## 5 Conclusions  
Overall, our study makes the following contributions to the research:  
* It proposes a time-based testing methodology for telecommunication churn data, showing how models behave under realistic delays.
* It demonstrates that partial-churn labels can serve as a good substitute for full-churn labeling, saving weeks of waiting time without losing much predictive power.
* It confirms that CatBoost remained reasonably robust in our investigated time windows, though drift could become larger in rapidly changing environments, requiring ongoing checks or updates.  
**Threshold Choices and Potential Extensions.** We found evidence that using a higher threshold can improve the performance of the full-churn prediction task. Instead of simply tuning thresholds, one might also consider assigning higher weights to the churn class during the training process. Although such strategies lie beyond the scope of this work, our results suggest they are promising directions. Future research could explore these techniques--along with dynamic threshold tuning, online learning, and cost-sensitive training--to see how well they reduce the impact of concept drift, particularly in more volatile markets or over longer time spans.  
Conceptualization, A.B. and R.K.; methodology, A.B., R.K. and V.C.; software, A.B., R.K. and V.C.; validation, A.B., R.K. and V.C.; formal analysis, A.B. and R.K.; investigation, A.B., R.K. and V.C.; resources, A.B.; data curation, A.B.; writing--original draft preparation, A.B. and R.K.; writing--review and editing, A.B., R.K. and V.C.; visualization, A.B. and V.C.; supervision, A.B. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The data used in this research are private data from the company.  
**Acknowledgments:** This article is dedicated to the memory of [PERSON] (1945-2023), whose novel contributions and unwavering support laid the foundation for this study. His vision and guidance will continue to inspire all of us in our academic community. We acknowledge that ChatGPT 4.0 was used to improve the text quality without the generation of new knowledge.  
**Conflicts of Interest:** The authors declare no conflicts of interest.  
param_space = {  'iterations': 2000,  'learning_rate': hp.loguniform('learning_rate', np.log(0.001), np .log(0.1)),  'depth': hp.quniform('depth', 4, 10, 1),  '12_leaf.reg': hp.loguniform('12_leaf_reg', np.log(1e-5), np.log  (10)),  'random_strength': hp.uniform('random_strength', 0, 1),  'rsm': hp.uniform('rsm', 0.5, 1.0),  'grow_policy': hp.choice('grow_policy', [  'SymmetricTree',  {  'grow_policy': 'Depthwise', 'min_data_in_leaf_depthwise': hp.quniform( 'min_data_in_leaf_depthwise', 1, 10, 1  ),  },  {  'grow_policy': 'Lossguide', 'min_data_in_leaf_lossguide': hp.quniform( 'min_data_in_leaf_lossguide', 1, 10, 1  ),  },  'bootstrap_type': hp.choice('bootstrap_type', [  {  'bootstrap_type': 'Bayesian',  'bagging_temperature': hp.uniform('bagging_temperature',  0, 1),  },  {  'bootstrap_type': 'Bernoulli', 'subsample_bernoulli': hp.uniform('subsample_bernoulli',  0.5, 1.0),  },  {  'bootstrap_type': 'No',  },  },  },  },  
Figure **A4**. Definition of the hyperparameter space using the Hyperopt library.