Related papers: A Subspace-based Approach for Dimensionality Reduc…

Experimental life sciences like biology or chemistry have seen in the recent decades an explosion of the data available from experiments. Laboratory instruments become more and more complex and report hundreds or thousands measurements for…

Standard approaches for variable selection in linear models are not tailored to deal properly with high-dimensional and incomplete data. Currently, methods dedicated to high-dimensional data handle missing values by ad-hoc strategies, like…

Bayesian inverse problems use observed data to update a prior probability distribution for an unknown state or parameter of a scientific system to a posterior distribution conditioned on the data. In many applications, the unknown parameter…

Sufficient dimension reduction aims for reduction of dimensionality of a regression without loss of information by replacing the original predictor with its lower-dimensional subspace. Partial (sufficient) dimension reduction arises when…

Multiple time scale stochastic dynamical systems are ubiquitous in science and engineering, and the reduction of such systems and their models to only their slow components is often essential for scientific computation and further analysis.…

Movement primitives are an important policy class for real-world robotics. However, the high dimensionality of their parametrization makes the policy optimization expensive both in terms of samples and computation. Enabling an efficient…

Variable selection in high-dimensional scenarios is of great interested in statistics. One application involves identifying differentially expressed genes in genomic analysis. Existing methods for addressing this problem have some limits or…

Dimensionality reduction techniques are fundamental for analyzing and visualizing high-dimensional data. With established methods like t-SNE and PCA presenting a trade-off between representational power and interpretability. This paper…

In many modern data sets, High dimension low sample size (HDLSS) data is prevalent in many fields of studies. There has been an increased focus recently on using machine learning and statistical methods to mine valuable information out of…

Dimensionality reduction has become an important research topic as demand for interpreting high-dimensional datasets has been increasing rapidly in recent years. There have been many dimensionality reduction methods with good performance in…

Data visualization is the process by which data of any size or dimensionality is processed to produce an understandable set of data in a lower dimensionality, allowing it to be manipulated and understood more easily by people. The goal of…

We develop a linear-algebraic framework for dimensional analysis in systems with constraints, particularly when variables are numerous or related by implicit relations so that direct elimination is impractical. By expressing both…

Large scale dynamical systems (e.g. many nonlinear coupled differential equations) can often be summarized in terms of only a few state variables (a few equations), a trait that reduces complexity and facilitates exploration of behavioral…

The unprecedented prowess of measurement techniques provides a detailed, multi-scale look into the depths of living systems. Understanding these avalanches of high-dimensional data -- by distilling underlying principles and mechanisms --…

We propose a new randomized optimization method for high-dimensional problems which can be seen as a generalization of coordinate descent to random subspaces. We show that an adaptive sampling strategy for the random subspace significantly…

The technique of subsampling has been extensively employed to address the challenges posed by limited computing resources and meet the needs for expedite data analysis. Various subsampling methods have been developed to meet the challenges…

Visual analytics now plays a central role in decision-making across diverse disciplines, but it can be unreliable: the knowledge or insights derived from the analysis may not accurately reflect the underlying data. In this dissertation, we…

Random projection is widely used as a method of dimension reduction. In recent years, its combination with standard techniques of regression and classification has been explored. Here we examine its use with principal component analysis…

Manifold learning is used for dimensionality reduction, with the goal of finding a projection subspace to increase and decrease the inter- and intraclass variances, respectively. However, a bottleneck for subspace learning methods often…

Modern day engineering problems are ubiquitously characterized by sophisticated computer codes that map parameters or inputs to an underlying physical process. In other situations, experimental setups are used to model the physical process…