Title: Integrating Selective State-Space Models and Bayesian Graph Attention for Uncertainty-aware Time-Series Analysis
Primary area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)
Keywords: mamba, transformer, bayesian networks

Abstract: We propose \textbf{Bi-Mamba \& Bayesian MAGAC}, a unified mathematical framework that integrates bidirectional Selective State-Space Models (Bi-Mamba) with Bayesian Multi-head Adaptive Graph Attention Convolution (MAGAC) for robust financial forecasting. Bi-Mamba reformulates sequential complexity into reversible state evolution, efficiently preserving both causal and anti-causal temporal dynamics in linear time. Concurrently, MAGAC constructs adaptive graph topologies by merging latent Gaussian kernels and multi-head attention mechanisms, followed by Chebyshev spectral filtering for scalable higher-order interactions. Our Bayesian enhancement of MAGAC treats graph adjacency and spectral filters as stochastic parameters, approximating their posterior distributions via Monte-Carlo DropEdge and Dropout sampling. This innovative mathematical integration delivers calibrated predictive uncertainty without additional computational overhead. The proposed architecture establishes a novel theoretical synergy between scalable state-space sequence modeling and principled Bayesian graph convolution, advancing risk-aware prediction methodologies in financial time-series analysis.

TL;DR: Bi-Mamba & Bayesian MAGAC combines bidirectional selective state-space models with Bayesian graph attention for scalable, uncertainty-aware financial forecasting in linear time.