CRAN/E | shattering

shattering

Estimate the Shattering Coefficient for a Particular Dataset

Installation

About

The Statistical Learning Theory (SLT) provides the theoretical background to ensure that a supervised algorithm generalizes the mapping f:X -> Y given f is selected from its search space bias F. This formal result depends on the Shattering coefficient function N(F,2n) to upper bound the empirical risk minimization principle, from which one can estimate the necessary training sample size to ensure the probabilistic learning convergence and, most importantly, the characterization of the capacity of F, including its under and overfitting abilities while addressing specific target problems. In this context, we propose a new approach to estimate the maximal number of hyperplanes required to shatter a given sample, i.e., to separate every pair of points from one another, based on the recent contributions by Har-Peled and Jones in the dataset partitioning scenario, and use such foundation to analytically compute the Shattering coefficient function for both binary and multi-class problems. As main contributions, one can use our approach to study the complexity of the search space bias F, estimate training sample sizes, and parametrize the number of hyperplanes a learning algorithm needs to address some supervised task, what is specially appealing to deep neural networks. Reference: de Mello, R.F. (2019) "On the Shattering Coefficient of Supervised Learning Algorithms" ; de Mello, R.F., Ponti, M.A. (2018, ISBN: 978-3319949888) "Machine Learning: A Practical Approach on the Statistical Learning Theory".

Key Metrics

Version 1.0.7
Published 2021-08-21 1143 days ago
Needs compilation? no
License GPL-3
CRAN checks shattering results

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Maintainer

Maintainer

Rodrigo F. de Mello

Authors

Rodrigo F. de Mello

aut / cre

Material

Reference manual
Package source

macOS

r-release

arm64

r-oldrel

arm64

r-release

x86_64

r-oldrel

x86_64

Windows

r-devel

x86_64

r-release

x86_64

r-oldrel

x86_64

Old Sources

shattering archive

Imports

FNN
pdist
slam
grDevices
Ryacas
rmarkdown
pracma
e1071
graphics
NMF
stats

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