منابع مشابه
Bump Hunting with Non-gaussian Kernels
It is well known that the number of modes of a kernel density estimator is monotone nonincreasing in the bandwidth if the kernel is a Gaussian density. There is numerical evidence of nonmonotonicity in the case of some non-Gaussian kernels, but little additional information is available. The present paper provides theoretical and numerical descriptions of the extent to which the number of modes...
متن کاملHunting with Non - Gaussian Kernels
It is well known that the number of modes of a kernel density estimator is monotone nonincreasing in the bandwidth if the kernel is a Gaussian density. There is numerical evidence of nonmonotonicity in the case of some non-Gaussian kernels, but little additional information is available. The present paper provides theoretical and numerical descriptions of the extent to which the number of modes...
متن کاملBump hunting in high-dimensional data
Many data analytic questions can be formulated as (noisy) optimization problems. They explicitly or implicitly involve ®nding simultaneous combinations of values for a set of (``input'') variables that imply unusually large (or small) values of another designated (``output'') variable. Speci®cally, one seeks a set of subregions of the input variable space within which the value of the output va...
متن کاملLearning with Hierarchical Gaussian Kernels
We investigate iterated compositions of weighted sums of Gaussian kernels and provide an interpretation of the construction that shows some similarities with the architectures of deep neural networks. On the theoretical side, we show that these kernels are universal and that SVMs using these kernels are universally consistent. We further describe a parameter optimization method for the kernel p...
متن کاملRejoinder: Discussion of Bump Hunting in High Dimensional Data
We thank all of the discussants for taking the time to contribute, and for both their compliments and helpful criticism. Before responding in detail, we address two general concerns that ran throughout many of the discussions. 1 Computation Several discussants raised the issue of the computational requirements of the peeling algorithm (Section 7). They were concerned about its ability to scale ...
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ژورنال
عنوان ژورنال: The Annals of Statistics
سال: 2004
ISSN: 0090-5364
DOI: 10.1214/009053604000000715