Cost Matters: A New Example-Dependent Cost-Sensitive Logistic Regression Model

Abstract

Connectivity and automation are evermore part of today’s cars. To provide automation, many gauges are integrated in cars to collect physical readings. In the automobile industry, the gathered multiple datasets can be used to predict whether a car repair is needed soon. This information gives drivers and retailers helpful information to take action early. However, prediction in real use cases shows new challenges: misclassified instances have not equal but different costs. For example, incurred costs for not predicting a necessarily needed tire change are usually higher than predicting a tire change even though the car could still drive thousands of kilometers. To tackle this problem, we introduce a new example-dependent cost sensitive prediction model extending the well-established idea of logistic regression. Our model allows different costs of misclassified instances and obtains prediction results leading to overall less cost. Our method consistently outperforms the state-of-the-art in example-dependent cost-sensitive logistic regression on various datasets. Applying our methods to vehicle data from a large European car manufacturer, we show cost savings of about 10%.

A Appendix

$$\begin{aligned}&\qquad \quad \frac{F_{a_i log^{b_i}}}{F_{a_i log^{b_i}}}=\frac{a_i \varGamma (b_i + 1, 0.6931)}{a_i (\varGamma (b_i +1)- \varGamma (b_i +1, 0.6931))} \mathop {=}\limits ^{!} c_i \cdot \frac{F_{log}}{T_{log}} \\&\Leftrightarrow \varGamma (b_i +1, 0.6931)\mathop {=}\limits ^{!} c_i \cdot \frac{F_{log}}{T_{log}} \cdot \varGamma (b_i +1)- c_i \cdot \frac{F_{log}}{T_{log}} \varGamma (b_i + 1, 0.6931) \\&\qquad \qquad \Leftrightarrow \frac{\varGamma (b_i +1)}{\varGamma (b_i +1, 0.6931)}\mathop {=}\limits ^{!} \frac{1+c_i \cdot \frac{F_{log}}{T_{log}}}{c_i \cdot \frac{F_{log}}{T_{log}}}=1+ \frac{T_{log}}{c_i \cdot F_{log}} \end{aligned}$$