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在线密度估计中的最大似然与序贯归一化最大似然Maximum Likelihood vs. Sequential Normalized Maximum Likelihood in On-line Density Estimation |
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| 课程网址: | http://videolectures.net/colt2011_kotlowski_maximum/ |
| 主讲教师: | Wojciech Kotlowski |
| 开课单位: | 波兰波兹南工业大学 |
| 开课时间: | 2011-08-02 |
| 课程语种: | 英语 |
| 中文简介: |  |
| 课程简介: | The paper considers sequential prediction of individual sequences with log loss (online density estimation) using an exponential family of distributions. We first analyze the regret of the maximum likelihood ("follow the leader") strategy. We find that this strategy is (1) suboptimal and (2) requires an additional assumption about boundedness of the data sequence. We then show that both problems can be be addressed by adding the currently predicted outcome to the calculation of the maximum likelihood, followed by normalization of the distribution. The strategy obtained in this way is known in the literature as the sequential normalized maximum likelihood or last-step minimax strategy. We show for the fi rst time that for general exponential families, the regret is bounded by the familiar (k=2) log n and thus optimal up to O(1). We also show the relationship to the Bayes strategy with Je reys' prior. |
| 关 键 词: | 对数损失; 序列预测; 线密度估计; 最大似然; 贝叶斯公式 |
| 课程来源: | 视频讲座网 |
| 最后编审: | 2019-10-17：cwx |
| 阅读次数: | 32 |