We introduce squared neural Poisson point processes (SNEPPPs) by
parameterising the intensity function by the squared norm of a two layer neural
network. When the hidden layer is fixed and the second layer has a single
neuron, our approach resembles previous uses of squared Gaussian process or
kernel methods, but allowing the hidden layer to be learnt allows for
additional flexibility. In many cases of interest, the integrated intensity
function admits a closed form and can be computed in quadratic time in the
number of hidden neurons. We enumerate a far more extensive number of such
cases than has previously been discussed. Our approach is more memory and time
efficient than naive implementations of squared or exponentiated kernel methods
or Gaussian processes. Maximum likelihood and maximum a posteriori estimates in
a reparameterisation of the final layer of the intensity function can be
obtained by solving a (strongly) convex optimisation problem using projected
gradient descent. We demonstrate SNEPPPs on real, and synthetic benchmarks, and
provide a software implementation. this https URL

通过将强度函数的参数化为一个两层神经网络的平方范数，引入了平方神经泊松点过程（SNEPPPs）。我们的方法在固定隐藏层且第二层只有一个神经元的情况下，类似于以前使用平方高斯过程或核方法的方法，但允许学习隐藏层可以提供额外的灵活性。在许多感兴趣的情况下，积分强度函数具有封闭形式，并且可以在隐藏神经元数量的二次时间内计算。我们列举了比以前讨论的更多这样的示例。我们的方法比平方或指数核方法或高斯过程的朴素实现更节省内存和时间。可以通过使用投影梯度下降解决（强）凸优化问题来获得强度函数最终层的重参数化的最大似然估计和最大后验估计。我们在真实和合成基准测试上演示了 SNEPPPs，并提供了一个软件实现。