Related papers: Sufficient Component Analysis for Supervised Dimen…
An important theme in modern inverse problems is the reconstruction of time-dependent data from only finitely many measurements. To obtain satisfactory reconstruction results in this setting it is essential to strongly exploit temporal…
Dimension reduction (DR) is inherently non-unique: multiple embeddings can preserve the structure of high-dimensional data equally well while differing in layout or geometry. In this paper, we formally define the Rashomon set for DR -- the…
Kernel Principal Component Analysis (KPCA) is a popular dimensionality reduction technique with a wide range of applications. However, it suffers from the problem of poor scalability. Various approximation methods have been proposed in the…
Probabilistic principal component analysis (PPCA) seeks a low dimensional representation of a data set in the presence of independent spherical Gaussian noise, Sigma = (sigma^2)*I. The maximum likelihood solution for the model is an…
High dimensional data has introduced challenges that are difficult to address when attempting to implement classical approaches of statistical process control. This has made it a topic of interest for research due in recent years. However,…
We propose a novel and computationally efficient approach for nonparametric conditional density estimation in high-dimensional settings that achieves dimension reduction without imposing restrictive distributional or functional form…
High-dimensional variable selection is an important issue in many scientific fields, such as genomics. In this paper, we develop a sure independence feature screening pro- cedure based on kernel canonical correlation analysis (KCCA-SIS, for…
Ultra-high dimensional longitudinal data are increasingly common and the analysis is challenging both theoretically and methodologically. We offer a new automatic procedure for finding a sparse semivarying coefficient model, which is widely…
This paper develops a method to detect model structural changes by applying a Corrected Kernel Principal Component Analysis (CKPCA) to construct the so-called central distribution deviation subspaces. This approach can efficiently identify…
Stochastic gradient descent (SGD) provides a simple and efficient way to solve a broad range of machine learning problems. Here, we focus on distribution regression (DR), involving two stages of sampling: Firstly, we regress from…
Unsupervised dimension selection is an important problem that seeks to reduce dimensionality of data, while preserving the most useful characteristics. While dimensionality reduction is commonly utilized to construct low-dimensional…
Sparse Principal Component Analysis (SPCA) is a fundamental technique for dimensionality reduction, and is NP-hard. In this paper, we introduce a randomized approximation algorithm for SPCA, which is based on the basic SDP relaxation. Our…
In this paper, we study the problem of high-dimensional sparse quadratic discriminant analysis (QDA). We propose a novel classification method, termed SSQDA, which is constructed via constrained convex optimization based on the sample…
Random projection is widely used as a method of dimension reduction. In recent years, its combination with standard techniques of regression and classification has been explored. Here we examine its use with principal component analysis…
Accurate Direction of Arrival (DoA) estimation is critical for applications in robotics and communication, but high costs and complexity of coherent multi-channel receivers hinder accessibility. This work proposes a cost-effective DoA…
Dimensionality reduction is an important step in processing the hyperspectral images (HSI) to overcome the curse of dimensionality problem. Linear dimensionality reduction methods such as Independent component analysis (ICA) and Linear…
Deep domain adaptation methods can reduce the distribution discrepancy by learning domain-invariant embedddings. However, these methods only focus on aligning the whole data distributions, without considering the class-level relations among…
We study semiparametric factor models in high-dimensional panels where the factor loadings consist of a nonparametric component explained by observed covariates and an idiosyncratic component capturing unobserved heterogeneity. A key…
In this paper, we propose a novel framework for non-stationary time-series analysis that replaces conventional correlation-based statistics with direct estimation of statistical dependence in the normalized joint density of input and target…
Precise control over dimension of nanocrystals is critical to tune the properties for various applications. However, the traditional control through experimental optimization is slow, tedious and time consuming. Herein a robust deep neural…