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In this work, we improve upon the stepwise analysis of noisy iterative learning algorithms initiated by Pensia, Jog, and Loh (2018) and recently extended by Bu, Zou, and Veeravalli (2019). Our main contributions are significantly improved mutual information bounds for Stochastic Gradient Langevin Dynamics via datadependent estimates. Our approach is based on the variational characterization of mutual information and the use of data-dependent priors that forecast the minibatch gradient based on a subset of the training samples. Our approach is broadly applicable within the information-theoretic framework of Russo and Zou (2015) and Xu and Raginsky (2017). Our bound can be tied to a measure of flatness of the empirical risk surface. As compared with other bounds that depend on the squared norms of gradients, empirical investigations show that the terms in our bounds are orders of magnitude smaller.

We study the tradeoff between the sum rate and the error probability in downlink of wireless networks. Using the recent results on the achievable rates of finite-length codewords, the problem is cast as a joint optimization of the network sum rate and the per-user error probability. Moreover, we develop an efficient algorithm based on the divide-and-conquer technique to simultaneously maximize the network sum rate and minimize the maximum users' error probability and to evaluate the effect of the codewords length on the system performance. The results show that, in delay-constrained scenarios, optimizing the per-user error probability plays a key role in achieving high throughput.

Regarding the high cost of PMU units, optimal placement and minimizing of their numbers are of great importance. Also, this paper proposes a new procedure for determining the optimal placement and less numbers of PMUs in distribution network based on the best state estimation criterion. For DSE solution, combination of Nelder-Mead (NM) simplex search and Ant Colony Optimization (ACO) algorithm have been used. The hybrid method can estimate voltage phasor at each node by minimizing difference between measured and calculated values of state variables and also, it can guarantee observability of distribution system under normal operation conditions. To demonstrate the effectiveness of new procedure, simulation studies are applied on 30-bus radial test feeder. Finally, achievement results for convergence characterestic of DSE solution and estimation error of state variables with regard to the optimal placement and numbers of PMUs in distribution test feeder have been presented.