摘要翻译：
在密度估计任务中，最大熵模型(Maxent)可以通过一定的约束，即不需要经验参数的线性约束，有效地利用可靠的先验信息。然而，可靠的先验信息往往是不够的，选择不确定的约束变得必要，但造成了相当大的实现复杂性。不确定约束的不当设置可能导致过拟合或欠拟合。为了解决这个问题，在Tsallis熵框架下，提出了Maxent的一个推广。该方法引入了一个凸二次约束来校正（期望）Tsallis熵偏差(TEB)。具体地说，我们证明了抽样分布的期望Tsallis熵小于潜在实分布的Tsallis熵。这种期望熵约简正是（期望的）TEB，它可以用一个封闭形式的公式表示，并起到一致和无偏的校正作用。TEB表明特定抽样分布的熵应相应增加。这就需要对最大原则进行定量的重新解释。通过补偿TEB，同时迫使结果分布接近抽样分布，我们的广义TEBC最大值可以预期地缓解过拟合和欠拟合。我们还提出了TEB和Lidstone估计之间的联系。通过对Lidstone中概率修正率的解析识别，得到了TEB-Lidstone估计器。大量的经验评估表明，TEBC Maxent和TEB-Lidstone与各种最先进的密度估计方法相比具有良好的性能。
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英文标题：
《On Tsallis Entropy Bias and Generalized Maximum Entropy Models》
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作者：
Yuexian Hou, Tingxu Yan, Peng Zhang, Dawei Song, Wenjie Li
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最新提交年份：
2010
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分类信息：

一级分类：Computer Science        计算机科学
二级分类：Machine Learning        机器学习
分类描述：Papers on all aspects of machine learning research (supervised, unsupervised, reinforcement learning, bandit problems, and so on) including also robustness, explanation, fairness, and methodology. cs.LG is also an appropriate primary category for applications of machine learning methods.
关于机器学习研究的所有方面的论文（有监督的，无监督的，强化学习，强盗问题，等等），包括健壮性，解释性，公平性和方法论。对于机器学习方法的应用，CS.LG也是一个合适的主要类别。
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一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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一级分类：Computer Science        计算机科学
二级分类：Artificial Intelligence        人工智能
分类描述：Covers all areas of AI except Vision, Robotics, Machine Learning, Multiagent Systems, and Computation and Language (Natural Language Processing), which have separate subject areas. In particular, includes Expert Systems, Theorem Proving (although this may overlap with Logic in Computer Science), Knowledge Representation, Planning, and Uncertainty in AI. Roughly includes material in ACM Subject Classes I.2.0, I.2.1, I.2.3, I.2.4, I.2.8, and I.2.11.
涵盖了人工智能的所有领域，除了视觉、机器人、机器学习、多智能体系统以及计算和语言（自然语言处理），这些领域有独立的学科领域。特别地，包括专家系统，定理证明（尽管这可能与计算机科学中的逻辑重叠），知识表示，规划，和人工智能中的不确定性。大致包括ACM学科类I.2.0、I.2.1、I.2.3、I.2.4、I.2.8和I.2.11中的材料。
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一级分类：Computer Science        计算机科学
二级分类：Information Theory        信息论
分类描述：Covers theoretical and experimental aspects of information theory and coding. Includes material in ACM Subject Class E.4 and intersects with H.1.1.
涵盖信息论和编码的理论和实验方面。包括ACM学科类E.4中的材料，并与H.1.1有交集。
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一级分类：Mathematics        数学
二级分类：Information Theory        信息论
分类描述：math.IT is an alias for cs.IT. Covers theoretical and experimental aspects of information theory and coding.
它是cs.it的别名。涵盖信息论和编码的理论和实验方面。
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英文摘要：
  In density estimation task, maximum entropy model (Maxent) can effectively use reliable prior information via certain constraints, i.e., linear constraints without empirical parameters. However, reliable prior information is often insufficient, and the selection of uncertain constraints becomes necessary but poses considerable implementation complexity. Improper setting of uncertain constraints can result in overfitting or underfitting. To solve this problem, a generalization of Maxent, under Tsallis entropy framework, is proposed. The proposed method introduces a convex quadratic constraint for the correction of (expected) Tsallis entropy bias (TEB). Specifically, we demonstrate that the expected Tsallis entropy of sampling distributions is smaller than the Tsallis entropy of the underlying real distribution. This expected entropy reduction is exactly the (expected) TEB, which can be expressed by a closed-form formula and act as a consistent and unbiased correction. TEB indicates that the entropy of a specific sampling distribution should be increased accordingly. This entails a quantitative re-interpretation of the Maxent principle. By compensating TEB and meanwhile forcing the resulting distribution to be close to the sampling distribution, our generalized TEBC Maxent can be expected to alleviate the overfitting and underfitting. We also present a connection between TEB and Lidstone estimator. As a result, TEB-Lidstone estimator is developed by analytically identifying the rate of probability correction in Lidstone. Extensive empirical evaluation shows promising performance of both TEBC Maxent and TEB-Lidstone in comparison with various state-of-the-art density estimation methods.
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PDF链接：
https://arxiv.org/pdf/1004.1061