Related papers: Dimensionality Reduction Techniques for Statistica…
High-resolution stellar spectra offer valuable insights into atmospheric parameters and chemical compositions. However, their inherent complexity and high-dimensionality present challenges in fully utilizing the information they contain. In…
We introduce the Linearized Diffusion Map (LDM), a novel linear dimensionality reduction method constructed via a linear approximation of the diffusion-map kernel. LDM integrates the geometric intuition of diffusion-based nonlinear methods…
Overparameterized models have proven to be powerful tools for solving various machine learning tasks. However, overparameterization often leads to a substantial increase in computational and memory costs, which in turn requires extensive…
Cosmography, as an integral branch of cosmology, strives to characterize the Universe without relying on pre-determined cosmological models. This model-independent approach utilizes Taylor series expansions around the current epoch,…
Data visualisation helps understanding data represented by multiple variables, also called features, stored in a large matrix where individuals are stored in lines and variable values in columns. These data structures are frequently called…
Neural networks appear to have mysterious generalization properties when using parameter counting as a proxy for complexity. Indeed, neural networks often have many more parameters than there are data points, yet still provide good…
Dimensionality Reduction (DR) techniques can generate 2D projections and enable visual exploration of cluster structures of high-dimensional datasets. However, different DR techniques would yield various patterns, which significantly affect…
Weak-lensing mass-mapping algorithms, which reconstruct the convergence field from galaxy shear measurements, are crucial for extracting higher-order statistics to constrain cosmological parameters. However, only limited research has…
Dimensionality reduction is a main step in the learning process which plays an essential role in many applications. The most popular methods in this field like SVD, PCA, and LDA, only can be applied to data with vector format. This means…
Bayesian optimization works effectively optimizing parameters in black-box problems. However, this method did not work for high-dimensional parameters in limited trials. Parameters can be efficiently explored by nonlinearly embedding them…
Sufficient dimension reduction [J. Amer. Statist. Assoc. 86 (1991) 316-342] has long been a prominent issue in multivariate nonparametric regression analysis. To uncover the central dimension reduction space, we propose in this paper an…
Precise estimation of cosmological parameters from the cosmic microwave background (CMB) remains a central goal of modern cosmology and a key test of inflationary physics. However, this task is fundamentally limited by strong foreground…
As an alternative to variable selection or shrinkage in high dimensional regression, we propose to randomly compress the predictors prior to analysis. This dramatically reduces storage and computational bottlenecks, performing well when the…
Dimensionality reduction is a crucial step for pattern recognition and data mining tasks to overcome the curse of dimensionality. Principal component analysis (PCA) is a traditional technique for unsupervised dimensionality reduction, which…
Practical applications of nonparametric density estimators in more than three dimensions suffer a great deal from the well-known curse of dimensionality: convergence slows down as dimension increases. We show that one can evade the curse of…
One of the central issues of several machine learning applications on real data is the choice of the input features. Ideally, the designer should select only the relevant, non-redundant features to preserve the complete information…
The ever-increasing parameter counts of deep learning models necessitate effective compression techniques for deployment on resource-constrained devices. This paper explores the application of information geometry, the study of…
A novel method images to estimate cosmological parameters based on images is presented. In this paper, we demonstrate the use of a convolutional neural network (CNN) for constraining the mass of dark matter particle. For this purpose, we…
Projection-based model reduction has become a popular approach to reduce the cost associated with integrating large-scale dynamical systems so they can be used in many-query settings such as optimization and uncertainty quantification. For…
Embedding nonlinear dynamical systems into artificial neural networks is a powerful new formalism for machine learning. By parameterizing ordinary differential equations (ODEs) as neural network layers, these Neural ODEs are…