Structure adaptive approach for dimension reduction

By M. Hristache, A. Juditsky, Jörg Polzehl, Vladimir Spokoiny. 2001

193 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/261cf15330d10eb5ae5355852b52d40ce88ee535

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

In Statistics and Probability

Citations in the corpus

Supervised principal component analysis: Visualization, classification and regression on subspaces and submanifolds (2011, methodology): “This body of research includes various approaches such as classical Fisher’s discriminant analysis (FDA) [3], the large family of methods known as metric learning (ML) [4–12], the family of sufficient dimension reduction (SDR) algorithms [13–20], and the method proposed by Bair et al.”
Contour regression: A general approach to dimension reduction (2005, unknown): “At the opposite end of the spectrum are adaptive methods that exploit local features of the dependence of Y on X [13, 23].”
Structural adaptation via Lp-norm oracle inequalities (2007, background): “It is also worth mentioning that there is vast literature on estimation of vectors ei, when fi are treated as nonparametric nuisance parameters; see, e.g., Huber (1985), Hall (1989), Hristache et al. (2001a, 2001b) and references therein.”
A Multiple-Index Model and Dimension Reduction (2008, methodology): “If we adopt the fixed trimming scheme of Härdle, Hall, and Ichimura (1993), this requirement can be removed.”
ON THE IDENTIFIABILITY OF ADDITIVE INDEX MODELS (2011, methodology): “The additive index model is closely related to a model that is often used for the purpose of sufficient dimension reduction (Li (2000); Hristache et al. (2001); Cook (2007)): f(x) = h(α′1x, . . . , α ′ Mx), (2.6) where α1, . . . , αM form an orthonormal basis.”
Gradient-Based Kernel Dimension Reduction for Regression (2014, methodology): “We call the method in Hristache et al. (2001) the iterative average derivative estimates (IADE) in the sequel.”
Gradient-based kernel method for feature extraction and variable selection (2012, methodology): “The IADE has seven parameters [11], and we tuned two of them ( h1 andρmin) manually to optimize the performance.”
BAYESIAN ESTIMATION IN SINGLE-INDEX MODELS (2004, methodology): “Recently, a sophisticated method of iterative improvement was introduced by Hristache, Juditsky and Spokoiny (2001a); this method extends to multiple-index models, see Hristache, Juditsky, Polzehl and Spokoiny (2001b) .”
A SINGLE-INDEX QUANTILE REGRESSION MODEL AND ITS ESTIMATION (2012, methodology): “Many estimators proposed for conditional mean regression can be applied here to serve this purpose, for example, the outer product of gradients (OPG) estimate (Samarov, 1993; Hristache et al., 2001; Xia et al., 2002).”
A constructive approach to the estimation of dimension reduction directions (2007, methodology): “To allow the estimation to be adaptive to the structure of the dependency of Y on X, we may follow the idea of Hristache et al (2001) and replace wij in (2.4) by wij = Kh(Σ̂ 1/2Xij), where Σ̂1/2 is a symmetric matrix with (Σ̂1/2)2 = Σ̂.”
Fuzzy model validation using the local statistical approach (2009, background): “Of course, dimensionality reduction is possible but this is another open research topic [20].”
Successive direction extraction for estimating the central subspace in a multiple-index regression (2008, methodology): “Furthermore, our method uses a two-dimensional kernel, whereas MAVE and SAE employ higher dimensional kernels, thus increasing the extent of local sparsity in kernel smoothing.”