Related papers: Sufficient Dimension Reduction for High-Dimensiona…
We consider supervised dimension reduction problems, namely to identify a low dimensional projection of the predictors $\-x$ which can retain the statistical relationship between $\-x$ and the response variable $y$. We follow the idea of…
We propose a new method, semi-penalized inference with direct false discovery rate control (SPIDR), for variable selection and confidence interval construction in high-dimensional linear regression. SPIDR first uses a semi-penalized…
In an era where big and high-dimensional data is readily available, data scientists are inevitably faced with the challenge of reducing this data for expensive downstream computation or analysis. To this end, we present here a new method…
In regression analysis, we employ contour projection (CP) to develop a new dimension reduction theory. Accordingly, we introduce the notions of the central contour subspace and generalized contour subspace. We show that both of their…
Deep neural networks dominate modern machine learning, while alternative function approximators remain comparatively underexplored at scale. In this work, we revisit kernel methods as drop-in components for standard deep learning pipelines.…
In recent years, accelerated MRI reconstruction based on deep learning has led to significant improvements in image quality with impressive results for high acceleration factors. However, from a clinical perspective image quality is only…
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…
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…
The development and use of dimension reduction methods is prevalent in modern statistical literature. This paper reviews a class of dimension reduction techniques which aim to simultaneously select relevant predictors and find clusters…
Density ratio estimation (DRE) is a paramount task in machine learning, for its broad applications across multiple domains, such as covariate shift adaptation, causal inference, independence tests and beyond. Parametric methods for…
We study principal components regression (PCR) in an asymptotic high-dimensional regression setting, where the number of data points is proportional to the dimension. We derive exact limiting formulas for the estimation and prediction…
Ensemble Conditional Variance Estimation (ECVE) is a novel sufficient dimension reduction (SDR) method in regressions with continuous response and predictors. ECVE applies to general non-additive error regression models. It operates under…
We propose methodologies to train highly accurate and efficient deep convolutional neural networks (CNNs) for image super resolution (SR). A cascade training approach to deep learning is proposed to improve the accuracy of the neural…
The current study proposes a dimension reduction method, stepwise support vector machine (SVM), to reduce the dimensions of large p small n datasets. The proposed method is compared with other dimension reduction methods, namely, the…
Many statistical estimation techniques for high-dimensional or functional data are based on a preliminary dimension reduction step, which consists in projecting the sample $\bX_1, \hdots, \bX_n$ onto the first $D$ eigenvectors of the…
Moment-based distributionally robust optimization (DRO) provides an optimization framework to integrate statistical information with traditional optimization approaches. Under this framework, one assumes that the underlying joint…
We present a general framework of semi-supervised dimensionality reduction for manifold learning which naturally generalizes existing supervised and unsupervised learning frameworks which apply the spectral decomposition. Algorithms derived…
Recent advances in machine learning allow us to analyze and describe the content of high-dimensional data like text, audio, images or other signals. In order to visualize that data in 2D or 3D, usually Dimensionality Reduction (DR)…
We develop an exact coordinate descent algorithm for high-dimensional regularized Huber regression. In contrast to composite gradient descent methods, our algorithm fully exploits the advantages of coordinate descent when the underlying…
In this paper, we consider regression models with a Hilbert-space-valued predictor and a scalar response, where the response depends on the predictor only through a finite number of projections. The linear subspace spanned by these…