時間依存型密度比推定による高次元変化検知

使用随时间变化的密度比估计进行高维变化检测

• 批准号: 13J03189
• 负责人: 柳 松
• 金额: $ 1.47万
• 依托单位: Tokyo Institute of Technology
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for JSPS Fellows
• 财政年份: 2013
• 资助国家: 日本
• 起止时间: 2013-04-01 至 2015-03-31
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-13J03189/
• 关键词: MACHINE LEARNING; DENSITY RATIO ESTIMATION; CHANGE DETECTION; GRAPHICAL MODEL; Change Detection; Markov Network; Density Ratio Estimation; Machine Learning

In this research, we have mainly focused on the problem of change detection in high-dimensional time-series, and more generally, on dependent dataset.We have spent most our time in the first year developing a methodology for change detection in Graphical Models, where we input two sets of data drawn from two different distributions with different interactions among random variables. In such methodology, we assumed that the changes between two stages are subtle and most of the interactions remain unchanged. As a consequence of this assumption, the sparsity is assumed in our statistical model and via Density Ratio Estimation method, the sparse changes between two Graphical Models are learned.In this year, we conducted a theoretical study for such methodology and give statistical guarantees of the superiority of the proposed change detection method. Specifically, we give the sufficient conditions that our change detection method works, in terms of sample complexity against the increasing number of changed edges and dimensions.Moreover, the above methodology itself is for learning changes from two sets of data. However, It is nature to ask that is it possible to apply such powerful method to the learning of the Graphical Model structure itself? Our new idea is simply learning the difference between the join distribution and the product of marginal distributions.To sum up, we have not only finished the research promised in the proposal, but also investigated a new (and important) application of the proposed method and theory.

在本研究中，我们主要关注高维时间序列的变化检测问题，更一般地说，是依赖数据集的变化检测问题。我们在第一年花费了大部分时间来开发图形模型中变化检测的方法，我们输入两组数据，这些数据来自两个不同的分布，随机变量之间具有不同的相互作用。在这种方法中，我们假设两个阶段之间的变化是微妙的，大多数相互作用保持不变。基于这一假设，我们在统计模型中假设了稀疏性，并通过密度比估计方法来学习两个图模型之间的稀疏变化。在这一年里，我们对这种方法进行了理论研究，并对所提出的变更检测方法的优越性进行了统计保证。具体来说，我们给出了我们的变化检测方法有效的充分条件，在增加变化边缘和维数的样本复杂度方面。此外，上述方法本身是用于从两组数据中学习变化。然而，人们自然会问，是否有可能将这种强大的方法应用于图形模型结构本身的学习？我们的新想法就是学习连接分布和边际分布的乘积之间的区别。综上所述，我们不仅完成了提案中承诺的研究，而且还研究了所提出的方法和理论的一个新的（也是重要的）应用。

项目成果

Support consistency of direct sparse-change learning in Markov Support consistency of direct sparse-change learning in Markov networksSupport consistency of direct sparse-change learning in Markov networks

支持马尔可夫网络中直接稀疏变化学习的一致性 支持马尔可夫网络中直接稀疏变化学习的一致性支持马尔可夫网络中直接稀疏变化学习的一致性

• 发表时间: 2015
• 作者: Liu;S. and Suzuki;T. and Sugiyama;M.
• 通讯作者: M.

Direct Learning of Sparse Changes in Markov Networks by Density Ratio Estimation

• DOI: 10.1162/neco_a_00589
• 发表时间: 2013-04
• 期刊: Neural Computation
• 影响因子: 2.9
• 作者: Song Liu;J. Quinn;Michael U Gutmann;Taiji Suzuki;Masashi Sugiyama

Bias Reduction and Metric Learng for Nearest-neighbor Estimation of Kullback-Leibler Divergence.

Kullback-Leibler 散度的最近邻估计的偏差减少和度量学习。

• 发表时间: 2014
• 作者: Sho Koyasu;Yuji Nakamoto;Hiroshi Harada;Yoshihisa Tsuji;Hiroyuki Kimura;Kohei Sano;Tomomi Nobashi;Kaori Togashi.;Yung-Kyun Noh
• 通讯作者: Yung-Kyun Noh