Abstract
In this work, we propose new objective functions to train deep neural network based density ratio estimators and apply it to a change point detection problem. Existing methods use linear combinations of kernels to approximate the density ratio function by solving a convex constrained minimization problem. Approximating the density ratio function using a deep neural network requires defining a suitable objective function to optimize. We formulate and compare objective functions that can be minimized using gradient descent and show that the network can effectively learn to approximate the density ratio function. Using our deep density ratio estimation objective function results in better performance on a seizure detection task than other (kernel and neural network based) density ratio estimation methods and other window-based change point detection algorithms. We also show that the method can still support other neural network architectures, such as convolutional networks.
Abstract (translated)
在这项工作中，我们提出了新的目标函数来训练基于深度神经网络的密度比估计，并将其应用于一个变点检测问题。现有的方法通过求解凸约束极小化问题，利用核的线性组合来近似密度比函数。使用深度神经网络近似密度比函数需要定义一个合适的目标函数来进行优化。通过对梯度下降法可最小化的目标函数的推导和比较，表明该网络能有效地逼近密度比函数。与其他（基于核和神经网络）密度比估计方法和其他基于窗口的变化点检测算法相比，使用我们的深密度比估计目标函数可以获得更好的检测性能。我们还表明，该方法仍然可以支持其他神经网络结构，如卷积网络。
URL
https://arxiv.org/abs/1905.09876
