Regularized Discriminant Analysis
TLDR
Alternatives to the usual maximum likelihood estimates for the covariance matrices are proposed, characterized by two parameters, the values of which are customized to individual situations by jointly minimizing a sample-based estimate of future misclassification risk.Abstract:
Linear and quadratic discriminant analysis are considered in the small-sample, high-dimensional setting. Alternatives to the usual maximum likelihood (plug-in) estimates for the covariance matrices are proposed. These alternatives are characterized by two parameters, the values of which are customized to individual situations by jointly minimizing a sample-based estimate of future misclassification risk. Computationally fast implementations are presented, and the efficacy of the approach is examined through simulation studies and application to data. These studies indicate that in many circumstances dramatic gains in classification accuracy can be achieved.read more
Citations
More filters
Journal ArticleDOI
Regularization and variable selection via the elastic net
Hui Zou,Trevor Hastie +1 more
TL;DR: It is shown that the elastic net often outperforms the lasso, while enjoying a similar sparsity of representation, and an algorithm called LARS‐EN is proposed for computing elastic net regularization paths efficiently, much like algorithm LARS does for the lamba.
Journal ArticleDOI
Statistical pattern recognition: a review
TL;DR: The objective of this review paper is to summarize and compare some of the well-known methods used in various stages of a pattern recognition system and identify research topics and applications which are at the forefront of this exciting and challenging field.
Journal ArticleDOI
Strictly Proper Scoring Rules, Prediction, and Estimation
TL;DR: The theory of proper scoring rules on general probability spaces is reviewed and developed, and the intuitively appealing interval score is proposed as a utility function in interval estimation that addresses width as well as coverage.
Journal ArticleDOI
Model-Based Clustering, Discriminant Analysis, and Density Estimation
Chris Fraley,Adrian E. Raftery +1 more
TL;DR: This work reviews a general methodology for model-based clustering that provides a principled statistical approach to important practical questions that arise in cluster analysis, such as how many clusters are there, which clustering method should be used, and how should outliers be handled.
Book
Applied Predictive Modeling
Max Kuhn,Kjell Johnson +1 more
TL;DR: This research presents a novel and scalable approach called “Smartfitting” that automates the very labor-intensive and therefore time-heavy and therefore expensive and expensive process of designing and implementing statistical models for regression models.
References
More filters
Book
Matrix Analysis
Roger A. Horn,Charles R. Johnson +1 more
TL;DR: In this article, the authors present results of both classic and recent matrix analyses using canonical forms as a unifying theme, and demonstrate their importance in a variety of applications, such as linear algebra and matrix theory.
Journal ArticleDOI
Classification and Regression Trees.
Book
Classification and regression trees
TL;DR: The methodology used to construct tree structured rules is the focus of a monograph as mentioned in this paper, covering the use of trees as a data analysis method, and in a more mathematical framework, proving some of their fundamental properties.