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.
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