Quantum Optimized Cost Based Feature Selection and Credit Scoring for Mobile Micro-financing

Abstract

Mobile e-commerce has grown rapidly in the last decade because of the development of mobile network services, computing capabilities and big data’s applications. Financial institutions have been undergoing fundamental transformation in credit risk areas, specifically to traditional credit policy, that is now inadequate for accurately evaluating an individual’s credit risk profile in a timely manner. A big-scale dataset representing deep mobile usage of 450,722 anonymous mobile users with a 28-month loan history and mobile behavior of both iOS and Android is designed, can add value for credit scoring in terms of better accuracy and lower feature acquisition cost by introducing a cost-based quantum-inspired evolutionary algorithm (QIEA) feature selection method. The QIEA adopts quantum-based individual representation and quantum rotation gate operator to improve feature exploration capability of conventional genetic algorithm (GA). The expected feature yield fitness function introduced in QIEA able to identify cost-effective feature subsets. Experimental results show that quantum-based method achieves good predictive performances even with only 70–80% number of features selected by GAs, and hence achieve lower feature acquisition costs with budget constraints. Additionally, computational time can be reduced by 30–60% compared with GAs depending on different feature set sizes.

Appendix

See Table 11.

Table 11 Table of data fields extracted from three sources of mobile device logs

1.1 Feature Variable Generation Measuring Credit Risk

This sub-section presents how to generate features in the Chinese credit dataset that reflect composite measurements of credit risk features for credit scoring. The behavior of mobile users is derived according to the following four types of indicator measurements:

• 1. Diversity:

  $${D}_{i}=\frac{-\sum_{j}^{N}{f}_{ij}log {f}_{ij} }{log P}$$

  The outcome value is between 0 and 1, with larger numbers meaning higher usage diversity. For example, someone with very high diversity spreads usage almost equitably across different times. The normalization by log P keeps the focus on quantifying the relative spread across bins and gives equal chance for a user with different level of usage to score high on this measurement.

• 2. Interest concentration:

  $${C}_{i}=\frac{{h}_{i}}{\sum_{j}^{N}{f}_{ij}}$$

  The outcome value is also between 0 and 1, with larger values indicating higher interest concentrations. For example, an individual with a very high interest concentration indicates that most of usage occur within the top three interest areas.

• 3. Consistency:

  $${CI}_{i}=1 - \frac{\sqrt{{({D}_{i}^{1}}- {D}_{i}^{T}{)}^{2} + {({C}_{i}^{1}}- {C}_{i}^{T}{)}^{2}}}{\sqrt{2}}$$

  where D_i¹ and D_i^T refer to the diversity in the first three months and the entire period, respectively. Similarly, C_i¹ and C_i^T correspond to the interest concentration in the same time frames. The output distance values CI_i are between 0 and 1, with 1 indicating absolute consistency (e.g., the two usage periods are identical, and hence the first three months and overall spending patterns are) and 0 indicating perfect inconsistency.

• 4. Overspending:

  $$O_{i}=cc_i/I_i$$

  For an overspending user who spends more than their earned income, this ratio should be over 1, and the higher the ratio is, the more “overspending” and hence financially risky someone is.