In this paper, we propose anew class of low-cardinality algorithm that generalizes the local update tomaximize asemidefinite relaxation derived from max-k-cut.

We study square loss in a realizable time-series framework with martingale difference noise.

We study square loss in a realizable time-series framework with martingale difference noise. Our main result is a fast rate excess risk bound which shows that whenever a trajectory hypercontractivity condition holds, the risk of the leastsquares estimator on dependent data matches the iid rate order-wise after a burn-in time. In comparison, many existing results in learning from dependent data have rates where the effective sample size is deflated by a factor of the mixing-time of the underlying process, even after the burn-in time. Furthermore, our results allow the covariate process to exhibit long range correlations which are substantially weaker than geometric ergodicity.

The concept of information structure is also fundamental to studying the phenomenon ofpartial observability.

Each pair of rain and object patches are visually similar. Wecompute thedifference (L1 distance) between the average kernels of each pair of confusing rain and object patches. We accumulate and average the differences of all pairs. We change the number of sampled kernels for computing the average kernel. In Figure 13(b), we report the difference of average kernels of the confusing patch pairs.

However,their desirable characteristics such asanalytic invertibility come atthe cost of restricting the functional forms.