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

Tensor decompositions (TDs) serve as a powerful tool for analyzing multiway data.

We present an algorithm for learning switched linear dynamical systems in discrete time from noisy observations of the system's full state or output. Switched linear systems use multiple linear dynamical modes to fit the data within some desired tolerance. They arise quite naturally in applications to robotics and cyberphysical systems. Learning switched systems from data is a NP-hard problem that is nearly identical to the k-linear regression problem of fitting k > 1 linear models to the data. A direct mixed-integer linear programming (MILP) approach yields time complexity that is exponential in the number of data points. In this paper, we modify the problem formulation to yield an algorithm that is linear in the size of the data while remaining exponential in the number of state variables and the desired number of modes. To do so, we combine classic ideas from the ellipsoidal method for solving convex optimization problems, and well-known oracle separation results in non-smooth optimization. We demonstrate our approach on a set of microbenchmarks and a few interesting real-world problems. Our evaluation suggests that the benefits of this algorithm can be made practical even against highly optimized off-the-shelf MILP solvers.

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

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

Due to the non-linearity of NNs, no analytic solution to the integral exists, even when the likelihood and the approximate posterior are both Gaussian. A low-cost, unbiased, stochastic approximation can be obtained via Monte Carlo (MC) integration: obtainS samples from the approximate posterior and then compute the empirical expectation of the likelihood w.r.t.