Related papers: Iterative Supervised Principal Components
Variable selection in ultra-high dimensional linear regression is often preceded by a screening step to significantly reduce the dimension. Here we develop a Bayesian variable screening method (BITS) guided by the posterior model…
Data analysis often requires methods that are invariant with respect to specific transformations, such as rotations in case of images or shifts in case of images and time series. While principal component analysis (PCA) is a widely-used…
A common task in inverse problems and imaging is finding a solution that is sparse, in the sense that most of its components vanish. In the framework of compressed sensing, general results guaranteeing exact recovery have been proven. In…
We propose a principal components regression method based on maximizing a joint pseudo-likelihood for responses and predictors. Our method uses both responses and predictors to select linear combinations of the predictors relevant for the…
Over the past decades, the increasing dimensionality of data has increased the need for effective data decomposition methods. Existing approaches, however, often rely on linear models or lack sufficient interpretability or flexibility. To…
Monitoring multichannel profiles has important applications in manufacturing systems improvement, but it is non-trivial to develop efficient statistical methods due to two main challenges. First, profiles are high-dimensional functional…
Bayesian computation of high dimensional linear regression models with a popular Gaussian scale mixture prior distribution using Markov Chain Monte Carlo (MCMC) or its variants can be extremely slow or completely prohibitive due to the…
One of the major challenges in the Bayesian solution of inverse problems governed by partial differential equations (PDEs) is the computational cost of repeatedly evaluating numerical PDE models, as required by Markov chain Monte Carlo…
Sufficient dimension reduction (SDR) is continuing an active research field nowadays for high dimensional data. It aims to estimate the central subspace (CS) without making distributional assumption. To overcome the large-$p$-small-$n$…
We present a new straightforward principal component analysis (PCA) method based on the diagonalization of the weighted variance-covariance matrix through two spectral decomposition methods: power iteration and Rayleigh quotient iteration.…
In this paper we propose a new iterative algorithm to solve the fair PCA (FPCA) problem. We start with the max-min fair PCA formulation originally proposed in [1] and derive a simple and efficient iterative algorithm which is based on the…
We consider forecasting a single time series when there is a large number of predictors and a possible nonlinear effect. The dimensionality was first reduced via a high-dimensional (approximate) factor model implemented by the principal…
We address the Statistical Process Control (SPC) of high-dimensional, dynamic industrial processes from two complementary perspectives: manifold fitting and manifold learning, both of which assume data lies on an underlying nonlinear, lower…
We consider the problem of reducing the dimensions of parameters and data in non-Gaussian Bayesian inference problems. Our goal is to identify an "informed" subspace of the parameters and an "informative" subspace of the data so that a…
Accurate predictions of pollutant concentrations at new locations are often of interest in air pollution studies on fine particulate matters (PM$_{2.5}$), in which data is usually not measured at all study locations. PM$_{2.5}$ is also a…
Over the years, Principal Component Analysis (PCA) has served as the baseline approach for dimensionality reduction in gene expression data analysis. It primary objective is to identify a subset of disease-causing genes from a vast pool of…
Approximate Bayesian computation (ABC) has gained popularity in recent years owing to its easy implementation, nice interpretation and good performance. Its advantages are more visible when one encounters complex models where maximum…
Convolutional Sparse Coding (CSC) is a well-established image representation model especially suited for image restoration tasks. In this work, we extend the applicability of this model by proposing a supervised approach to convolutional…
This paper investigates the high-dimensional linear regression with highly correlated covariates. In this setup, the traditional sparsity assumption on the regression coefficients often fails to hold, and consequently many model selection…
Monotone missing data is a common problem in data analysis. However, imputation combined with dimensionality reduction can be computationally expensive, especially with the increasing size of datasets. To address this issue, we propose a…