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We show how universal codes can be used for solving some of the most important statistical problems for time series. By definition, a universal code (or a universal lossless data compressor) can compress any sequence generated by a stationary and ergodic source asymptotically to the Shannon entropy, which, in turn, is the best achievable ratio for lossless data compressors. We consider finite-alphabet and real-valued time series and the following problems: estimation of the limiting probabilities for finite-alphabet time series and estimation of the density for real-valued time series, the on-line prediction, regression, classification (or problems with side information) for both types of the time series and the following problems of hypothesis testing: goodness-of-fit testing, or identity testing, and testing of serial independence. It is important to note that all problems are considered in the framework of classical mathematical statistics and, on the other hand, everyday methods of data compression (or archivers) can be used as a tool for the estimation and testing. It turns out, that quite often the suggested methods and tests are more powerful than known ones when they are applied in practice.
We provide statistical theory for conditional and unconditional Wasserstein generative adversarial networks (WGANs) in the framework of dependent observations. We prove upper bounds for the excess Bayes risk of the WGAN estimators with respect to a m
Distributed source coding is the task of encoding an input in the absence of correlated side information that is only available to the decoder. Remarkably, Slepian and Wolf showed in 1973 that an encoder that has no access to the correlated side info
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Recently, a series of models have been proposed to predict future movements of people. Meanwhile, dictionary coding algorithms are used to estimate the predictability limit of human mobility. Although dictionary coding is optimal, it takes long time
One of the main focus in federated learning (FL) is the communication efficiency since a large number of participating edge devices send their updates to the edge server at each round of the model training. Existing works reconstruct each model updat