ZILN-Net: Zero-Inflated Lognormal deep learning for probabilistic demand forecasting

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We propose ZILN-Net, a deep learning framework for probabilistic time-series forecasting that explicitly models mixed zero/non-zero outcomes. The model decomposes each prediction into two components: an event probability (modeled by a binary output head) and a continuous magnitude distribution (modeled by a log-normal output head). This zero-inflated lognormal (ZILN) formulation allows learning to exploit the prevalence of zero-demand events while modeling positive values, and categorical embeddings capture cross-series heterogeneity. We evaluate the approach on four retail demand benchmarks spanning heterogeneous sparsity (raw M5 Walmart unit sales, Rossmann store sales, Favorita, and StoreItem) under a rolling-origin cross-validation protocol with three random seeds and three folds, comparing against seasonal-naive and moving-average baselines, a log-normal-only network, an independently trained two-stage model, a Tweedie (compound Poisson–gamma) network, and a DeepAR-like LSTM run under the identical protocol. Under extreme sparsity (M5, validation zero rate 0.60), ZILN-Net attains the best or tied-best mean on five of the six reported metrics—event discrimination (AUC 0.777 ±0.008 versus 0.500 for the log-normal-only baseline), point magnitude (MASE 0.764 ±0.008, ahead of the best simple baseline at 0.907), and probabilistic accuracy (CRPS 0.582 ±0.005)—improving significantly over every single-model baseline ( p < 1 0 − 4 ) while matching an independently trained two-stage model of twice the size (a statistical tie, per-series p up to 0.54) at half the parameters and under a single joint likelihood. On the moderately sparse Rossmann data ZILN-Net’s event discrimination is strong (AUC 0.941 ±0.051) and its point accuracy matches the moving-average baseline, while the Tweedie baseline attains the best CRPS—a sharpness limitation of the log-normal magnitude head on high-magnitude data that we report openly. On the dense Favorita and StoreItem controls all neural models perform similarly and modestly beat the simple baselines, confirming that the decomposition’s specific advantage is concentrated where zeros are frequent. A target-normalization ablation shows that with standardized inputs and median point forecasts, raw-scale training is preferable and a log ( 1 + y ) transform is unnecessary. The results indicate that explicit event–magnitude decomposition is most beneficial for event discrimination, point accuracy, and probabilistic calibration under high sparsity.

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