Related papers: Dimension reduction of high-dimension categorical …
We propose a method for testing whether hierarchically ordered groups of potentially correlated variables are significant for explaining a response in a high-dimensional linear model. In presence of highly correlated variables, as is very…
We introduce a new technique for the efficient management of large sequences of multidimensional data, which takes advantage of regularities that arise in real-world datasets and supports different types of aggregation queries. More…
Dimension reduction is a common strategy to study non-linear dynamical systems composed by a large number of variables. The goal is to find a smaller version of the system whose time evolution is easier to predict while preserving some of…
In this study, we propose a new statical approach for high-dimensionality reduction of heterogenous data that limits the curse of dimensionality and deals with missing values. To handle these latter, we propose to use the Random Forest…
Regression aims at estimating the conditional mean of output given input. However, regression is not informative enough if the conditional density is multimodal, heteroscedastic, and asymmetric. In such a case, estimating the conditional…
The quest for simplification in physics drives the exploration of concise mathematical representations for complex systems. This Dissertation focuses on the concept of dimensionality reduction as a means to obtain low-dimensional…
In this paper we propose a new methodology to represent the results of the robust ordinal regression approach by means of a family of representative value functions for which, taken two alternatives $a$ and $b$, the following two conditions…
This paper explores the extension of dimension reduction (DR) techniques to the multi-dimension case by using the Einstein product. Our focus lies on graph-based methods, encompassing both linear and nonlinear approaches, within both…
This paper addresses the problem of mapping high-dimensional data to a low-dimensional space, in the presence of other known features. This problem is ubiquitous in science and engineering as there are often controllable/measurable features…
The principal support vector machines method (Li et al., 2011) is a powerful tool for sufficient dimension reduction that replaces original predictors with their low-dimensional linear combinations without loss of information. However, the…
We propose dimension reduction methods for sparse, high-dimensional multivariate response regression models. Both the number of responses and that of the predictors may exceed the sample size. Sometimes viewed as complementary, predictor…
Dimension reduction plays a pivotal role in analysing high-dimensional data. However, observations with missing values present serious difficulties in directly applying standard dimension reduction techniques. As a large number of dimension…
This article provides, through theoretical analysis, an in-depth understanding of the classification performance of the empirical risk minimization framework, in both ridge-regularized and unregularized cases, when high dimensional data are…
Relations between categorical variables can be analyzed conveniently by multiple correspondence analysis (MCA). %It is well suited to discover relations that may exist between categories of different variables. The graphical representation…
Nowadays, massive datasets are typically dispersed across multiple locations, encountering dual challenges of high dimensionality and huge sample size. Therefore, it is necessary to explore sufficient dimension reduction (SDR) methods for…
We explore two primary classes of approaches to dimensionality reduction (DR): Independent Dimensionality Reduction (IDR) and Simultaneous Dimensionality Reduction (SDR). In IDR methods, of which Principal Components Analysis is a…
To date, testing interactions in high dimensions has been a challenging task. Existing methods often have issues with sensitivity to modeling assumptions and heavily asymptotic nominal p-values. To help alleviate these issues, we propose a…
We propose a general index model for survival data, which generalizes many commonly used semiparametric survival models and belongs to the framework of dimension reduction. Using a combination of geometric approach in semiparametrics and…
Coupled problems with various combinations of multiple physics, scales, and domains are found in numerous areas of science and engineering. A key challenge in the formulation and implementation of corresponding coupled numerical models is…
This paper proposes a new method for estimating high-dimensional binary choice models. We consider a semiparametric model that places no distributional assumptions on the error term, allows for heteroskedastic errors, and permits endogenous…