Related papers: Dimension reduction in spatial regression with ker…
Quantile regression (QR) is becoming increasingly popular due to its relevance in many scientific investigations. There is a great amount of work about linear and nonlinear QR models. Specifically, nonparametric estimation of the…
We propose a method for the approximation of high- or even infinite-dimensional feature vectors, which play an important role in supervised learning. The goal is to reduce the size of the training data, resulting in lower storage…
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…
We present a novel kernel-based machine learning algorithm for identifying the low-dimensional geometry of the effective dynamics of high-dimensional multiscale stochastic systems. Recently, the authors developed a mathematical framework…
In this paper, we systematically study the consistency of sliced average variance estimation (SAVE). The findings reveal that when the response is continuous, the asymptotic behavior of SAVE is rather different from that of sliced inverse…
In machine learning models, the estimation of errors is often complex due to distribution bias, particularly in spatial data such as those found in environmental studies. We introduce an approach based on the ideas of importance sampling to…
We aim at finding the value of an explanatory variable, through its expression in a large data-vector, without knowing the link function between the explanatory variable and the data-space. Sliced Inverse Regression (SIR) method allows for…
Learned image compression methods have shown superior rate-distortion performance and remarkable potential compared to traditional compression methods. Most existing learned approaches use stacked convolution or window-based self-attention…
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…
Sufficient dimension reduction (SDR) provides a framework for reducing the predictor space dimension in regression problems. We consider SDR in the context of deterministic functions of several variables such as those arising in computer…
In the field of gestural action recognition, many studies have focused on dimensionality reduction along the spatial axis, to reduce both the variability of gestural sequences expressed in the reduced space, and the computational complexity…
While high-dimensional embedding vectors are being increasingly employed in various tasks like Retrieval-Augmented Generation and Recommendation Systems, popular dimensionality reduction (DR) methods such as PCA and UMAP have rarely been…
We address the problem of sufficient dimension reduction for feature matrices, which arises often in sensor network localization, brain neuroimaging, and electroencephalography analysis. In general, feature matrices have both row- and…
In this paper, we apply shrinkage strategies to estimate regression coefficients efficiently for the high-dimensional multiple regression model, where the number of samples is smaller than the number of predictors. We assume in the sparse…
Censored quantile regression (CQR) has become a valuable tool to study the heterogeneous association between a possibly censored outcome and a set of covariates, yet computation and statistical inference for CQR have remained a challenge…
In this paper, we analyze the spatial information of deep features, and propose two complementary regressions for robust visual tracking. First, we propose a kernelized ridge regression model wherein the kernel value is defined as the…
We introduce data structures for solving robust regression through stochastic gradient descent (SGD) by sampling gradients with probability proportional to their norm, i.e., importance sampling. Although SGD is widely used for large scale…
We propose an algorithmic framework, that employs active subspace techniques, for scalable global optimization of functions with low effective dimension (also referred to as low-rank functions). This proposal replaces the original…
We consider the problem of high-dimensional classification between the two groups with unequal covariance matrices. Rather than estimating the full quadratic discriminant rule, we propose to perform simultaneous variable selection and…
There has been a lot of interest in sufficient dimension reduction (SDR) methodologies as well as nonlinear extensions in the statistics literature. In this note, we use classical results regarding metric spaces and positive definite…