  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.
