论文标题
用经验PAC贝叶斯学习部分知名的随机动力学
Learning Partially Known Stochastic Dynamics with Empirical PAC Bayes
论文作者
论文摘要
神经随机微分方程模拟了一个动力环境，其神经网将其漂移和扩散项分配。其非线性的高表达能力是在识别大型自由参数时以不稳定为代价的。本文提出了一个配方，以三个步骤提高此类模型的预测准确性：i）通过假设概率权重来解决认知不确定性，ii）纳入状态动力学的部分知识，iii）通过从PAC-Bayesian普通化界限中得出的目标来训练所得的混合模型。我们在实验中观察到，该食谱将部分和嘈杂的先验知识有效地转化为改进的模型拟合。
Neural Stochastic Differential Equations model a dynamical environment with neural nets assigned to their drift and diffusion terms. The high expressive power of their nonlinearity comes at the expense of instability in the identification of the large set of free parameters. This paper presents a recipe to improve the prediction accuracy of such models in three steps: i) accounting for epistemic uncertainty by assuming probabilistic weights, ii) incorporation of partial knowledge on the state dynamics, and iii) training the resultant hybrid model by an objective derived from a PAC-Bayesian generalization bound. We observe in our experiments that this recipe effectively translates partial and noisy prior knowledge into an improved model fit.
