Evaluating environmental variables that vary stochastically is the principal topic for
designing better environmental management and restoration schemes. Both the upper and …

Environmental variables that fluctuate randomly and dynamically over time, such as water
quality indices, are considered to be stochastic. They exhibit sub-exponential memory …

Environmental variables such as streamflow discharge and water quality indices vary
stochastically over time and often exhibit long (subexponential) memory. Their dynamics are …

The modeling and identification of time series data with a long memory are important in
various fields. The streamflow discharge is one such example that can be reasonably …

We address the problem of the achievable regret rates with online logistic regression. We
derive lower bounds with logarithmic regret under $ L_1 $, $ L_2 $, and $ L_\infty …

The normalized maximum likelihood (NML) is one of the most important distribution in
coding theory and statistics. NML is the unique solution (if exists) to the pointwise minimax …

A fundamental principle of learning theory is that there is a trade-off between the complexity
of a prediction rule and its ability to generalize. Modern machine learning models do not …

In this paper, we propose a novel robust stochastic optimization approach with a distinctive
consideration for rare events, in which divergence measures are used to bound the event …

Relaxing the iid assumption: Adaptively minimax optimal regret via root-entropic
regularization Page 1 The Annals of Statistics 2023, Vol. 51, No. 4, 1850–1876 https://doi.org/10.1214/23-AOS2315 …

We study online logistic regression with binary labels and general feature values in which a
learner tries to predict an outcome/label based on data/features received in rounds. Our goal …