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Choosing Weak Classifiers for Comparison and Boosting

Article Quant Q&A · Author: Stu
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Summary

The document explains that a classifier is not inherently a weak learner: its performance depends on the structure of the data and the task. Linear methods may perform poorly on nonlinear data, while their performance can differ when classes are linearly separable. It names k-nearest neighbors, Naive Bayes, learning vector quantization, linear discriminant analysis, and linear regression as simple classifiers to consider, and notes that distributional assumptions can limit some methods.

The answer cautions that weak learners are most directly relevant in boosting, where an ensemble combines them to improve performance. For a general comparison of classifiers, the questioner may instead want to compare models or study ensemble diversity. The response offers no benchmark dataset, evaluation protocol, or measured error rates, and its guidance is qualitative. Model choice and claims of weakness therefore need to be assessed on the particular data, with care not to treat one classifier as universally weak.

Key ideas

  • A classifier's weakness depends on the data and the shape of the decision boundary.
  • Simple candidates include nearest-neighbor, probabilistic, discriminant, and linear models.
  • Distributional assumptions and nonlinear structure can cause particular classifiers to perform poorly.
  • Weak learners are closely associated with boosting, which combines them into a stronger model.
  • Classifier comparisons should be evaluated on the relevant data rather than against a universal weak baseline.

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Full text
# Choosing a weak learner


# Choosing a weak learner












I want to compare different error rates of different classifiers with the error rate from a weak learner (better than random guessing). So, my question is, what are a few choices for a simple, easy to process weak learner? Or, do I understand the concept incorrectly, and is a weak learner simply any benchmark that I choose (for example, a linear regression)?

If this question belongs to a different stackexchange, please let me know!

## Answer by user6430 (score 1, accepted)

https://quant.stackexchange.com/a/9663

A classifier can be weak for a number of reasons, and it mainly depends on characteristics of the data. For example, if the data are not linearly separable, then linear regression will be weak (poor correlation between predicted class and true class labels). However, if the data are linearly separable, then other classifiers may not work as well as linear regression. If you used ensemble methods (committee of classifiers), you could compare results across classifiers. You didn't mention anything about boosting, which is fundamental to weak learner applications. Without going into detail, you could start with the most basic classifiers such as k-nearest neighbors(kNN), Naive Bayes classifier(NBC), learning vector quantization(LVQ), linear discriminant analysis(LDA), and then linear regression. If the data depart from normality, then LDA may breakdown since covariance matrices are used, and if nonlinearly-separable data are present, regression may have larger error. Certainly, as you increase classifier complexity such as with support vector machines, random forests, artificial neural networks, the earlier mentioned classifiers (kNN, NBC, LDA, LREG) may not work as well. The main issue is that, as soon as you mention "weakness," the theory of boosting overarches everything you are doing, and boosting involves more complex methods for making a weak learner stronger. Hence, to pursue what you want to do, you may get "trapped" in boosting theory and become forced to only consider boosting issues -- which has its own unique assumptions. Make sure you really have to work with a weak classifier instead of comparing classifiers via an ensemble. (See Kuncheva's papers on the diversity issue for an ensemble of classifiers).

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.