论文标题
加性泊松过程：随机过程中高阶相互作用的学习强度
Additive Poisson Process: Learning Intensity of Higher-Order Interaction in Stochastic Processes
论文作者
论文摘要
我们提出了添加泊松过程（APP），这是一个新型框架，可以使用较低的尺寸投影在随机过程中对强度函数的高阶相互作用效应进行建模。我们的模型将信息几何形状中的技术结合在一起，以模拟统计歧管上的高阶相互作用，并在广义添加剂模型中使用低维投影来克服维度诅咒的影响。我们的方法通过最大程度地减少了从较低维投影中的样本分布到由随机过程中强度函数建模的分布来解决凸优化问题。我们的经验结果表明，我们的模型能够使用在较低维空间中观察到的样品来估计具有极为稀疏的观测值的高阶强度函数。
We present the Additive Poisson Process (APP), a novel framework that can model the higher-order interaction effects of the intensity functions in stochastic processes using lower dimensional projections. Our model combines the techniques in information geometry to model higher-order interactions on a statistical manifold and in generalized additive models to use lower-dimensional projections to overcome the effects from the curse of dimensionality. Our approach solves a convex optimization problem by minimizing the KL divergence from a sample distribution in lower dimensional projections to the distribution modeled by an intensity function in the stochastic process. Our empirical results show that our model is able to use samples observed in the lower dimensional space to estimate the higher-order intensity function with extremely sparse observations.
