Bayesian Neural Networks with Regularization for Sparse Zero-Inflated Data Modeling

Zero inflation is pervasive across text mining, event log, and sensor analytics, and it often degrades the predictive performance of analytical models. Classical approaches, most notably the zero-inflated Poisson (ZIP) and zero-inflated negative binomial (ZINB) models, address excess zeros but rely on rigid parametric assumptions and fixed model structures, which can limit flexibility in high-dimensional, sparse settings. We propose a Bayesian neural network (BNN) with regularization for sparse zero-inflated data modeling. The method separately parameterizes the zero inflation probability and the count intensity under ZIP/ZINB likelihoods, while employing Bayesian regularization to induce sparsity and control overfitting. Posterior inference is performed using variational inference. We evaluate the approach through controlled simulations with varying zero ratios and a real-world dataset, and we compare it against Poisson generalized linear models, ZIP, and ZINB baselines. The present study focuses on predictive performance measured by mean squared error (MSE). Across all settings, the proposed method achieves consistently lower prediction error and improved uncertainty problems, with ablation studies confirming the contribution of the regularization components. These results demonstrate that a regularized BNN provides a flexible and robust framework for sparse zero-inflated data analysis in information-rich environments.