相关论文: Sequential and Simultaneous Distance-based Dimensi…

Residual minimization is a widely used technique for solving Partial Differential Equations in variational form. It minimizes the dual norm of the residual, which naturally yields a saddle-point (min-max) problem over the so-called trial…

Real-world data usually have high dimensionality and it is important to mitigate the curse of dimensionality. High-dimensional data are usually in a coherent structure and make the data in relatively small true degrees of freedom. There are…

This paper proposes a novel kernel approach to linear dimension reduction for supervised learning. The purpose of the dimension reduction is to find directions in the input space to explain the output as effectively as possible. The…

Different unsupervised models for dimensionality reduction like PCA, LLE, Shannon's mapping, tSNE, UMAP, etc. work on different principles, hence, they are difficult to compare on the same ground. Although they are usually good for…

With the increase in the amount of data and the expansion of model scale, distributed parallel training becomes an important and successful technique to address the optimization challenges. Nevertheless, although distributed stochastic…

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…

Sufficient dimension reduction is widely applied to help model building between the response $Y$ and covariate $X$. While the target of interest is the relationship between $(Y,X)$, in some applications we also collect additional variable…

R2 score is the standard metric for evaluating regression tasks, offering a normalized magnitude-agnostic measure of accuracy that captures variance. However, R2 has three key limitations: it is limited to at most two dimensional inputs, it…

Dimension reduction techniques, such as Sufficient Dimension Reduction (SDR), are indispensable for analyzing high-dimensional datasets. This paper introduces a novel SDR method named Principal Square Response Forward Regression (PSRFR) for…

Precise characterization of three-dimensional heterogeneous media is indispensable in finding the relationships between structure and macroscopic physical properties (permeability, conductivity, and others). The most widely used…

Document image dewarping remains a challenging task in the deep learning era. While existing methods have improved by leveraging text line awareness, they typically focus only on a single horizontal dimension. In this paper, we propose a…

We revisit the widely used bss eval metrics for source separation with an eye out for performance. We propose a fast algorithm fixing shortcomings of publicly available implementations. First, we show that the metrics are fully specified by…

This paper introduces AdaSDCA: an adaptive variant of stochastic dual coordinate ascent (SDCA) for solving the regularized empirical risk minimization problems. Our modification consists in allowing the method adaptively change the…

The state-of-the-art methods for solving optimization problems in big dimensions are variants of randomized coordinate descent (RCD). In this paper we introduce a fundamentally new type of acceleration strategy for RCD based on the…

Dimension reduction is often the first step in statistical modeling or prediction of multivariate spatial data. However, most existing dimension reduction techniques do not account for the spatial correlation between observations and do not…

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

In this paper, we focus on a class of decentralized constraint-coupled optimization problem: $\min_{x_i \in \mathbb{R}^{d_i}, i \in \mathcal{I}; y \in \mathbb{R}^p}$ $\sum_{i=1}^n\left(f_i(x_i) + g_i(x_i)\right) + h(y) \ \text{s.t.} \…

Recently, Su and Cook proposed a dimension reduction technique called the inner envelope which can be substantially more efficient than the original envelope or existing dimension reduction techniques for multivariate regression. However,…

Multivariate signal processing is often based on dimensionality reduction techniques. We propose a new method, Dynamical Component Analysis (DyCA), leading to a classification of the underlying dynamics and - for a certain type of dynamics…

High-resolution remote sensing images contain densely distributed objects with pronounced scale variations and complex boundaries, which impose higher demands on both the geometric localization and semantic prediction capabilities of…