基于Sharma-Mittal发散的广义孪生高斯过程
Generalized Twin Gaussian Processes using Sharma-Mittal Divergence
摘要：
由于互信息测度在机器学习和计算机视觉中的广泛应用，使得互信息测度受到越来越多的关注。在本文中，我们提出了一个广义结构化回归框架的基础上Shama-Mittal分歧，相对熵的措施，这是介绍给机器学习社区在这项工作中。Sharma-Mittal（SM）散度是广泛使用的Rényi、Tsallis、Bhattacharyya和Kullback-Leibler（KL）相对熵的广义互信息度量。具体地说，我们研究Sharma-Mittal分歧作为一个成本函数的背景下的孪生高斯过程（TGP）~ \citep{Bo:2010}，推广了KL-分歧没有计算惩罚。我们通过理论分析显示了Sharma-Mittal TGP（SMTGP）的有趣特性，该理论分析涵盖了传统TGP制定中缺失的见解。然而，我们推广这个理论的基础上SM-分歧，而不是KL-分歧，这是一个特殊的情况。实验上，我们评估了几个数据集上的SMTGP框架。结果表明，SMTGP比基于KL的TGP达到了更好的预测，因为它通过我们从数据中学习的参数提供了更大的模型类别。
英文摘要：
There has been a growing interest in mutual information measures due to their wide range of applications in Machine Learning and Computer Vision. In this paper, we present a generalized structured regression framework based on Shama-Mittal divergence, a relative entropy measure, which is introduced to the Machine Learning community in this work. Sharma-Mittal (SM) divergence is a generalized mutual information measure for the widely used Rényi, Tsallis, Bhattacharyya, and Kullback-Leibler (KL) relative entropies. Specifically, we study Sharma-Mittal divergence as a cost function in the context of the Twin Gaussian Processes (TGP)~\citep{Bo:2010}, which generalizes over the KL-divergence without computational penalty. We show interesting properties of Sharma-Mittal TGP (SMTGP) through a theoretical analysis, which covers missing insights in the traditional TGP formulation. However, we generalize this theory based on SM-divergence instead of KL-divergence which is a special case. Experimentally, we evaluated the proposed SMTGP framework on several datasets. The results show that SMTGP reaches better predictions than KL-based TGP, since it offers a bigger class of models through its parameters that we learn from the data.
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