发表机构
Eindhoven University of Technology; Lviv Polytechnic National University; Lazy Dynamics（埃因霍温理工大学; 利沃夫国立理工大学; 拉齐动力公司）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究在Forney风格因子图上推导自然梯度消息传递（NGMP），其比变分消息传递更准确，在泊松平滑等实验中主要提升不确定性校准效果。
AI 中文摘要
我们证明，变分推断的自然梯度平稳条件在Forney风格因子图上具有边局部形式。我们从Bethe自由能出发，将选定的边边际约束到指数族。在平稳点，该边的自然参数等于两个投影消息之和，每个投影消息来自一个关联因子。每个投影消息是当前接收边际处精确信念传播对数消息的自然梯度投影，等价于其在所谓均值坐标中的期望梯度。我们将所得方案称为自然梯度消息传递（NGMP）。该规则是局部的，每条边可携带自身的指数族，因子发送的消息取决于接收它的边际。与变分消息传递相比，NGMP保留接收族可表示的精确消息部分，而非在相邻信念下对因子取平均。当进入非共轭因子的边不确定性消失时，二者一致；当该不确定性持续存在时，NGMP更准确，例如沿部分观测的隐链或通过连续数据批次过滤参数时。在泊松平滑、异方差回归和每小时ETTh预测上的实验证实了这一点，且增益主要出现在不确定性校准上。
英文摘要
We show that the natural-gradient stationary condition of variational inference has an edge-local form on a Forney-style factor graph. We start from the Bethe free energy and constrain a selected edge marginal to an exponential family. At a stationary point, the natural parameter of that edge equals the sum of two projected messages, one from each incident factor. Each projected message is the natural-gradient projection of the exact belief-propagation log-message at the current receiving marginal, or equivalently, the gradient of its expectation in the so-called mean coordinates. We call the resulting scheme natural-gradient message passing (NGMP). The rule is local; each edge may carry its own exponential family, and the message a factor sends depends on the marginal that receives it. Compared with variational message passing, NGMP keeps the part of the exact message that the receiving family can represent instead of averaging the factor under the neighboring beliefs. The two coincide when the uncertainty on the edges entering a non-conjugate factor vanishes, and NGMP is more accurate when that uncertainty persists, for example, along a partially observed latent chain or when parameters are filtered through successive data batches. Experiments on Poisson smoothing, heteroskedastic regression, and hourly ETTh forecasting confirm this and show that the gain appears mainly in uncertainty calibration.
