests general relativity…
Testing for a mediation effect is important in many disciplines, but is made difficult - even asymptotically - by the influence of nuisance parameters. Classical tests such as likelihood ratio (LR) and Wald (Sobel) tests have very poor…
The statistics of gravitational arcs in galaxy clusters is a powerful probe of cluster structure and may provide complementary cosmological constraints. Despite recent progresses, discrepancies still remain among modelling and observations…
Multi-label image recognition with partial labels (MLR-PL) is designed to train models using a mix of known and unknown labels. Traditional methods rely on semantic or feature correlations to create pseudo-labels for unidentified labels…
The use of data-random graphs in statistical testing of spatial patterns is introduced recently. In this approach, a random directed graph is constructed from the data using the relative positions of the points from various classes.…
One of the major goals of cosmological observations is to test theories of structure formation. The most straightforward way to carry out such tests is to compute the likelihood function L, the probability of getting the data given the…
Previous analyses of cosmic rays above 40 EeV observed by the AGASA experiment have suggested that their arrival directions may be clustered. However, estimates of the chance probability of this clustering signal vary from 10^{-2} to…
Spectral clustering is one of the most popular clustering methods for finding clusters in a graph, which has found many applications in data mining. However, the input graph in those applications may have many missing edges due to error in…
The most widely used internal measure for clustering evaluation is the silhouette coefficient, whose naive computation requires a quadratic number of distance calculations, which is clearly unfeasible for massive datasets. Surprisingly,…
In the context of cluster analysis and graph partitioning, many external evaluation measures have been proposed in the literature to compare two partitions of the same set. This makes the task of selecting the most appropriate measure for a…
In this paper the influence of galaxy cluster halo environment on the deflection properties of its galaxies is investigated. For this purpose circular and elliptical projected cluster haloes obeying Einasto density profiles are multiply…
Accurate modelling of spectra produced by X-ray sources requires the use of Monte-Carlo simulations. These simulations need to evaluate physical processes, such as those occurring in accretion processes around compact objects by sampling a…
Local general depth ($LGD$) functions are used for describing the local geometric features and mode(s) in multivariate distributions. In this paper, we undertake a rigorous systematic study of $LGD$ and establish several analytical and…
We derive adjusted signed likelihood ratio statistics for a general class of extreme value regression models. The adjustments reduce the error in the standard normal approximation to the distribution of the signed likelihood ratio…
Super-sample covariance (SSC) is the dominant source of statistical error on large scale structure (LSS) observables for both current and future galaxy surveys. In this work, we concentrate on the SSC of cluster counts, also known as sample…
Galaxy cluster surveys offer great promise for measuring cosmological parameters, but survey analysis methods have not been widely studied. Using methods developed decades ago for galaxy clustering studies, it is shown that nearly exact…
Population annealing is a powerful sequential Monte Carlo algorithm designed to study the equilibrium behavior of general systems in statistical physics through massive parallelism. In addition to the remarkable scaling capabilities of the…
Landing probabilities (LP) of random walks (RW) over graphs encode rich information regarding graph topology. Generalized PageRanks (GPR), which represent weighted sums of LPs of RWs, utilize the discriminative power of LP features to…