CLVAE: A Variational Autoencoder for Long-Term Customer Revenue Forecasting

In non-contractual settings, firms must routinely infer customers' long-term future revenue from transaction data that record only purchase timing and monetary value. Customers differ substantially in their underlying purchase propensities, spending levels, and attrition propensities, yet these differences are only indirectly reflected in sparse transaction data. Attrition itself is not directly observed, so a period without purchases is inherently ambiguous, as a customer may be temporarily inactive or may have permanently discontinued purchasing. The structure of the observed transaction records makes learning these differences difficult. Additionally, purchase behavior is highly heterogeneous, with up to 50% of customers purchasing only once while others transact repeatedly. Even among repeat buyers, transaction records are sparse and irregular. Purchases occur at uneven intervals and are separated by long stretches with no transactions. Finally, observation windows vary with customer tenure and are often short relative to the forecasting horizon. As a result, the observed records contain limited information to infer customer-specific propensities and predict long-run revenue.

In non-contractual settings, predicting customers' long-term revenue is crucial for effective marketing resource allocation. However, existing approaches face a trade-off between structural stability and flexibility. Traditional probabilistic models offer robust long-term forecasts through strong structural assumptions, while flexible machine learning models require substantial training data and careful tuning. The challenge is whether it is possible to retain the structural strengths of traditional probabilistic models while relaxing their restrictive assumptions about latent heterogeneity by leveraging deep learning techniques.

This paper proposes a variational autoencoder (VAE)-based model, CLVAE, which combines the process-based likelihood of traditional attrition-transaction-spend models with a flexible latent representation learned by encoder-decoder networks. The CLVAE model provides a single model for customer attrition, transactions, and spending, remains reliable without contextual covariates, and flexibly incorporates rich covariates and nonlinear effects when available. Compared to state-of-the-art methods, the CLVAE model demonstrates greater robustness and scalability when handling sparse and irregular transaction data.

• �� The CLVAE model is based on the variational autoencoder (VAE) framework, utilizing a generative latent-variable model to achieve flexible high-dimensional data modeling through variational inference.
• �� It retains the process-based likelihood of traditional attrition-transaction-spend models while replacing the restrictive parametric mixing distribution with a flexible latent representation learned by encoder-decoder networks.
• �� The model provides a single framework for customer attrition, transactions, and spending, maintaining reliability without contextual covariates and flexibly incorporating nonlinear effects when rich covariates are available.
• �� By compressing observed recency and frequency data into latent variables, the model achieves a nonparametric extension of traditional probabilistic models.

The paper evaluates the CLVAE model across multiple real-world datasets and prediction horizons. The experimental design includes using actual transaction datasets, setting different prediction horizons, and comparing with the latest benchmark models. The results show that the CLVAE model outperforms existing state-of-the-art methods in prediction accuracy, particularly excelling in long-term predictions. Ablation studies confirm the robustness and accuracy of the CLVAE model across different datasets.

Across multiple real-world datasets and prediction horizons, the CLVAE model improved prediction accuracy compared to the latest benchmarks. For instance, on a specific dataset, the prediction error was reduced by 15%. This improvement directly benefits businesses, as better assessments of future customer revenues enhance campaign targeting efficiency. Ablation studies confirmed the robustness and accuracy of the CLVAE model across different datasets, particularly excelling in long-term predictions.

The CLVAE model can be directly applied to marketing resource allocation in non-contractual settings, improving campaign targeting efficiency. By better assessing future customer revenues, businesses can optimize resource allocation, enhancing customer retention and revenue. Additionally, the CLVAE model can be used in other fields requiring long-term predictions, such as financial risk assessment and customer relationship management.

Despite the CLVAE model's excellent performance across multiple real-world datasets, it may perform poorly with extremely sparse data, as it relies on a certain amount of historical data to learn latent representations. Training the model can be time-consuming, especially on large-scale datasets. Additionally, the model's performance may be affected by the choice of covariates and parameter tuning. Future research directions include exploring the application of the CLVAE model across broader industries and data environments, and further optimizing computational efficiency.