Sufficient dimension reduction based on an ensemble of minimum average variance estimators

We introduce a class of dimension reduction estimators based on an ensemble of the minimum average variance estimates of functions that characterize the central subspace, such as the characteristic functions, the Box--Cox transformations and wavelet basis. The ensemble estimators exhaustively estimate the central subspace without imposing restrictive conditions on the predictors, and have the same convergence rate as the minimum average variance estimates. They are flexible and easy to implement, and allow repeated use of the available sample, which enhances accuracy. They are applicable to both univariate and multivariate responses in a unified form. We establish the consistency and convergence rate of these estimators, and the consistency of a cross validation criterion for order determination. We compare the ensemble estimators with other estimators in a wide variety of models, and establish their competent performance.Comment: Published in at http://dx.doi.org/10.1214/11-AOS950 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Canonical correlation analysis based on information theory

AbstractIn this article, we propose a new canonical correlation method based on information theory. This method examines potential nonlinear relationships between p×1 vector Y-set and q×1 vector X-set. It finds canonical coefficient vectors a and b by maximizing a more general measure, the mutual information, between aTX and bTY. We use a permutation test to determine the pairs of the new canonical correlation variates, which requires no specific distributions for X and Y as long as one can estimate the densities of aTX and bTY nonparametrically. Examples illustrating the new method are presented

The Dual Central Subspaces in dimension reduction

Existing dimension reduction methods in multivariate analysis have focused on reducing sets of random vectors into equivalently sized dimensions, while methods in regression settings have focused mainly on decreasing the dimension of the predictor variables. However, for problems involving a multivariate response, reducing the dimension of the response vector is also desirable and important. In this paper, we develop a new concept, termed the Dual Central Subspaces (DCS), to produce a method for simultaneously reducing the dimensions of two sets of random vectors, irrespective of the labels predictor and response. Different from previous methods based on extensions of Canonical Correlation Analysis (CCA), the recovery of this subspace provides a new research direction for multivariate sufficient dimension reduction. A particular model-free approach is detailed theoretically and the performance investigated through simulation and a real data analysis. (C) 2015 Elsevier Inc. All rights reserved

High-dimensional Variable Screening via Conditional Martingale Difference Divergence

Variable screening has been a useful research area that deals with ultrahigh-dimensional data. When there exist both marginally and jointly dependent predictors to the response, existing methods such as conditional screening or iterative screening often suffer from instability against the selection of the conditional set or the computational burden, respectively. In this article, we propose a new independence measure, named conditional martingale difference divergence (CMDH), that can be treated as either a conditional or a marginal independence measure. Under regularity conditions, we show that the sure screening property of CMDH holds for both marginally and jointly active variables. Based on this measure, we propose a kernel-based model-free variable screening method, which is efficient, flexible, and stable against high correlation among predictors and heterogeneity of the response. In addition, we provide a data-driven method to select the conditional set. In simulations and real data applications, we demonstrate the superior performance of the proposed method

On Differential Equations Derived from the Pseudospherical Surfaces

We construct two metric tensor fields; by means of these metric tensor fields, sinh-Gordon equation and elliptic sinh-Gordon equation are obtained, which describe pseudospherical surfaces of constant negative Riemann curvature scalar σ = −2, σ = −1, respectively. By employing the Bäcklund transformation, nonlinear superposition formulas of sinh-Gordon equation and elliptic sinh-Gordon equation are derived; various new exact solutions of the equations are obtained

Towards Al3+-Induced Manganese-Containing Superoxide Dismutase Inactivation and Conformational Changes: An Integrating Study with Docking Simulations

Superoxide dismutase (SOD, EC 1.15.1.1) plays an important antioxidant defense role in skins exposed to oxygen. We studied the inhibitory effects of Al3+ on the activity and conformation of manganese-containing SOD (Mn-SOD). Mn-SOD was significantly inactivated by Al3+ in a dose-dependent manner. The kinetic studies showed that Al3+ inactivated Mn-SOD follows the first-order reaction. Al3+ increased the degree of secondary structure of Mn-SOD and also disrupted the tertiary structure of Mn-SOD, which directly resulted in enzyme inactivation. We further simulated the docking between Mn-SOD and Al3+ (binding energy for Dock 6.3: −14.07 kcal/mol) and suggested that ASP152 and GLU157 residues were predicted to interact with Al3+, which are not located in the Mn-contained active site. Our results provide insight into the inactivation of Mn-SOD during unfolding in the presence of Al3+ and allow us to describe a ligand binding via inhibition kinetics combined with the computational prediction