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Deep neural networks have exhibited remarkable performance in image super-resolution (SR) tasks by learning a mapping from low-resolution (LR) images to high-resolution (HR) images. However, the SR problem is typically an ill-posed problem…
Graph Contrastive Learning (GCL) has shown promising performance in graph representation learning (GRL) without the supervision of manual annotations. GCL can generate graph-level embeddings by maximizing the Mutual Information (MI) between…
We propose a metric learning paradigm, Regression-based Elastic Metric Learning (REML), which optimizes the elastic metric for geodesic regression on the manifold of discrete curves. Geodesic regression is most accurate when the chosen…
In the regression setting, dimension reduction allows for complicated regression structures to be detected via visualization in a low-dimension framework. However, some popular dimension reduction methodologies fail to achieve this aim when…
High-dimensional data analysis has been an active area, and the main focuses have been variable selection and dimension reduction. In practice, it occurs often that the variables are located on an unknown, lower-dimensional nonlinear…
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…
Sliced Inverse Regression (SIR) is an effective method for dimension reduction in high-dimensional regression problems. The original method, however, requires the inversion of the predictors covariance matrix. In case of collinearity…
Linear dimensionality reduction methods are a cornerstone of analyzing high dimensional data, due to their simple geometric interpretations and typically attractive computational properties. These methods capture many data features of…
A major family of sufficient dimension reduction (SDR) methods, called inverse regression, commonly require the distribution of the predictor $X$ to have a linear $E(X|\beta^\mathsf{T}X)$ and a degenerate $\mathrm{var}(X|\beta^\mathsf{T}X)$…
This paper presents a unified framework for sufficient dimension reduction (SDR) that generalizes several existing SDR techniques and offers new insights into the connection between inverse conditional moment independence and dimension…
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…
Scene coordinate regression (SCR) methods have emerged as a promising area of research due to their potential for accurate visual localization. However, many existing SCR approaches train on samples from all image regions, including dynamic…
Utilizing recently developed abstract notions of sectional curvature, we introduce a method for constructing a curvature-based geometric profile of discrete metric spaces. The curvature concept that we use here captures the metric relations…
Rank regression offers robustness to outliers and heavy-tailed response distributions, invariance to monotonic transformations, and improved efficiency under non-Gaussian errors, making it a versatile tool for analyzing complex data. This…
The goal of supervised representation learning is to construct effective data representations for prediction. Among all the characteristics of an ideal nonparametric representation of high-dimensional complex data, sufficiency, low…
Computer experiments with quantitative and qualitative inputs are widely used to study many scientific and engineering processes. Much of the existing work has focused on design and modeling or process optimization for such experiments.…
Graph Contrastive Learning (GCL) has emerged as a powerful tool for extracting consistent representations from graphs, independent of labeled information. However, existing methods predominantly focus on undirected graphs, disregarding the…
Considering the case where the response variable is a categorical variable and the predictor is a random function, two novel functional sufficient dimensional reduction (FSDR) methods are proposed based on mutual information and square loss…
Sufficient dimension reduction (SDR) is a valuable approach for handling high-dimensional data. Outer Product Gradient (OPG) is an popular approach. However, because of focusing the mean regression function, OPG may ignore some directions…
Sufficient dimension reduction is used pervasively as a supervised dimension reduction approach. Most existing sufficient dimension reduction methods are developed for data with a continuous response and may have an unsatisfactory…