An apparent paradox: a classifier based on a partially classified sample may have smaller expected error rate than that if the sample were completely classified

Ahfock, Daniel; McLachlan, Geoffrey J.

doi:10.1007/s11222-020-09971-5

Cited by 9 publications

(18 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Following on from the exploratory examination by Ahfock and McLachlan (2019) of partially classified data sets, Ahfock and McLachlan (2020) proposed to treat the labels of the unclassified features as missing data and to introduce a framework for their missingness as in the pioneering work of Rubin (1976) for missingness in incomplete-data analysis. Within this framework, they postulated the dependence of the conditional probability that a label is missing given the data by the logistic model with covariate equal to an entropy-based measure.…”

Section: Modelling Missingness For Unobserved Class Labelsmentioning

confidence: 99%

“…This is not surprising as entities with features in such regions would tend to be representative of entities that would be difficult to classify correctly, as illustrated for three datasets in the previous section. Ahfock and McLachlan (2020) showed how this dependency on the missingness pattern can be leveraged to provide additional information about the parameters in the optimal classifier specified by the Bayes' rule.…”

Section: Modelling Missingness For Unobserved Class Labelsmentioning

confidence: 99%

“…To simplify the numerical computation in the particular case of only g = 2 classes with the two-class homoscedastic normal model (3), Ahfock and McLachlan (2020) replaced log e j (θ) in ( 19) by minus the square of the discriminant function d j = d(y j ; β) as defined by (4) so that…”

Section: Modelling Missingness For Unobserved Class Labelsmentioning

confidence: 99%

“…The general expression for the ARE of R(full) PC for π 1 = π 2 is available in the supplementary material of Ahfock and McLachlan (2020). They noted that this ARE is not sensitive to the value π 1 in the range (0.2, 0.8), so that Theorem 2 can provide useful guidelines for arbitrary prior probabilities.…”

Section: Modelling Missingness For Unobserved Class Labelsmentioning

confidence: 99%

“…However, theoretical analysis of SSL has so far been scarce. But last year, Ahfock and McLachlan (2020) provided an asymptotic basis on how to increase in certain situations the accuracy of the commonly used linear discriminant function formed from a partially classified sample as in SSL (Ahfock and McLachlan, 2020). The increase in accuracy can be of sufficient magnitude for this SSL-based classifier to have smaller error rate than that if it were formed from a completely classified sample.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Semi-Supervised Learning of Classifiers from a Statistical Perspective: A Brief Review

Ahfock¹,

McLachlan²

2021

Preprint

Self Cite

View full text Add to dashboard Cite

There has been increasing attention to semi-supervised learning (SSL) approaches in machine learning to forming a classifier in situations where the training data for a classifier consists of a limited number of classified observations but a much larger number of unclassified observations. This is because the procurement of classified data can be quite costly due to high acquisition costs and subsequent financial, time, and ethical issues that can arise in attempts to provide the true class labels for the unclassified data that have been acquired. We provide here a review of statistical SSL approaches to this problem, focussing on the recent result that a classifier formed from a partially classified sample can actually have smaller expected error rate than that if the sample were completely classified. This rather paradoxical outcome is able to be achieved by introducing a framework with a missingness mechanism for the missing labels of the unclassified observations. It is most relevant in commonly occurring situations in practice, where the unclassified data occur primarily in regions of relatively high entropy in the feature space thereby making it difficult for their class labels to be easily obtained.

show abstract

Section: Modelling Missingness For Unobserved Class Labelsmentioning

confidence: 99%

Section: Modelling Missingness For Unobserved Class Labelsmentioning

confidence: 99%

Section: Modelling Missingness For Unobserved Class Labelsmentioning

confidence: 99%

Section: Modelling Missingness For Unobserved Class Labelsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Semi-Supervised Learning of Classifiers from a Statistical Perspective: A Brief Review

Ahfock¹,

McLachlan²

2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

EM Algorithm

McLachlan¹,

Ng²,

Nguyen³

2022

Wiley StatsRef: Statistics Reference Online

View full text Add to dashboard Cite

We supplement the article of Meng (2006) on the EM algorithm and its applications, providing also an update on its more recent developments and applications. The expectation–maximization algorithm, popularly known as the EM algorithm, is a general‐purpose algorithm for maximum‐likelihood estimation in a wide variety of situations best described as incomplete‐data problems. The name EM algorithm was given by Dempster et al . (1997) in a celebrated paper read before the Royal Statistical Society in 1976 and published in its journal in 1977.

show abstract

Estimation of Classification Rules From Partially Classified Data

McLachlan

Ahfock

2021

Data Analysis and Rationality in a Complex World

View full text Add to dashboard Cite

An apparent paradox: a classifier based on a partially classified sample may have smaller expected error rate than that if the sample were completely classified

Cited by 9 publications

References 18 publications

Semi-Supervised Learning of Classifiers from a Statistical Perspective: A Brief Review

Semi-Supervised Learning of Classifiers from a Statistical Perspective: A Brief Review

EM Algorithm

Estimation of Classification Rules From Partially Classified Data

Contact Info

Product

Resources

About