| 研究実績の概要 |
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.
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