How to check the quality of recommendations without dividing data into train and test?

If it is not possible to split data into train and test sets, you can use quality assessment methods for recommendations without explicit splitting, such as:

• Cross-validation: split the data into several parts and sequentially use each as a test set, with the others as training sets.
• Offline metric evaluation: use metrics that do not require a separate test set, such as Precision@K, Recall@K, MAP, NDCG, calculated on historical data.
• Using A/B testing: if the system is already operational, you can evaluate recommendation quality on real users by comparing different recommendation options.
• Bootstrap methods: random sampling with replacement to assess model stability.

Thus, even without an explicit train/test split, it is possible to get an idea of recommendation quality using statistical methods and online experiments.