Portfolio selection with transaction costs
Mathematics of Operations Research
Fundamentals of speech recognition
Fundamentals of speech recognition
COLT' 98 Proceedings of the eleventh annual conference on Computational learning theory
The Cost of Achieving the Best Portfolio in Hindsight
Mathematics of Operations Research
Universal Portfolios With and Without Transaction Costs
Machine Learning - Special issue: computational learning theory, COLT '97
Statistical Language Learning
Efficient algorithms for universal portfolios
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Internal Regret in On-Line Portfolio Selection
Machine Learning
Algorithms for portfolio management based on the Newton method
ICML '06 Proceedings of the 23rd international conference on Machine learning
Can we learn to beat the best stock
Journal of Artificial Intelligence Research
IEEE Transactions on Signal Processing
UAI'98 Proceedings of the Fourteenth conference on Uncertainty in artificial intelligence
Universal Piecewise Linear Prediction Via Context Trees
IEEE Transactions on Signal Processing - Part II
Universal portfolios with side information
IEEE Transactions on Information Theory
Context weighting for general finite-context sources
IEEE Transactions on Information Theory
Coding for a binary independent piecewise-identically-distributed source
IEEE Transactions on Information Theory - Part 2
Low-complexity sequential lossless coding for piecewise-stationary memoryless sources
IEEE Transactions on Information Theory
The context-tree weighting method: basic properties
IEEE Transactions on Information Theory
Online portfolio selection: A survey
ACM Computing Surveys (CSUR)
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In this paper, we consider sequential decision problems in which the decision at each time is taken as a convex-combination of observations and whose performance metric is multiplicatively compounded over time. Such sequential decision problems arise in gambling, investing and in a host of signal processing applications from statistical language modeling to mixed-modality multimedia signal processing. Using a competitive algorithm framework, we construct sequential strategies that asymptotically achieve the performance of the best piecewise-convex strategy that could have been chosen by observing the entire sequence of outcomes in advance. Using the notion of context-trees, a mixture approach is able to asymptotically achieve the performance of the best choice of both the partitioning of the space of past observations and convex strategies within each region, for every sequence of outcomes. This performance is achieved with linear complexity in the depth of the context-tree, per decision. For the application of sequential investment, we also investigate transaction costs incurred for each decision. An explicit algorithmic description and examples demonstrating the performance of the algorithms are given. Our methods can be used to sequentially combine probability distributions produced by different statistical language models used in speech recognition or natural language processing and by different modalities in multimedia signal processing.