Variational Inference for Dynamic Mixtures in Probabilistic Time-Series Forecasting

Probabilistic time-series forecasting requires modeling complex, dynamic, and often multimodal conditional distributions while maintaining computational efficiency. We propose a lightweight finite mixture framework that uses a mixture sieve model and an analytically derived optimal posterior for reconstruction, thereby reducing the variational inference problem for conditional distribution estimation to a multi-class classification task. The framework defines the model output in the fractionally differenced domain, which alleviates distribution shift in the target variable and yields a dynamic mixture representation with time-varying component locations on the original scale. The proposed objective provides a quantization-level distributional approximation guarantee and has bounded logit-level gradients. Experiments on real-world benchmarks demonstrate that our method consistently outperforms existing probabilistic forecasting approaches while generating plausible future trajectories and competitive point estimates.