Bandwidth choice for nonparametric classification
By Peter Hall, Kee-Hoon Kang. 2005
76 citations recorded by the source corpus.
It is shown that, for kernel-based classification with univariate distributions and two populations, optimal bandwidth choice has a dichotomous character. If the two densities cross at just one point, where their curvatures have the same signs, then minimum Bayes risk is achieved using bandwidths which are an order of magnitude larger than those which minimize pointwise estimation error. On the other hand, if the curvature signs are different, or if there are multiple crossing points, then bandwidths of conventional size are generally appropriate. The range of different modes of behavior is narrower in multivariate settings. There, the optimal size of bandwidth is generally the same as that which is appropriate for pointwise density estimation. These properties motivate empirical rules for bandwidth choice.
Subfields: Artificial Intelligence, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/7bda09a9f05012d006a14df2d319339265be3f1b
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Artificial Intelligence
- Richard J. Samworth
- Tarn Duong
- Peter Hall
- David Mason
- Wolfgang Polonik
- Byeong U. Park
- H. Muller
- Aurore Delaigle
In Statistics and Probability
- Richard J. Samworth
- Tarn Duong
- Byeong U. Park
- Peter Hall
- David Mason
- Wolfgang Polonik
- H. Muller
- Han Lin Shang
Citations in the corpus
- Asymptotic normality of plug-in level set estimates. (2009, background): “Hartigan (1975) introduced a notion of clustering via maximally connected components of density level sets.”
- Optimal weighted nearest neighbour classifiers (2011, result): “Surprisingly, it is only recently that detailed understanding of the nature of the error probabilities has emerged (Hall et al., 2008). Arguably the most obvious defect with the k-nearest neighbour classifier is that it places equal weight on the class labels of each of the k nearest neighbours to t”
- Choice of neighbor order in nearest-neighbor classification (2008, background): “See, for example, formulae (3) of Kharin (1982) and (A.2) of Hall and Kang (2005).”
- ks: Kernel Density Estimation and Kernel Discriminant Analysis for Multivariate Data in R (2007, methodology): “An alternative is to select bandwidths which satisfy an error measure tailored to discriminant analysis, as is done by Hall and Kang (2005).”