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Conference Papers Year : 2023

Optimal Scaling: New Insights Into an Old Problem


Processing qualitative variables with a very large number of categories in Machine Learning is an opportunity to revisit the theory of optimal scaling and its applications. Coding (or scoring) a qualitative variable consists in assigning numerical values to its modalities, thus transforming it into a discrete numerical variable. Scoring qualitative variables has a long history going back to K. Pearson, R.A. Fisher, L. Guttman, C.Hayashi, etc. It was the origin of correspondence analysis. The 1970s and early 1980s were the years of the search for optimal scoring (aka optimal scaling) in supervised and unsupervised contexts, performed with alternating least squares. For nearly 30 years, the topic did not generate much research; applications became routine, such as risk scores in banking and insurance. With the availability of massive data, machine-learning researchers and practitioners were confronted with categorical data, ill-suited to neural networks with moreover a large number of categories (eg zip codes). Generally ignoring the work of statisticians, dozens of encoding methods have flourished like Hash encoding, or methods where the encoding only depends on the response variable (conditional average) as well as the One-Hot Encoding which is nothing else than the disjunctive form with as many indicators as modalities. The large size of some categorical data raises problems of stability and overfitting that were neglected in classical statistical applications where the number of modalities is small and where the learning-testing approach was not frequent. The confrontation of these two worlds allows us to consider a renewal of the coding methods and how correspondence analysis may be reinterpreted from a non-linear point of view.
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hal-04123670 , version 1 (09-06-2023)


  • HAL Id : hal-04123670 , version 1


Gilbert Saporta. Optimal Scaling: New Insights Into an Old Problem. ASMDA 2023, 20th Applied Stochastic Models and Data Analysis Conference, Hellenic Mediterranean University, Jun 2023, Heraklion - Crete, Greece. ⟨hal-04123670⟩
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