Hierarchical Bayesian Deep Learning for return on advertising spend prediction: A probabilistic approach to e-commerce advertising

In the highly competitive landscape of e-commerce advertising, maximizing return on advertising spend (ROAS) is crucial yet inherently uncertain due to auction-based bidding dynamics and fluctuating market conditions. Traditional deterministic models struggle 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. The architecture was motivated by initial exploratory analysis using a Bayesian Belief Network (BBN) to map structural dependencies, while the final deep learning model overcomes scalability limitations using self-attention mechanisms and a Mixture Density Network (MDN) for full distributional modeling of ROAS. The BBN captures dependencies among campaign variables, enhancing interpretability, while the hierarchical deep learning architecture leverages self-attention mechanisms to address scalability challenges in high-dimensional settings. Experimental results reveal that the proposed framework achieves 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 R 2 of 98% with an inference speed of 5.2 ms per campaign, confirming its feasibility for real-time bidding applications which typically require sub-10ms latency, enabling a feasible real-time bidding. 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. • Proposed Hierarchical Bayesian Deep Learning model improves ROAS prediction accuracy. • Achieves 22.8% lower RMSE and 27.4% better Negative Log Likelihood than SOTA. • Combines Bayesian Belief and Mixture Density Networks for precise, uncertainty-aware predictions. • Enables real-time bidding with an inference speed of 5.2 ms per campaign. • Utilizes attention-driven feature selection for scalable and explainable predictions.