One approach is with hybrid systems, which are dynamical systems characterized by piecewise continuous trajectories with a finite number of discontinuities introduced by discrete events [5].

Indeed, the results in Table 1, which shows13 the mean absolute percentage errors (MAPE), demonstrates this. The ac-14 curacy of neural ODE for the Poisson process is on par with our neural15 JSDE. However, for the Hawkes process (Exponential), Hawkes process16 (Power-Law), and self-correcting process, neural ODE gives much larger17 predictions errors. Forthesocial/medicaldatasets,weuseda20/64-24 dimensional latent state and parameterized the functions with two-hidden-layer MLPs with 32/64 hidden units. The time series modeling software that we used is designed for long event sequences and ignores the idle time after31 thelastevent.

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

Thenetworkconsists ofalifting layer,followed bytwo residual blocks with spatial max-pooling using a kernel size 2 after each group equivariant layer.

The type of symmetry is typically fixed and has to be chosen in advance.

Since weak learners perform only marginallybetter than random guesses, such subroutines constitute aweakerassumption than the availability of an accurate supervised learning oracle. Weprovethat the sample complexity and running time bounds of the proposed method do not explicitly dependonthenumberofstates. While existing results on boosting operate on convex losses, the value function over policies is non-convex.

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

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