Related papers: Sufficient Dimension Reduction via Random-Partitio…

Over the past few decades, we have witnessed a large family of algorithms that have been designed to provide different solutions to the problem of dimensionality reduction (DR). The DR is an essential tool to excavate the important…

Supervised dimension reduction (SDR) has been a topic of growing interest in data science, as it enables the reduction of high-dimensional covariates while preserving the functional relation with certain response variables of interest.…

Prediction, in regression and classification, is one of the main aims in modern data science. When the number of predictors is large, a common first step is to reduce the dimension of the data. Sufficient dimension reduction (SDR) is a well…

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…

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…

Scalability of statistical estimators is of increasing importance in modern applications and dimension reduction is often used to extract relevant information from data. A variety of popular dimension reduction approaches can be framed as…

Dimensionality reduction techniques play important roles in the analysis of big data. Traditional dimensionality reduction approaches, such as principal component analysis (PCA) and linear discriminant analysis (LDA), have been studied…

For multiple index models, it has recently been shown that the sliced inverse regression (SIR) is consistent for estimating the sufficient dimension reduction (SDR) space if and only if $\rho=\lim\frac{p}{n}=0$, where $p$ is the dimension…

We propose a novel approach to sufficient dimension reduction in regression, based on estimating contour directions of small variation in the response. These directions span the orthogonal complement of the minimal space relevant for the…

This paper discusses the critical decision process of extracting or selecting the features in a supervised learning context. It is often confusing to find a suitable method to reduce dimensionality. There are pros and cons to deciding…

Sufficient dimension reduction (SDR) in regression, which reduces the dimension by replacing original predictors with a minimal set of their linear combinations without loss of information, is very helpful when the number of predictors is…

We provide here a framework to analyze the phase transition phenomenon of slice inverse regression (SIR), a supervised dimension reduction technique introduced by \cite{Li:1991}. Under mild conditions, the asymptotic ratio $\rho= \lim p/n$…

The statistical problem of estimating the effective dimension-reduction (EDR) subspace in the multi-index regression model with deterministic design and additive noise is considered. A new procedure for recovering the directions of the EDR…

Stochastic gradient descent (SGD) provides a simple and efficient way to solve a broad range of machine learning problems. Here, we focus on distribution regression (DR), involving two stages of sampling: Firstly, we regress from…

We consider the problem of sufficient dimension reduction (SDR) for multi-index models. The estimators of the central mean subspace in prior works either have slow (non-parametric) convergence rates, or rely on stringent distributional…

Data are not only ubiquitous in society, but are increasingly complex both in size and dimensionality. Dimension reduction offers researchers and scholars the ability to make such complex, high dimensional data spaces simpler and more…

In NMR spectroscopy, undersampling in the indirect dimensions causes reconstruction artifacts whose size can be bounded using the so-called {\it coherence}. In experiments with multiple indirect dimensions, new undersampling approaches were…

Dimensionality reduction (DR) algorithms compress high-dimensional data into a lower dimensional representation while preserving important features of the data. DR is a critical step in many analysis pipelines as it enables visualisation,…

Dimensionality reduction (DR) on the manifold includes effective methods which project the data from an implicit relational space onto a vectorial space. Regardless of the achievements in this area, these algorithms suffer from the lack of…

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…