Related papers: Dimensionality Reduction Techniques for Statistica…
We introduce a data-driven order reduction method for nonlinear control systems, drawing on recent progress in machine learning and statistical dimensionality reduction. The method rests on the assumption that the nonlinear system behaves…
Utilizing recently developed abstract notions of sectional curvature, we introduce a method for constructing a curvature-based geometric profile of discrete metric spaces. The curvature concept that we use here captures the metric relations…
We propose a class of dimension reduction methods for right censored survival data using a counting process representation of the failure process. Semiparametric estimating equations are constructed to estimate the dimension reduction…
Linear models are used in online decision making, such as in machine learning, policy algorithms, and experimentation platforms. Many engineering systems that use linear models achieve computational efficiency through distributed systems…
The vast majority of Dimensionality Reduction (DR) techniques rely on second-order statistics to define their optimization objective. Even though this provides adequate results in most cases, it comes with several shortcomings. The methods…
We derive constraints on a coupled quintessence model with pure momentum exchange from the public $\sim$1000 deg$^2$ cosmic shear measurements from the Kilo-Degree Survey and the $\it{Planck}$ 2018 Cosmic Microwave Background data. We…
An efficient computational approach for optimal reconstructing parameters of binary-type physical properties for models in biomedical applications is developed and validated. The methodology includes gradient-based multiscale optimization…
CMB anisotropy data could put powerful constraints on theories of the evolution of our Universe. Using the observations of the large number of CMB experiments, many studies have put constraints on cosmological parameters assuming different…
Bayesian statistics and Markov Chain Monte Carlo (MCMC) algorithms have found their place in the field of Cosmology. They have become important mathematical and numerical tools, especially in parameter estimation and model comparison. In…
Model compression is a critical area of research in deep learning, in particular in vision, driven by the need to lighten models memory or computational footprints. While numerous methods for model compression have been proposed, most focus…
The recent increase in dimensionality of data has thrown a great challenge to the existing dimensionality reduction methods in terms of their effectiveness. Dimensionality reduction has emerged as one of the significant preprocessing steps…
Weak gravitational lensing is a powerful probe of cosmology, with second-order shear statistics commonly used to constrain parameters such as the matter density $\Omega_\mathrm{m}$ and the clustering amplitude $S_8$. However, parameter…
In this paper, we study the cosmological implications of the 100 square degree Weak Lensing survey (the CFHTLS-Wide, RCS, VIRMOS-DESCART and GaBoDS surveys). We combine these weak lensing data with the cosmic microwave background (CMB)…
Dimension reduction is often an important step in the analysis of high-dimensional data. PCA is a popular technique to find the best low-dimensional approximation of high-dimensional data. However, classical PCA is very sensitive to…
We use the spherical collapse method to investigate the non-linear density perturbations of pressureless matter in the cosmological models with the extended quintessence as dark energy in the metric and Palatini formalisms. We find that for…
The problem of finding a reduced dimensionality representation of categorical variables while preserving their most relevant characteristics is fundamental for the analysis of complex data. Specifically, given a co-occurrence matrix of two…
Motivation: Biomedical studies increasingly produce multi-view high-dimensional datasets (e.g., multi-omics) that demand integrative analysis. Existing canonical correlation analysis (CCA) and generalized CCA methods address at most two of…
Linear dimensionality reduction methods are commonly used to extract low-dimensional structure from high-dimensional data. However, popular methods disregard temporal structure, rendering them prone to extracting noise rather than…
We present cosmological constraints derived from peak counts, minimum counts, and the angular power spectrum of the Subaru Hyper Suprime-Cam first-year (HSC Y1) weak lensing shear catalog. Weak lensing peak and minimum counts contain…
Autoencoders (AE) provide a useful method for nonlinear dimensionality reduction but are ill-suited for low data regimes. Conversely, Principal Component Analysis (PCA) is data-efficient but is limited to linear dimensionality reduction,…