Dynamical System Modeling and Stability Investigation�DSMSI-2025

May 08-10, 2025, Kyiv, Ukraine

COST-SENSITIVE DECISION TREES WITH PROSPECT THEORY FOR CHURN PREDICTION

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Ihor Cherevko, Halyna Melnyk, and Vasyl Melnyk

Yuriy Fedkovych Chernivtsi National University�

Relevance of the Topic

• In the digital economy, customer retention is far more cost-effective than acquiring new customers, making it a central focus for sustainable business growth.
• High churn rates in online retail directly impact profitability, especially when high-value customers are lost.
• Traditional machine learning models often aim to maximize prediction accuracy, but they overlook the economic implications of false positives and false negatives.
• This research emphasizes the need to align churn prediction models with business goals by factoring in customer lifetime value (CLV) and the cost of promotional interventions.
• By integrating economic reasoning into churn modeling, businesses can optimize decision-making and improve the return on investment for retention campaigns.

Dynamical System Modeling and Stability Investigation, DSMSI-2025

Aim and Objectives

• Goal: Develop a churn prediction model that integrates economic utility and behavioral decision-making

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• Tasks:
• Data preprocessing and feature engineering
• Implementation of cost-sensitive decision trees
• Integration of Cumulative Prospect Theory (CPT)
• Evaluation based on utility-driven metrics

Dynamical System Modeling and Stability Investigation, DSMSI-2025

Literature Review

Summary of relevant works:

• Traditional machine learning approaches (Logistic Regression, Decision Trees)
• Cost-sensitive modeling (Verbraken et al., Bahnsen et al.)
• Prospect Theory (Kahneman and Tversky)

Dynamical System Modeling and Stability Investigation, DSMSI-2025

Theoretical Foundations

• Customer Lifetime Value (CLV) quantifies the projected revenue a business can expect from a customer over the entire relationship, making it a crucial factor in prioritizing retention efforts.
• In the proposed model, CLV is used not just as a feature, but as a core element in calculating the expected economic utility of intervention.
• Cumulative Prospect Theory (CPT), introduced by Kahneman and Tversky, reflects how people evaluate potential gains and losses under risk, often deviating from purely rational decisions.
• CPT incorporates concepts like loss aversion, where losses are weighted more heavily than equivalent gains, and nonlinear probability weighting, where people overestimate small probabilities and underestimate large ones.
• These psychological effects are mathematically modeled through value and weighting functions, which are embedded in the utility function used by the churn prediction model.

Dynamical System Modeling and Stability Investigation, DSMSI-2025

Theoretical Foundations

• Customer Lifetime Value (CLV) quantifies the projected revenue a business can expect from a customer over the entire relationship, making it a crucial factor in prioritizing retention efforts.
• In the proposed model, CLV is used not just as a feature, but as a core element in calculating the expected economic utility of intervention.
• Cumulative Prospect Theory (CPT), introduced by Kahneman and Tversky, reflects how people evaluate potential gains and losses under risk, often deviating from purely rational decisions.
• CPT incorporates concepts like loss aversion, where losses are weighted more heavily than equivalent gains, and nonlinear probability weighting, where people overestimate small probabilities and underestimate large ones.
• These psychological effects are mathematically modeled through value and weighting functions, which are embedded in the utility function used by the churn prediction model.

Dynamical System Modeling and Stability Investigation, DSMSI-2025

Dataset and Feature Engineering

• The dataset consists of online retail customer data, including demographic, behavioral, and transactional attributes for 600 customers.

Dynamical System Modeling and Stability Investigation, DSMSI-2025

Dataset and Feature Engineering

• Key engineered features include Return Ratio (returns per purchase), Purchase Frequency, Customer Lifetime Value (CLV), and an Engagement Score derived from interactions with marketing campaigns.

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• Categorical variables such as Gender, Promotion Response, and Email Opt-in status were converted using one-hot encoding to ensure compatibility with machine learning models.

Dynamical System Modeling and Stability Investigation, DSMSI-2025

Dataset and Feature Engineering

• The core of the model is the Expected Utility formula:

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• This formula quantifies the economic benefit of targeting a customer, guiding the model toward decisions that prioritize profitability over mere predictive accuracy.

Dynamical System Modeling and Stability Investigation, DSMSI-2025

 Customers 0, 1, 2, 6, and 7 show negative utility, indicating dissatisfaction or risk of leaving

Model Architecture

• The core model is a cost-sensitive Decision Tree classifier, chosen for its interpretability and ability to incorporate decision-specific economic parameters.
• Trains the model using `sample_weight`, focusing the model’s learning more heavily on customers who represent higher potential gains or losses (utility-driven).

Dynamical System Modeling and Stability Investigation, DSMSI-2025

Model Architecture

• During training, sample weights were adjusted using a utility-based function that prioritized accurate predictions for high-CLV customers with a high probability of churn.
• This approach allows the model to focus on economically impactful errors, minimizing costly false negatives and avoiding unnecessary retention efforts.
• Unlike traditional models that optimize for accuracy alone, this classifier was trained and evaluated based on expected financial utility.
• As a result, the model’s structure and splits were aligned with maximizing profit, not just statistical performance.

Dynamical System Modeling and Stability Investigation, DSMSI-2025

Evaluation Metrics

• Precision (Positive class: "1" - Churn): 0.57 Indicates that out of all customers predicted to churn, 57% actually churned. The model is moderately good at correctly identifying actual churn cases.
• Recall (Positive class: "1" - Churn): 0.55 Indicates that the model correctly detected 55% of all customers who actually churned. There's room for improvement to better capture customers who might churn.
• F1-score (Positive class: "1" - Churn): 0.56 Represents a balance between precision and recall. It's slightly above average, showing the model is fairly balanced but could benefit from further tuning.
• Accuracy: 0.53 (53%) Slightly better than random (50%), suggesting that the model provides value but has considerable potential for optimization.

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• The model's decisions resulted in a total financial impact of $49,879.37, which reflects the economic value of targeting customers effectively using predicted churn probabilities and Customer Lifetime Value (CLV).

Dynamical System Modeling and Stability Investigation, DSMSI-2025

Results and Key Findings

• The cost-sensitive Decision Tree classifier achieved approximately 53% accuracy, prioritizing economic value over traditional metrics.
• It demonstrated higher precision in detecting high-risk churners with high CLV, improving targeted retention.
• The model reduced the number of promotions sent to low-CLV customers, preserving marketing budget and improving ROI.
• The total utility (financial impact) from model decisions was nearly $49,879, highlighting the value of profit-aware modeling.

Dynamical System Modeling and Stability Investigation, DSMSI-2025

Economic Impact

• The model integrates Customer Lifetime Value (CLV) to prioritize which customers should receive retention efforts, ensuring high-value customers are targeted first.
• As a result, the number of promotions is reduced, but their effectiveness increases, leading to a higher return on investment (ROI).
• By incorporating Cumulative Prospect Theory (CPT), the model accounts for customer risk perceptions and behavioral biases, which helps reduce overfitting to anomalous or extreme cases.
• This economically grounded approach enables smarter allocation of retention budgets and maximizes the financial return of each model-driven decision.

Dynamical System Modeling and Stability Investigation, DSMSI-2025

Limitations and Challenges

• The model was trained and evaluated on a relatively small dataset (600 customers), which may limit its generalizability to larger or more diverse populations.
• The moderate accuracy (~53%) indicates room for improvement, highlighting the potential value of exploring more advanced algorithms such as ensemble methods or deep learning.
• The dataset lacked rich behavioral or contextual variables (e.g., browsing history, support ticket sentiment), which are often critical for accurately predicting churn and tailoring interventions.
• These limitations suggest a clear direction for future enhancements through data enrichment and methodological sophistication.

Dynamical System Modeling and Stability Investigation, DSMSI-2025

Conclusions

• Integrating behavioral economics through Cumulative Prospect Theory and cost-sensitive machine learning provides clear business value by aligning model predictions with financial outcomes.
• Traditional churn prediction focused only on accuracy; this research demonstrates that incorporating economic context, such as CLV and intervention cost, leads to smarter, more profitable decisions.
• The approach forms a practical foundation for data-driven retention strategies that balance customer value with marketing efficiency.
• This work also establishes the groundwork for future enhancements, such as the use of reinforcement learning, Bayesian decision models, or deep contextual bandits to support real-time, adaptive churn interventions.

Dynamical System Modeling and Stability Investigation, DSMSI-2025

Future Work

• Expanding the approach to larger and more diverse datasets will improve model robustness and generalizability across different customer segments and industries.
• A key direction is the integration of real-time decision systems, enabling instant churn risk evaluation and immediate, personalized retention actions.
• Future studies should explore deep learning techniques and contextual bandit algorithms, which can better handle high-dimensional data and adapt to dynamic customer behaviors.
• These advances will support more scalable, personalized, and profitable churn management strategies driven by continuous learning and economic utility optimization.

Dynamical System Modeling and Stability Investigation, DSMSI-2025

Thank you for your attention