This editorial contains Vladimir V’yugin’s short biography and a selective review of his contributions to several areas of mathematics, computer science, and their applications.

This paper surveys the Weak Aggregating Algorithm for prediction with expert advice under bounded convex loss functions. It shows how bounds for various scenarios can be obtained and explicates the connection with the adversarial bandit framework. The paper is aimed at practitioners wishing to apply the algorithms in real-life situations.

In this paper, prediction with expert advice is surveyed focusing on Vovk’s Aggregating Algorithm. The established theory as well as extensions developed in the recent decade are considered. The paper is aimed at practitioners and covers important application scenarios.

We propose to apply the method of online prediction with expert advice for estimation of Value at Risk. We show that in some cases the combination of different methods can produce better results compared to a single model. Our approach is based on Weak Aggregating Algorithm (WAA), which is similar to the Bayesian method, where the prediction is the average over all models based on the likelihood of the available data. WAA provides a theoretical guarantee that the prediction strategy is asymptotically as good as the best expert. We propose two ways of combining predictions of different experts. The first approach combines predictions of normal distribution experts, whereas the second method combines predictions of conventional models that are used to estimate Value at Risk. The experimental results on three stocks show that WAA performs close to or better than the best expert model. In addition, backtesting with Kupiec unconditional coverage test and Christoffersen conditional coverage test shows that WAA is the only method that fails to reject the null hypothesis for all test cases.

Here we introduce a data staging algorithm designed to reconstruct multiple time series databases into a partitioned and regularised database. The Data Aggregation Partition Reduction Algorithm, or DAPRA for short, was designed to solve the practical issue of effective and meaningful visualisation of irregularly sampled time series data. This paper firstly discusses the rationale for DAPRA, walking through its design and introduces the theoretical foundation of any DAPRA application. Later we report empirical evidence that demonstrates the practical relevance of DAPRA by its application with large and complex time series datasets from two distinct domains (financial and travel).

We apply online prediction with expert advice to construct a universal algorithm for multi-class classification problem. Our experts are generalised linear regression models with multidimensional outputs, i.e. neural networks with multiple output nodes but no hidden nodes. We allow the final layer transfer function to be a softmax function with linear activations to all output neurons. We build an online algorithm competitive with all the experts of relevant models of this type and derive an upper bound on the cumulative loss of the algorithm. We carry out experiments on three data sets and compare cumulative losses of our algorithm and a single neuron with multiple output nodes.

This paper formulates a protocol for prediction of packs, which is a special case of on-line prediction under delayed feedback. Under the prediction of packs protocol, the learner must make a few predictions without seeing the respective outcomes and then the outcomes are revealed in one go. The paper develops the theory of prediction with expert advice for packs by generalising the concept of mixability. We propose a number of merging algorithms for prediction of packs with tight worst case loss upper bounds similar to those for Vovk’s Aggregating Algorithm. Unlike existing algorithms for delayed feedback settings, our algorithms do not depend on the order of outcomes in a pack. Empirical experiments on sports and house price datasets are carried out to study the performance of the new algorithms and compare them against an existing method.