Theory and applications of competitive prediction
Theory and applications of competitive prediction
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发表时间：
2011
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通讯作者：
Fedor Zhdanov
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作者：
Fedor Zhdanov
预测未来是机器学习研究的一个重要目的。在在线学习中，预测是按顺序给出的，而不是一次全部给出。人们希望在日常生活中的许多情况下连续做出明智的决定，无论是按月，按天还是按分钟。在竞争预测中，预测是由一组专家和一个学习者做出的。预测的质量由损失函数来衡量。学习者的目标是在任何情况下做出可靠的预测。学习者将他的损失与集合中最好的专家的损失进行比较，并确保他的表现不会更差。在这篇论文中，一个通用的方法被描述为许多预测问题提供强有力的性能保证的算法。特别注意的是平方损失函数，广泛用于评估预测的质量。本文考虑了四种类型的专家集：有限个自由专家集（不需要遵循任何策略）、有限维空间中遵循策略的专家集、无限维Hilbert空间中遵循策略的专家集和无限维Banach空间中遵循策略的专家集。在各种预测算法的推导中说明了该方法的力量。本论文主要探讨两种核心方法：聚合演算法与防御性预测。在许多有趣的情况下，这些方法彼此接近。然而，防御性预测更一般，涵盖了一些无法使用聚合算法解决的问题。聚合算法更具体，通常计算效率更高。在人工或真实的世界数据集上验证了新算法的经验性能和属性。强调了算法可以应用的具体领域。
Predicting the future is an important purpose of machine learning research. In online learning, predictions are given sequentially rather than all at once. People wish to make sensible decisions sequentially in many situations of everyday life, whether month-by-month, day-by-day, or minute-by-minute. In competitive prediction, the predictions are made by a set of experts and by a learner. The quality of the predictions is measured by a loss function. The goal of the learner is to make reliable predictions under any circumstances. The learner compares his loss with the loss of the best experts from the set and ensures that his performance is not much worse. In this thesis a general methodology is described to provide algorithms with strong performance guarantees for many prediction problems. Specific attention is paid to the square loss function, widely used to assess the quality of predictions. Four types of the sets of experts are considered in this thesis: sets with finite number of free experts (which are not required to follow any strategy), sets of experts following strategies from finite-dimensional spaces, sets of experts following strategies from infinite-dimensional Hilbert spaces, and sets of experts following strategies from infinite-dimensional Banach spaces. The power of the methodology is illustrated in the derivations of various prediction algorithms. Two core approaches are explored in this thesis: the Aggregating Algorithm and Defensive Forecasting. These approaches are close to each other in many interesting cases. However, Defensive Forecasting is more general and covers some problems which cannot be solved using the Aggregating Algorithm. The Aggregating Algorithm is more specific and is often more computationally efficient. The empirical performance and properties of new algorithms are validated on artificial or real world data sets. Specific areas where the algorithms can be applied are emphasized.