Related papers: Ridge partial correlation screening for ultrahigh-…
Given $m$ $d$-dimensional responsors and $n$ $d$-dimensional predictors, sparse regression finds at most $k$ predictors for each responsor for linear approximation, $1\leq k \leq d-1$. The key problem in sparse regression is subset…
This article considers ultrahigh-dimensional forecasting problems with survival response variables. We propose a two-step model averaging procedure for improving the forecasting accuracy of the true conditional mean of a survival response…
Machine learning methods usually depend on internal parameters -- so called hyperparameters -- that need to be optimized for best performance. Such optimization poses a burden on machine learning practitioners, requiring expert knowledge,…
Ordered Weighted $L_{1}$ (OWL) regularized regression is a new regression analysis for high-dimensional sparse learning. Proximal gradient methods are used as standard approaches to solve OWL regression. However, it is still a burning issue…
Feature screening for ultrahigh-dimension, in general, proceeds with two essential steps. The first step is measuring and ranking the marginal dependence between response and covariates, and the second is determining the threshold. We…
We study a ridge estimator for the high-dimensional two-way fixed effect regression model with a sparse bipartite network. We develop concentration inequalities showing that when the ridge parameters increase as the log of the network size,…
Conventional seismic techniques for detecting the subsurface geologic features are challenged by limited data coverage, computational inefficiency, and subjective human factors. We developed a novel data-driven geological feature detection…
A new method is proposed for variable screening, variable selection and prediction in linear regression problems where the number of predictors can be much larger than the number of observations. The method involves minimizing a penalized…
Screening for ultrahigh dimensional features may encounter complicated issues such as outlying observations, heteroscedasticity or heavy-tailed distribution, multi-collinearity and confounding effects. Standard correlation-based marginal…
In many areas, practitioners need to analyze large datasets that challenge conventional single-machine computing. To scale up data analysis, distributed and parallel computing approaches are increasingly needed. Here we study a fundamental…
Variable selection in ultra-high dimensional regression problems has become an important issue. In such situations, penalized regression models may face computational problems and some pre screening of the variables may be necessary. A…
This paper carries out a large dimensional analysis of a variation of kernel ridge regression that we call \emph{centered kernel ridge regression} (CKRR), also known in the literature as kernel ridge regression with offset. This modified…
We are concerned with an approximation problem for a symmetric positive semidefinite matrix due to motivation from a class of nonlinear machine learning methods. We discuss an approximation approach that we call {matrix ridge…
We introduce a very general method for high-dimensional classification, based on careful combination of the results of applying an arbitrary base classifier to random projections of the feature vectors into a lower-dimensional space. In one…
We study the problem of detecting multiple change points in the mean vectors of an independent sequence of high-dimensional observations. We propose a family of ridge-regularized CUSUM statistics built upon the adaptable ridge-regularized…
Subset selection in multiple linear regression aims to choose a subset of candidate explanatory variables that tradeoff fitting error (explanatory power) and model complexity (number of variables selected). We build mathematical programming…
In this paper, we are concerned with how to select significant variables in semiparametric modeling. Variable selection for semiparametric regression models consists of two components: model selection for nonparametric components and…
Pruning of redundant or irrelevant instances of data is a key to every successful solution for pattern recognition. In this paper, we present a novel ranking-selection framework for low-length but highly correlated instances. Instead of…
The generalized Ridge penalty is a powerful tool for dealing with overfitting and for high-dimensional regressions. The generalized Ridge regression can be derived as the mean of a posterior distribution with a Normal prior and a given…
High-dimensional covariates often admit linear factor structure. To effectively screen correlated covariates in high-dimension, we propose a conditional variable screening test based on non-parametric regression using neural networks due to…