Hierarchical Bayesian deep learning for return on advertising spend prediction: A probabilistic approach to e-commerce advertising.

Abstract

In the highly competitive landscape of e-commerce advertising, maximizing Return on Advertising Spend (ROAS) is critical, yet remains inherently uncertain due to auction-based bidding dynamics and fluctuating market conditions. Traditional deterministic models fail to capture this uncertainty, necessitating a probabilistic approach that balances predictive accuracy with interpretability. To address this challenge, the paper proposes a novel Hierarchical Bayesian Deep Learning framework that integrates a Bayesian Belief Network (BBN) for structured probabilistic reasoning and a Mixture Density Network (MDN) for full distributional modeling of ROAS. The BBN models dependencies among campaign variables, offering interpretable insights, while the hierarchical deep learning architecture overcomes scalability limitations in high-dimensional settings through self-attention mechanisms. Experiments demonstrate up to 22.8% lower RMSE and 27.4% better Negative Log Likelihood (NLL) and up to 31.2% lower Kullback-Leibler divergence (KLD) than state-of-the-art methods (DeepAR, Prophet, NGBoost), achieving an R² of 98% with an inference speed of 5.2 ms per campaign, making real-time bidding feasible. Ablation studies confirm that attention-driven feature selection and calibrated uncertainty quantification significantly enhance both predictive performance and explainability, identifying key drivers of campaign success. By providing precise, uncertainty-aware, and explainable predictions, this approach enables adaptive bidding strategies, optimized budget allocation, and risk management, setting a new benchmark for intelligent decision-making in digital advertising.