Title: Maximum Entropy Flow Networks,
Abstract: Maximum entropy modeling is a flexible and popular framework for formulating
statistical models given partial knowledge. In this paper, rather than the
traditional method of optimizing over the continuous density directly, we learn
a smooth and invertible transformation that maps a simple distribution to the
desired maximum entropy distribution. Doing so is nontrivial in that the
objective being maximized (entropy) is a function of the density itself. By
exploiting recent developments in normalizing flow networks, we cast the
maximum entropy problem into a finite-dimensional constrained optimization, and
solve the problem by combining stochastic optimization with the augmented
Lagrangian method. Simulation results demonstrate the effectiveness of our
method, and applications to finance and computer vision show the flexibility
and accuracy of using maximum entropy flow networks.