In the context of hyperspectral image analysis in planetology, we show how to estimate the physical parameters that generate the spectral infrared signal reflected by Mars. The training approach we develop is based on the estimation of the functional relationship between parameters and spectra, using a database of synthetic spectra generated by a physical model. The high dimension of spectra is...

It is computationally expensive to predict reliability using physical models at the design stage if many random input variables exist. This work introduces a dimension reduction technique based on generalized sliced inverse regression (GSIR) mitigate curse of dimensionality. The proposed high dimensional method enables active learning integrate GSIR, Gaussian Process (GP) modeling, and Importan...

Sufficient dimension reduction (sdr) is an effective tool for reducing highdimensional predictor spaces in regression problems. sdr achieves dimension reduction without loss of any regression information and without the need to assume any particular parametric form of a model. This is particularly useful for high-dimensional applications such as data mining, marketing, and bioinformatics. Howev...

In this paper, we study the manifold regularization for the Sliced Inverse Regression (SIR). The manifold regularization improves the standard SIR in two aspects: 1) it encodes the local geometry for SIR and 2) it enables SIR to deal with transductive and semi-supervised learning problems. We prove that the proposed graph Laplacian based regularization is convergent at rate root-n. The projecti...

It is known that for a certain class of single index models (SIMs) [Formula: see text], support recovery is impossible when X ~ 𝒩(0, 𝕀 p×p ) and a model complexity adjusted sample size is below a critical threshold. Recently, optimal algorithms based on Sliced Inverse Regression (SIR) were suggested. These algorithms work provably under the assumption that the design X comes from an i.i.d. Gaus...

Dimension reduction is helpful and often necessary in exploring nonlinear or nonparametric regression structures with a large number of predictors. We consider using the canonical variables from the design space whose correlations with a spline basis in the response space are significant. The method can be viewed as a variant of sliced inverse regression (SIR) with simple slicing replaced by Bs...