時間依存型密度比推定による高次元変化検知

在这项研究中，我们主要关注高维时间序列中的变化检测问题，更广泛地说，是在相依数据集上。我们在第一年花费了大部分时间来开发一种图形化模型中的变化检测方法，其中我们输入了来自两个不同分布的数据，这些数据在随机变量之间具有不同的交互作用。在这种方法中，我们假设两个阶段之间的变化是微妙的，而大多数交互作用保持不变。基于这一假设，我们假设统计模型具有稀疏性，并通过密度比估计方法学习两个图形模型之间的稀疏变化。今年，我们对这种方法进行了理论研究，并从统计上保证了所提变化检测方法的优越性。具体地说，在样本复杂度方面，我们给出了变化检测方法有效的充分条件，并且，上述方法本身用于从两组数据中学习变化。然而，人们自然会问，是否有可能将如此强大的方法应用于图形模型结构本身的学习？我们的新想法是简单地学习联合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，而且探索了所提出的方法和理论的新的(也是重要的)应用。

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.