arXiv cs/05050832005-05-30cs.LGcs.AI

Defensive forecasting

Vladimir Vovk, Akimichi Takemura, Glenn Shafer

备注：: 15 pages, 2 figures, to appear in the AIStats'2005 electronic proceedings
发表信息：: Proceedings of the Tenth International Workshop on Artificial Intelligence and Statistics, 2005, pages 365--372.

英文摘要：

We consider how to make probability forecasts of binary labels. Our main mathematical result is that for any continuous gambling strategy used for detecting disagreement between the forecasts and the actual labels, there exists a forecasting strategy whose forecasts are ideal as far as this gambling strategy is concerned. A forecasting strategy obtained in this way from a gambling strategy demonstrating a strong law of large numbers is simplified and studied empirically.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

Defensive forecasting for optimal prediction with expert advice

Royal Holloway, University of London（伦敦大学皇家霍洛威学院）

The method of defensive forecasting is applied to the problem of prediction with expert advice for binary outcomes. It turns out that defensive forecasting is not only competitive with the Aggregating Algorithm but also handles the case of "second-guessing" experts, whose advice depends on the learner's prediction; this paper assumes that the dependence on the learner's prediction is continuous.

2007-08-10cs.LG

Continuous and randomized defensive forecasting: unified view

Defensive forecasting is a method of transforming laws of probability (stated in game-theoretic terms as strategies for Sceptic) into forecasting algorithms. There are two known varieties of defensive forecasting: "continuous", in which Sceptic's moves are assumed to depend on the forecasts in a (semi)continuous manner and which produces deterministic forecasts, and "randomized", in which the dependence of Sceptic's moves on the forecasts is arbitrary and Forecaster's moves are allowed to be randomized. This note shows that the randomized variety can be obtained from the continuous variety by …

2007-08-23cs.LG

为防御性预测辩护

In Defense of Defensive Forecasting

Departments of Computer Science & Engineering and Data Science, New York University（纽约大学计算机科学与工程系和数据科学系）；Department of Electrical Engineering and Computer Sciences, University of California, Berkeley（加州大学伯克利分校电气工程与计算机科学系）

本文综述防御性预测算法，该方法通过纠正过去错误而非预言来生成预测，并推导出在线学习、校准、专家建议预测及在线共形预测的简单近优算法。

2025-10-24cs.LGstat.ML

Defensive forecasting for linear protocols

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 observations; Forecaster, whose goal is to predict the observations; and Skeptic, who tries to make money on any lack of agreement between Forecaster's predictions and the actual observations. 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 a…

2005-09-24cs.LG

面向在线概率预测的防御性提升算法

Defensive Boosting for Online Probabilistic Forecasting

本研究提出防御提升器算法，可同时满足在线梯度提升与在线弱到强提升的两种保证，效率高且在合成和真实数据流上预测性能强劲、运行速度快。

2026-08-14cs.CCcs.DScs.LG

足球博彩的演变——一种用于比赛结果预测和博彩公司赔率估计的机器学习方法

The Evolution of Football Betting- A Machine Learning Approach to Match Outcome Forecasting and Bookmaker Odds Estimation

Deloitte（德勤）

本研究利用机器学习算法分析历史数据预测英超比赛结果并辅助博彩公司赔率估计，识别了最有效的预测模型和关键影响因素，为体育分析领域的知情决策开辟了新途径。

2024-03-24cs.LG

更多相关论文收起更多论文

Supermartingales in Prediction with Expert Advice

Computer Learning Research Centre（计算机学习研究中心）；Royal Holloway, University of London（伦敦大学皇家霍洛威学院）

We apply the method of defensive forecasting, based on the use of game-theoretic supermartingales, to prediction with expert advice. In the traditional setting of a countable number of experts and a finite number of outcomes, the Defensive Forecasting Algorithm is very close to the well-known Aggregating Algorithm. Not only the performance guarantees but also the predictions are the same for these two methods of fundamentally different nature. We discuss also a new setting where the experts can give advice conditional on the learner's future decision. Both the algorithms can be adapted to the …

2010-03-10cs.LG

Prediction with Advice of Unknown Number of Experts

Royal Holloway, University of London（伦敦大学皇家霍洛威学院）

In the framework of prediction with expert advice, we consider a recently introduced kind of regret bounds: the bounds that depend on the effective instead of nominal number of experts. In contrast to the NormalHedge bound, which mainly depends on the effective number of experts and also weakly depends on the nominal one, we obtain a bound that does not contain the nominal number of experts at all. We use the defensive forecasting method and introduce an application of defensive forecasting to multivalued supermartingales.

2010-06-02cs.LG

Prediction with Advice of Unknown Number of Experts

Royal Holloway, University of London（伦敦大学皇家霍洛威学院）

In the framework of prediction with expert advice, we consider a recently introduced kind of regret bounds: the bounds that depend on the effective instead of nominal number of experts. In contrast to the Normal- Hedge bound, which mainly depends on the effective number of experts but also weakly depends on the nominal one, we obtain a bound that does not contain the nominal number of experts at all. We use the defensive forecasting method and introduce an application of defensive forecasting to multivalued supermartingales.

2014-08-09cs.LGstat.ML

Prediction with expert evaluators' advice

We introduce a new protocol for prediction with expert advice in which each expert evaluates the learner's and his own performance using a loss function that may change over time and may be different from the loss functions used by the other experts. The learner's goal is to perform better or not much worse than each expert, as evaluated by that expert, for all experts simultaneously. If the loss functions used by the experts are all proper scoring rules and all mixable, we show that the defensive forecasting algorithm enjoys the same performance guarantee as that attainable by the Aggregating…

2009-03-23cs.LG