首个基于扩散模型的神经估计算法,可解析复杂系统的信息构成。
DIPHINE: Diffusion-based $Φ$-ID Neural Estimator

- 用扩散模型统一估计信息分解所需的所有互信息项
- 在合成数据上准确恢复16个信息原子,优于传统方法
- 无需分布假设,适用于真实生理数据中的信息结构分析
揭示真实复杂系统的内在信息架构,需分离其组件如何独特存储、冗余共享及协同整合信息。集成信息分解(ΦID)框架将多变量系统的信息动态分解为16个非重叠的原子,刻画冗余、独特与协同的信息存储、传递和整合模式。现有方法仅限于高斯或离散系统,无法应用于连续非高斯动力系统。本文提出DIPHINE(Diffusion-based Φ-ID Neural Estimator),首个利用基于得分的扩散模型的神经估计算法,通过单一可复用网络联合估计ΦID所需的全部互信息项,并通过莫比乌斯反演恢复16个原子。我们对反演过程中的误差传播进行理论分析,表明从互信息到原子的映射雅可比矩阵为整数,且协同-协同原子理论上最难估计。在合成基准测试中实现了对真实原子的精确恢复,性能优于已有互信息估计算法,并在无需分布假设的情况下,成功提取真实数据中的生理可解释信息动态结构。
原文摘要 · Abstract (English)
Uncovering the true informational architecture of real-world complex systems requires disentangling how their components uniquely store, redundantly share, and synergistically integrate information over time. Integrated Information Decomposition ($Φ$ID) is a framework for decomposing the information dynamics of multivariate systems into sixteen non-overlapping atoms that characterize redundant, unique, and synergistic modes of information storage, transfer, and integration. Existing methods to compute $Φ$ID are restricted to Gaussian or discrete systems, preventing its application to continuous non-Gaussian dynamical systems. We address this limitation by proposing DIPHINE (Diffusion-based $Φ$-ID Neural Estimator), the first neural estimator that leverages score-based diffusion models to jointly estimate all the mutual information terms required by $Φ$ID from a single amortized network, recovering the sixteen atoms through Möbius inversion. We provide a theoretical analysis of error propagation through the inversion, showing that the Jacobian of the mapping from mutual informations to atoms is integer-valued and that the synergy-to-synergy atom is provably the hardest to estimate. We demonstrate accurate recovery of ground-truth atoms on synthetic benchmarks, superior performance compared to established mutual information estimators, and the ability to extract physiologically interpretable information-dynamic structure on an application involving real data without any distributional assumptions.
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