Integrating Selective State-Space Models and Bayesian Graph Attention for Uncertainty-aware Time-Series Analysis

Quang-Vinh Dang, SonAn Nguyen Ngoc

Keywords: mamba, transformer, bayesian networks

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.

Abstract:

This paper presents \textbf{BIMAMBA \& Bayesian-MAGAC}, a unified framework that integrates bidirectional Selective State-Space Models with Bayesian Multi-head Adaptive Graph Attention Convolution for uncertainty-aware financial forecasting. The framework addresses two fundamental challenges: capturing long-range temporal dependencies across volatile market regimes while maintaining linear complexity, and learning adaptive cross-sectional structure with calibrated predictive uncertainty. BIMAMBA processes sequences bidirectionally via reversible state-space filters, extracting complementary temporal features while preserving strict causality. MAGAC constructs dynamic adjacencies through Gaussian kernel and attention blending, followed by Chebyshev spectral filtering for multi-scale aggregation. The Bayesian extension treats adjacencies and spectral filters as stochastic variables via Monte Carlo Dropout and DropEdge, yielding posterior predictive distributions with closed-form variance propagation at $\mathcal{O}(N)$ complexity. Comprehensive evaluations on U.S. equity indices demonstrate that the architecture achieves substantial improvements in both point prediction accuracy and uncertainty calibration compared to established baselines, with statistically significant correlation between predicted uncertainty and prediction difficulty, suggesting practical utility for risk-aware decision making in financial applications.
\textit{The code is available on GitHub but has been hidden to preserve anonymity during the review process.}

Primary Area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)

Submission Number: 6564