György Ottucsák

Sequential Prediction of Unbounded Stationary Time Series

A simple on-line procedure is considered for the prediction of a real-valued sequence. The algorithm is based on a combination of several simple predictors. If the sequence is a realization of an unbounded stationary and ergodic random process then the average of squared errors converges, almost surely, to that of the optimum, given by the Bayes predictor. An analog result is offered for the classification of binary processes

Nonparametric sequential prediction of time series

Time series prediction covers a vast field of everyday statistical applications in medical, environmental and economic domains. In this paper, we develop nonparametric prediction strategies based on the combination of a set of ‘experts’ and show the universal consistency of these strategies under a minimum of conditions. We perform an in-depth analysis of real-world data sets and show that these nonparametric strategies are more flexible, faster and generally outperform ARMA methods in terms of normalised cumulative prediction error.

Adaptive Routing Using Expert Advice

Machine learning algorithms for combining expert advice in sequential decision problems are considered. The goal of these algorithms is to perform, for any behavior of the system, asymptotically as well as the best expert. We provide a survey of these algorithms and show how they can be used for adaptive routing in different packet switched networks.

Machine learning for financial engineering

On the History of the Growth Optimal Portfolio (M M Christensen) Empirical Log-Optimal Portfolio Selections: A Survey (L Gyorfi et al.) Log-Optimal Portfolio Selection with Proportional Transaction Costs (L Gyorfi & H Walk) Log-Optimal Portfolio with Short Selling and Leverage (M Horvath & A Urban) Nonparametric Sequential Prediction of Stationary Time Series (L Gyorfi & G Ottuscak) Empirical Pricing American Put Options (L Gyorfi & A Telcs).

Hannan consistency in on-line learning in case of unbounded losses under partial monitoring

In this paper the sequential prediction problem with expert advice is considered when the loss is unbounded under partial monitoring scenarios. We deal with a wide class of the partial monitoring problems: the combination of the label efficient and multi-armed bandit problem, that is, where the algorithm is only informed about the performance of the chosen expert with probability e≤1. For bounded losses an algorithm is given whose expected regret scales with the square root of the loss of the best expert. For unbounded losses we prove that Hannan consistency can be achieved, depending on the growth rate of the average squared losses of the experts.

The shortest path problem under partial monitoring

The on-line shortest path problem is considered under partial monitoring scenarios. At each round, a decision maker has to choose a path between two distinguished vertices of a weighted directed acyclic graph whose edge weights can change in an arbitrary (adversarial) way such that the loss of the chosen path (defined as the sum of the weights of its composing edges) be small. In the multi-armed bandit setting, after choosing a path, the decision maker learns only the weights of those edges that belong to the chosen path. For this scenario, an algorithm is given whose average cumulative loss in n rounds exceeds that of the best path, matched off-line to the entire sequence of the edge weights, by a quantity that is proportional to 1/√n and depends only polynomially on the number of edges of the graph. The algorithm can be implemented with linear complexity in the number of rounds n and in the number of edges. This result improves earlier bandit-algorithms which have performance bounds that either depend exponentially on the number of edges or converge to zero at a slower rate than O(1/√n). An extension to the so-called label efficient setting is also given, where the decision maker is informed about the weight of the chosen path only with probability e < 1. Applications to routing in packet switched networks along with simulation results are also presented.

The Growth Optimal Investment Strategy Is Secure, Too

This paper is a revisit of discrete time, multi period and sequential investment strategies for financial markets showing that the log-optimal strategies are secure, too. Using exponential inequality of large deviation type, the rate of convergence of the average growth rate is bounded both for memoryless and for Markov market processes. A kind of security indicator of an investment strategy can be the market time achieving a target wealth. It is shown that the log-optimal principle is optimal in this respect.

Sequential prediction of binary sequence with side information only

A simple on-line procedure is considered for the prediction of a binary-valued sequence in the setup introduced and studied by Weissman and Merhav [2001], [2004], where only side information is available for the algorithm. The (non-randomized) algorithm is based on a convex combination of several simple predictors. If the side information is also binary-valued (i.e. original sequence is corrupted by a binary sequence) and both processes are realizations of stationary and ergodic random processes then the average of the loss converges, almost surely, to that of the optimum, given by the Bayes predictor. An analog result is offered for the classification of binary processes.