Maximum Entropy Flow Networks
This work addresses the problem of efficiently learning maximum entropy models for researchers and practitioners in fields like finance and computer vision, representing an incremental improvement by applying existing flow network techniques to a known bottleneck.
The paper tackles the challenge of learning maximum entropy distributions by proposing a method that uses normalizing flow networks to map simple distributions to target distributions, transforming the problem into finite-dimensional constrained optimization solved with stochastic optimization and augmented Lagrangian methods. Simulation results demonstrate effectiveness, with applications in finance and computer vision showing flexibility and accuracy.
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.