Defensive Forecasting for Linear Protocols
Defensive Forecasting for Linear Protocols
复制标题
线性协议的防御性预测
DOI：
10.1007/11564089_35
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发表时间：
2005
期刊：
影响因子：
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通讯作者：
G. Shafer
中科院分区：
文献类型：
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作者：
V. Vovk;I. Nouretdinov;A. Takemura;G. Shafer
我们考虑一类一般的预测协议，称为“线性协议”，并讨论了几个重要的特殊情况下，包括多类预测。预测被形式化为三个玩家之间的游戏：现实，其角色是生成对象及其标签;预测者，其目标是预测标签;和怀疑论者，试图在预测者的预测和实际标签之间缺乏一致性时赚钱。我们的主要数学结果是，对于任何连续的战略怀疑在一个线性协议存在一个战略的预测，不允许怀疑的资本增长。这个结果是一个元定理，它允许人们将线性协议中的任何构造性概率定律转换为预测策略，该预测策略的预测保证满足该定律。我们将这个元定理应用于内积空间中的弱大数定律，以获得线性协议的K29预测算法的一个版本，并表明该版本在适当选择其核参数的情况下也满足适当校准和分辨率的吸引力特性，而无需假设数据的生成方式。
We consider a general class of forecasting protocols, called “linear protocols”, and discuss several important special cases, including multi-class forecasting. Forecasting is formalized as a game between three players: Reality, whose role is to generate objects and their labels; Forecaster, whose goal is to predict the labels; and Skeptic, who tries to make money on any lack of agreement between Forecaster’s predictions and the actual labels. Our main mathematical result is that for any continuous strategy for Skeptic in a linear protocol there exists a strategy for Forecaster that does not allow Skeptic’s capital to grow. This result is a meta-theorem that allows one to transform any constructive law of probability in a linear protocol into a forecasting strategy whose predictions are guaranteed to satisfy this law. We apply this meta-theorem to a weak law of large numbers in inner product spaces to obtain a version of the K29 prediction algorithm for linear protocols and show that this version also satisfies the attractive properties of proper calibration and resolution under a suitable choice of its kernel parameter, with no assumptions about the way the data is generated.