Neural Information Processing Systems http://nips.cc/

Normalizing flows can be used to construct high quality generative probabilistic models, but training and sample generation require repeated evaluation of Jacobian determinants and function inverses. To make such computations feasible, current approaches employ highly constrained architectures that produce diagonal, triangular, or low rank Jacobian matrices. As an alternative, we investigate a set of novel normalizing flows based on the circular and symmetric convolutions. We show that these transforms admit efficient Jacobian determinant computation and inverse mapping (deconvolution) in O(N logN) time. Additionally, element-wise multiplication, widely used in normalizing flow architectures, can be combined with these transforms to increase modeling flexibility. We further propose an analytic approach to designing nonlinear elementwise bijectors that induce special properties in the intermediate layers, by implicitly introducing specific regularizers in the loss. We show that these transforms allow more effective normalizing flow models to be developed for generative image models.

We consider maximum likelihood estimation of linear dynamical systems with generalized-linear observation models. Maximum likelihood is typically considered to be hard in this setting since latent states and transition parameters must be inferred jointly. Given that expectation-maximization does not scale and is prone to local minima, moment-matching approaches from the subspace identification literature have become standard, despite known statistical efficiency issues. In this paper, we instead reconsider likelihood maximization and develop an optimization based strategy for recovering the latent states and transition parameters. Key to the approach is a two-view reformulation of maximum likelihood estimation for linear dynamical systems that enables the use of global optimization algorithms for matrix factorization. We show that the proposed estimation strategy outperforms widely-used identification algorithms such as subspace identification methods, both in terms of accuracy and runtime.

We consider maximum likelihood estimation of linear dynamical systems with generalized-linear observation models. Maximum likelihood is typically considered to be hard in this setting since latent states and transition parameters must be inferred jointly. Given that expectation-maximization does not scale and is prone to local minima, moment-matching approaches from the subspace identification literature have become standard, despite known statistical efficiency issues. In this paper, we instead reconsider likelihood maximization and develop an optimization based strategy for recovering the latent states and transition parameters. Key to the approach is a two-view reformulation of maximum likelihood estimation for linear dynamical systems that enables the use of global optimization algorithms for matrix factorization. We show that the proposed estimation strategy outperforms widely-used identification algorithms such as subspace identification methods, both in terms of accuracy and runtime.