Generating customer's credit behavior with deep generative models

Rogelio Andrade Mancisidor, Michael Kampffmeyer, Kjersti Aas, Robert Jenssen

Abstract: Banks collect data x1<math><msub is="true"><mrow is="true"><mi mathvariant="bold-italic" is="true">x</mi></mrow><mrow is="true"><mn is="true">1</mn></mrow></msub></math> in loan applications to decide whether to grant credit and accepted applications generate new data x2<math><msub is="true"><mrow is="true"><mi mathvariant="bold-italic" is="true">x</mi></mrow><mrow is="true"><mn is="true">2</mn></mrow></msub></math> throughout the loan period. Hence, banks have two measurement-modalities, which provide a complete picture about customers. If we can generate x2<math><msub is="true"><mrow is="true"><mi mathvariant="bold-italic" is="true">x</mi></mrow><mrow is="true"><mn is="true">2</mn></mrow></msub></math> conditioned on x1<math><msub is="true"><mrow is="true"><mi mathvariant="bold-italic" is="true">x</mi></mrow><mrow is="true"><mn is="true">1</mn></mrow></msub></math> keeping the relationship between these two modalities, credit and behavior scoring may be enabled simultaneously (at the time x1<math><msub is="true"><mrow is="true"><mi mathvariant="bold-italic" is="true">x</mi></mrow><mrow is="true"><mn is="true">1</mn></mrow></msub></math> is obtained) to support cross-selling, launching of new products or marketing campaigns. Therefore, we develop a novel conditional bi-modal discriminative (CBMD) model for credit scoring, which is able to generate x2<math><msub is="true"><mrow is="true"><mi mathvariant="bold-italic" is="true">x</mi></mrow><mrow is="true"><mn is="true">2</mn></mrow></msub></math> based on x1<math><msub is="true"><mrow is="true"><mi mathvariant="bold-italic" is="true">x</mi></mrow><mrow is="true"><mn is="true">1</mn></mrow></msub></math> and can classify the outcome of loans in an unified framework. The idea behind CBMD is to learn joint (among modalities) latent representations that are useful to generate x2<math><msub is="true"><mrow is="true"><mi mathvariant="bold-italic" is="true">x</mi></mrow><mrow is="true"><mn is="true">2</mn></mrow></msub></math> using the available data x1<math><msub is="true"><mrow is="true"><mi mathvariant="bold-italic" is="true">x</mi></mrow><mrow is="true"><mn is="true">1</mn></mrow></msub></math> during the application process. The classifier model introduced in CBMD encourages the generative process to generate x2<math><msub is="true"><mrow is="true"><mi mathvariant="bold-italic" is="true">x</mi></mrow><mrow is="true"><mn is="true">2</mn></mrow></msub></math> accurately. Further, CBMD optimizes a novel objective function introduced in this research, which maximizes mutual information between the latent representation z<math><mi mathvariant="bold-italic" is="true">z</mi></math> and the modality x2<math><msub is="true"><mrow is="true"><mi mathvariant="bold-italic" is="true">x</mi></mrow><mrow is="true"><mn is="true">2</mn></mrow></msub></math> to improve the generative process in the model. We benchmark the generative process of our proposed model and CBMD outperforms other multi-learning models. Similarly, the classification performance of CBMD is tested under different scenarios and it achieves higher or on a par model performance compared to the state-of-the-art in multi-modal learning models.