Causal Customer Churn Analysis with Low-rank Tensor Block Hazard Model (2405.11377v1)

Abstract: This study introduces an innovative method for analyzing the impact of various interventions on customer churn, using the potential outcomes framework. We present a new causal model, the tensorized latent factor block hazard model, which incorporates tensor completion methods for a principled causal analysis of customer churn. A crucial element of our approach is the formulation of a 1-bit tensor completion for the parameter tensor. This captures hidden customer characteristics and temporal elements from churn records, effectively addressing the binary nature of churn data and its time-monotonic trends. Our model also uniquely categorizes interventions by their similar impacts, enhancing the precision and practicality of implementing customer retention strategies. For computational efficiency, we apply a projected gradient descent algorithm combined with spectral clustering. We lay down the theoretical groundwork for our model, including its non-asymptotic properties. The efficacy and superiority of our model are further validated through comprehensive experiments on both simulated and real-world applications.

• The paper introduces a novel tensorized latent factor block hazard model using low-rank parameter tensor constraints to identify homogeneous intervention groups and extract latent customer factors from binary churn data.
• The model addresses the 1-bit tensor completion challenge for binary churn data and provides robust non-asymptotic analysis with theoretical guarantees on estimation and clustering accuracy.
• Utilizing projected gradient descent and spectral clustering for efficiency, the model demonstrates superior performance in real-world data experiments, offering practical utility for optimizing customer retention strategies.

The paper "Causal Customer Churn Analysis with Low-rank Tensor Block Hazard Model" presents a novel approach to understanding the impact of various interventions on customer churn using a sophisticated statistical model. The researchers introduce a tensorized latent factor block hazard model, which leverages tensor completion techniques within a causal framework to effectively analyze and predict customer churn dynamics. Particularly, the model accounts for the binary and sequential nature of churn data, capturing latent customer characteristics and uncovering temporal elements in customer behavior.

Key Contributions

1. Tensorized Latent Factor Block Hazard Model: The proposed model operates by applying low-rank constraints to a parameter tensor, rather than directly to the data tensor, enabling the extraction of latent unit and temporal factors while identifying homogeneous intervention groups. This approach helps in grouping interventions with similar effects, thereby simplifying the intervention space.
2. 1-Bit Tensor Completion: The model tackles the 1-bit tensor completion problem, where churn is represented as binary data with a time-monotonic pattern, making it challenging to directly apply traditional low-rank constraints. This methodological insight addresses typical challenges in causal analysis of binary outcome data.
3. Non-Asymptotic Properties: The researchers perform a non-asymptotic analysis showing that the estimation and clustering errors for the model converge as the sample size increases. This theoretical framework includes upper bound estimations for the recovery accuracy of the parameter tensor and clustering, thus providing robust guarantees on the model's performance.
4. Spectral Clustering and Projected Gradient Descent: For computational efficiency, the model employs a projected gradient descent algorithm in combination with spectral clustering. This allows the optimization of the inverse probability treatment weighted (IPTW) loss function and the automatic identification of intervention clusters.
5. Real-World Applicability: Experimentation on real-world datasets demonstrates the practical utility of the proposed method. It effectively captures the causal impact of interventions and shows potential in devising optimal strategies to increase customer retention.

Theoretical Insights

• Assumptions and Framework: The model operates under the potential outcomes framework, and includes standard assumptions such as SUTVA (Stable Unit Treatment Value), no unmeasured confounders, non-informative censoring, and positive selection probabilities.
• Tensor Algebra: The paper provides detailed tensor algebra techniques, including Tucker decomposition and mode-$k$ tensor-matrix products, crucial for formulating the tensorized model.
• Optimization Strategy: Implementation of projected gradient descent and nearest-neighbor search for optimal clustering enhances the model's computational tractability and scalability for large datasets.

Experimental Results

The model is validated through synthetic experiments and real-data applications, where it demonstrates superior performance over traditional models, such as logistic regression, support vector machines, and various boosting methods, especially in cumulative regret and decision accuracy for optimal intervention search.

Conclusion

This research advances the understanding of customer churn by framing it within a causal inference context using advanced tensor-based models. By clustering interventions with similar effects and providing robust non-asymptotic guarantees, it expands the toolkit for customer retention strategies, potentially impacting various industries where customer lifecycle analysis is crucial.