Some theory for Fisher''s linear discriminant function

By Peter J. Bickel, Elizaveta Levina. 2004

628 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Information Systems

View Paper: https://www.semanticscholar.org/paper/ddc393abbf689e68203d314d1789b7e630380464

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Citations in the corpus

A Selective Overview of Variable Selection in High Dimensional Feature Space (2009, methodology): “As demonstrated by Bickel and Levina (2004), the Fisher discrimination method no longer performs well in high dimensional settings due to the diverging spectra and singularity of the sample covariance matrix.”
High Dimensional Classification Using Features Annealed Independence Rules. (2007, methodology): “the variation in the data such as tumor classiﬁcation using gene expression data, using all features will increase the misclassiﬁcation rate. To illustrate the idea, we study the independence rule of Bickel and Levina (2004). Speciﬁcally, we give an explicit formula how the signal and noise aﬀect th”
Truncated Importance Sampling (2008, background): “Other statistical examples of this principle are naive Bayes (Bickel and Levina 2004), wavelet thresholding (Donoho and Johnstone 1994), and perhaps shrinkage techniques in general.”
Classification Accuracy as a Proxy for Two Sample Testing (2016, methodology): “As mentioned earlier, the idea of using diag(Σ̂) in place of Σ̂ has also been justified in the high-dimensional classification problem (Bickel and Levina, 2004).”
An extension of Fisher's discriminant analysis for stochastic processes (2008, neutral): “• Standard Fisher’s LDA may break down if p/N →∞ (Bickel and Levina, 2004).”
High-Dimensional Asymptotics of Prediction: Ridge Regression and Classification (2015, methodology): “When p is on the same order as n , however, the matrix inverse (cid:98) Σ − 1 c is unstable and the performance of LDA declines, as discussed among others by Bickel and Levina (2004).”
Covariance Estimation: The GLM and Regularization Perspectives (2011, methodology): “Bickel and Levina (2008a) provide conditions ensuring consistency in the operator norm (spectral norm) for precision matrix estimates based on banded Cholesky factors. Chang and Tsay (2010) extend the Huang et al. (2006) setup using an equi-angular penalty which imposes different penalty on each reg”
Generalized Thresholding of Large Covariance Matrices (2009, background): “…here is that variables far apart are only weakly correlated, and estimators that take advantage of this have been proposed by Wu and Pourahmadi (2003); Bickel and Levina (2004); Huang et al. (2006); Furrer and Bengtsson (2007); Bickel and Levina (2008); Levina, Rothman, and Zhu (2008); and others.”
Feature Selection in High-Dimensional Classification (2013, background): “For the above Gaussian discriminant analysis, Bickel & Levina (2004) show that the classical low dimensional normal-based linear discriminant analysis (LDA) is asymptotically equivalent to random guessing when the dimension p increases at a rate comparable to the sample size n.”
Spectrum estimation for large dimensional covariance matrices using random matrix theory (2006, background): “See for instance, the interesting papers ( Bickel and Levina, 2004 ) and for even more generality - beyond Toeplitz matrices - (Bickel and Levina, 2006).”
On Sliced Inverse Regression With High-Dimensional Covariates (2006, background): “Bickel and Levina (2004) investigated the asymptotic properties for Fisher’s linear discriminant analysis (for relevant data analysis see Levina 2002).”
Sure independence screening for ultrahigh dimensional feature space (2006, background): “In addition, Condition 4 holds for the covariance matrix of a stationary time series (see Bickel and Levina, 2004, 2008).”