标题： 在线性不等式约束下的高斯过程调制Cox过程 显示英文标题

标题： Gaussian Process Modulated Cox Processes under Linear Inequality Constraints

摘要： 高斯过程（GP）调制的Cox过程被广泛用于建模点模式。现有方法需要在无约束的GP和正强度函数之间建立一个映射（链接函数）。这通常导致没有闭合形式的解，或者仅限于特定的协方差函数。我们引入了一种新颖的有限GP调制Cox过程的近似方法，在该方法中可以直接对GP施加正性条件，并且对协方差函数没有任何限制。我们的方法还可以确保其他类型的不等式约束（例如，单调性、凸性），从而产生更通用的模型，可以用于其他类别的点过程（例如， renewal 过程）。我们在合成数据和真实数据上证明了我们的框架能够准确推断出强度函数。当单调性是过程的一个特征时，我们能够在推断中包含这一点以改进结果。 显示英文摘要

摘要： Gaussian process (GP) modulated Cox processes are widely used to model point patterns. Existing approaches require a mapping (link function) between the unconstrained GP and the positive intensity function. This commonly yields solutions that do not have a closed form or that are restricted to specific covariance functions. We introduce a novel finite approximation of GP-modulated Cox processes where positiveness conditions can be imposed directly on the GP, with no restrictions on the covariance function. Our approach can also ensure other types of inequality constraints (e.g. monotonicity, convexity), resulting in more versatile models that can be used for other classes of point processes (e.g. renewal processes). We demonstrate on both synthetic and real-world data that our framework accurately infers the intensity functions. Where monotonicity is a feature of the process, our ability to include this in the inference improves results.