Related papers: Simultaneous Dimensionality Reduction: A Data Effi…

Dimensionality reduction plays an important role in computer vision problems since it reduces computational cost and is often capable of yielding more discriminative data representation. In this context, Partial Least Squares (PLS) has…

In ordinary Dimensionality Reduction (DR), each data instance in a high dimensional space (original space), or on a distance matrix denoting original space distances, is mapped to (projected onto) one point in a low dimensional space…

Image retrieval (IR) has emerged as a promising approach for self-localization in unmanned aerial vehicles (UAVs). However, IR-based methods face several challenges: 1) Pre- and post-processing incur significant computational and storage…

Kernel dimensionality reduction (KDR) algorithms find a low dimensional representation of the original data by optimizing kernel dependency measures that are capable of capturing nonlinear relationships. The standard strategy is to first…

Bias is a common problem inherent in recommender systems, which is entangled with users' preferences and poses a great challenge to unbiased learning. For debiasing tasks, the doubly robust (DR) method and its variants show superior…

Distribution Regression (DR) on stochastic processes describes the learning task of regression on collections of time series. Path signatures, a technique prevalent in stochastic analysis, have been used to solve the DR problem. Recent…

Image registration is an ill-posed dense vision task, where multiple solutions achieve similar loss values, motivating probabilistic inference. Variational inference has previously been employed to capture these distributions, however…

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 $\rho= \lim p/n$…

Localizing more sources than sensors with a sparse linear array (SLA) has long relied on minimizing a distance between two covariance matrices and recent algorithms often utilize semidefinite programming (SDP). Although deep neural network…

Dimensionality reduction techniques are widely used for visualizing high-dimensional data in two dimensions. Existing methods are typically designed to preserve either local (e.g., $t$-SNE, UMAP) or global (e.g., MDS, PCA) structure of the…

Existing methods have demonstrated effective performance on a single degradation type. In practical applications, however, the degradation is often unknown, and the mismatch between the model and the degradation will result in a severe…

We develop theory for nonlinear dimensionality reduction (NLDR). A number of NLDR methods have been developed, but there is limited understanding of how these methods work and the relationships between them. There is limited basis for using…

Sliced inverse regression (SIR) is a popular sufficient dimension reduction method that identifies a few linear transformations of the covariates without losing regression information with the response. In high-dimensional settings, SIR can…

Missing data present challenges in data analysis. Naive analyses such as complete-case and available-case analysis may introduce bias and loss of efficiency, and produce unreliable results. Multiple imputation (MI) is one of the most widely…

Due to the intrinsic complexity of high-dimensional (HD) data, dimensionality reduction (DR) techniques cannot preserve all the structural characteristics of the original data. Therefore, DR techniques focus on preserving either local…

This paper introduces robust twoblock (RTB) simultaneous dimension reduction, which is the first statistically robust method to perform simultaneous dimension reduction in two blocks of variables and allows to fine-tune the model complexity…

Reduced-rank linear discriminant analysis (RRLDA) is a foundational method of dimension reduction for classification that has been useful in a wide range of applications. The goal is to identify an optimal subspace to project the…

With the excellent representation capabilities of Pre-Trained Models (PTMs), remarkable progress has been made in non-rehearsal Class-Incremental Learning (CIL) research. However, it remains an extremely challenging task due to three…

In order to process efficiently ever-higher dimensional data such as images, sentences, or audio recordings, one needs to find a proper way to reduce the dimensionality of such data. In this regard, SVD-based methods including PCA and…

Regularization schemes for regression have been widely studied in learning theory and inverse problems. In this paper, we study distribution regression (DR) which involves two stages of sampling, and aims at regressing from probability…