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Advances in Data Analysis and Classification

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04-07-2015 | Regular Article

Advances in credit scoring: combining performance and interpretation in kernel discriminant analysis

Authors: Caterina Liberati, Furio Camillo, Gilbert Saporta

Published in: Advances in Data Analysis and Classification | Issue 1/2017

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Abstract

Due to the recent financial turmoil, a discussion in the banking sector about how to accomplish long term success, and how to follow an exhaustive and powerful strategy in credit scoring is being raised up. Recently, the significant theoretical advances in machine learning algorithms have pushed the application of kernel-based classifiers, producing very effective results. Unfortunately, such tools have an inability to provide an explanation, or comprehensible justification, for the solutions they supply. In this paper, we propose a new strategy to model credit scoring data, which exploits, indirectly, the classification power of the kernel machines into an operative field. A reconstruction process of the kernel classifier is performed via linear regression, if all predictors are numerical, or via a general linear model, if some or all predictors are categorical. The loss of performance, due to such approximation, is balanced by better interpretability for the end user, which is able to order, understand and to rank the influence of each category of the variables set in the prediction. An Italian bank case study has been illustrated and discussed; empirical results reveal a promising performance of the introduced strategy.

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$$\begin{aligned} \mathcal {\bar{I}}=\frac{m}{m-1}\left( \sum _{l} \lambda _{l}^{2}-\frac{j-m}{m}\right) ^{2} \end{aligned}$$

(3)

where j is the sum of the levels of the nominal variables.

The choice of employing the same window width for all the discriminant function allows a competitive comparison among different models. Alternative values of $\delta $ has been applied $\delta =5,10,20$ but they produced the same rank in terms of good prediction.

In order to preserve the ease of interpretation we choose to not include in the multiple regression any interaction among original variables.

Test data is a random set of 4997 companies, sampled among all the instances not included in the training set.

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Title: Advances in credit scoring: combining performance and interpretation in kernel discriminant analysis
Authors: Caterina Liberati
Furio Camillo
Gilbert Saporta
Publication date: 04-07-2015
Publisher: Springer Berlin Heidelberg
Published in: Advances in Data Analysis and Classification / Issue 1/2017
Print ISSN: 1862-5347
Electronic ISSN: 1862-5355
DOI: https://doi.org/10.1007/s11634-015-0213-y

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