631 research outputs found
Bandwidth choice for nonparametric classification
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.Comment: Published at http://dx.doi.org/10.1214/009053604000000959 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Bandwidth choice for nonparametric classification
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
Correcting for selection bias via cross-validation in the classification of microarray data
There is increasing interest in the use of diagnostic rules based on
microarray data. These rules are formed by considering the expression levels of
thousands of genes in tissue samples taken on patients of known classification
with respect to a number of classes, representing, say, disease status or
treatment strategy. As the final versions of these rules are usually based on a
small subset of the available genes, there is a selection bias that has to be
corrected for in the estimation of the associated error rates. We consider the
problem using cross-validation. In particular, we present explicit formulae
that are useful in explaining the layers of validation that have to be
performed in order to avoid improperly cross-validated estimates.Comment: Published in at http://dx.doi.org/10.1214/193940307000000284 the IMS
Collections (http://www.imstat.org/publications/imscollections.htm) by the
Institute of Mathematical Statistics (http://www.imstat.org
Assessing the performance of an allocation rule
AbstractThe problem of estimating the error rates of a sample-based rule on the basis of the same sample used in its construction is considered. The apparent error rate is an obvious nonparametric estimate of the conditional error rate of a sample rule, but unfortunately it provides too optimistic an assessment. Attention is focussed on the formation of improved estimates, mainly through appropriate bias correction of the apparent error rate. In this respect the role of the bootstrap, a computer-based methodology, is highlighted
A Comparison of Depth Functions in Maximal Depth Classification Rules
Data depth has been described as alternative to some parametric approaches in analyzing many multivariate data. Many depth functions have emerged over two decades and studied in literature. In this study, a nonparametric approach to classification based on notions of different data depth functions is considered and some properties of these methods are studied. The performance of different depth functions in maximal depth classifiers is investigated using simulation and real data with application to agricultural industry
Analyzing and Predicting Effort Associated with Finding and Fixing Software Faults
Context: Software developers spend a significant amount of time fixing faults. However, not many papers have addressed the actual effort needed to fix software faults. Objective: The objective of this paper is twofold: (1) analysis of the effort needed to fix software faults and how it was affected by several factors and (2) prediction of the level of fix implementation effort based on the information provided in software change requests. Method: The work is based on data related to 1200 failures, extracted from the change tracking system of a large NASA mission. The analysis includes descriptive and inferential statistics. Predictions are made using three supervised machine learning algorithms and three sampling techniques aimed at addressing the imbalanced data problem. Results: Our results show that (1) 83% of the total fix implementation effort was associated with only 20% of failures. (2) Both safety critical failures and post-release failures required three times more effort to fix compared to non-critical and pre-release counterparts, respectively. (3) Failures with fixes spread across multiple components or across multiple types of software artifacts required more effort. The spread across artifacts was more costly than spread across components. (4) Surprisingly, some types of faults associated with later life-cycle activities did not require significant effort. (5) The level of fix implementation effort was predicted with 73% overall accuracy using the original, imbalanced data. Using oversampling techniques improved the overall accuracy up to 77%. More importantly, oversampling significantly improved the prediction of the high level effort, from 31% to around 85%. Conclusions: This paper shows the importance of tying software failures to changes made to fix all associated faults, in one or more software components and/or in one or more software artifacts, and the benefit of studying how the spread of faults and other factors affect the fix implementation effort
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