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Causal Customer Churn Analysis with Low-rank Tensor Block Hazard Model
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Proposes a tensorized latent factor block hazard model that applies 1-bit tensor completion to a parameter tensor with clustered treatments, fit by IPTW-weighted projected gradient descent with spectral clustering, and reports non-asymptotic error bounds plus churn experiments on simulated and bank/e-commerce data.
Problem
Estimating customer churn survival probabilities under all combinations of retention interventions from observational data where only one treatment is observed per customer, with binary, time-monotone churn outcomes and confounded treatment assignment.
Approach
Low-rank Tucker structure is placed on the latent parameter tensor (not the binary outcome tensor) of a discrete-time hazard model, with the third (treatment) mode constrained to a block/membership structure learned by spectral clustering, and IPTW with covariate-balancing (entropy-balanced) propensity weights to handle confounding.
Key results
- On the bank churn dataset the proposed model reaches C-index 0.58 and average AUC 0.57, above the best baseline (gradBoost C-index 0.50, SVM AUC 0.47).
- On the e-commerce churn dataset the proposed model achieves the best average AUC (0.44) and a C-index of 0.41, second to RF (0.42).
- In simulations the normalized tensor MSE decreases with N (e.g., about 0.42 to 0.18 for N=100 to 2000 at T=5, k=2 with 10000 iterations).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use the tensorized latent factor block hazard model | customer churn modeling · Bank customer churn | C-index: 0.50 ± 0.01 -> 0.58 ± 0.02 | Helped |
| use the tensorized latent factor block hazard model | customer churn modeling · Bank customer churn | average AUC: 0.47 ± 0.12 -> 0.57 ± 0.02 | Helped |
| use the tensorized latent factor block hazard model | customer churn modeling · E-commerce customer churn | average AUC: 0.41 ± 0.01 -> 0.44 ± 0.03 | Helped |
| add latent factors for customers and time (ablation) | tensorized latent factor block hazard model · Synthetic churn, N=100, T=5, k=2 | normalized tensor mean squared error: 0.53 (0.02) -> 0.42 (0.07) | Helped |
| add treatment grouping (ablation) | tensorized latent factor block hazard model · Synthetic churn, N=100, T=5, k=2 | normalized tensor mean squared error: 0.58 (0.02) -> 0.42 (0.07) | Helped |
| add inverse probability treatment weighting (ablation) | tensorized latent factor block hazard model · Synthetic churn, N=100, T=5, k=2 | normalized tensor mean squared error: 0.54 (0.03) -> 0.42 (0.07) | Helped |
| add treatment grouping (ablation) | tensorized latent factor block hazard model · Synthetic churn, N=2000, T=5, k=2 | normalized tensor mean squared error: 0.15 (0.02) -> 0.18 (0.01) | Hurt |
| add inverse probability treatment weighting (ablation) | tensorized latent factor block hazard model · Synthetic churn, N=2000, T=5, k=2 | normalized tensor mean squared error: 0.18 (0.01) -> 0.18 (0.01) | No clear effect |
Surprising findings
- On the e-commerce data the proposed method is not best on C-index (RF 0.42 vs proposed 0.41).
- Ablation shows the factor model without grouping (factor-w) beats the group model at k=3 with N=1000 or more, and at k=2 with N=2000.
Limitations
- Assumes time-invariant treatment and no unmeasured confounding (treatment ignorability).
- Theory relies on regularity conditions (positivity, incoherence, balanced clustering) and bounds that are not shown to be tight.
- Code will be released only after acceptance; real-data evaluation is limited to two Kaggle datasets.
Experimental setup
Datasets: Simulated churn tensor data Bank customer churn (Kaggle) E-commerce customer churn (Kaggle)
Benchmarks: Simulated churn tensor data Bank customer churn (Kaggle) E-commerce customer churn (Kaggle)
Metrics: cumulative regret decision accuracy normalized tensor MSE misclassification rate C-index average time-dependent AUC
Baselines: logistic regression random forest neural network classifier SVM gradient boosting AdaBoost Cox proportional hazard survival random forest Cox gradient boosting Cox model boosting
Builds on: 1-bit matrix completion tensor block model covariate balancing propensity score entropy balancing
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