Probabilistic graphical modeling is a framework which can be used to succinctly<br>represent multivariate probability distributions of time series in terms of each time<br>series’s dependence on others. In general, it is computationally prohibitive to sta-<br>tistically infer an arbitrary model from data. However, if we constrain the model to<br>have a tree topology, the corresponding learning algorithms become tractable. The<br>expressive power of tree-structured distributions are low, since only n − 1 dependen-<br>cies are explicitly encoded for an n node tree. One way to improve the expressive<br>power of tree models is to combine many of them in a mixture model. This work<br>presents and uses simulations to validate extensions of the standard mixtures of trees<br>model for i.i.d data to the setting of time series data. We also consider the setting<br>where the tree mixture itself forms a hidden Markov chain, which could be better<br>suited for approximating time-varying seasonal data in the real world. Both of these<br>are evaluated on artificial data sets.<br><br>
| Identifer | oai:union.ndltd.org:purdue.edu/oai:figshare.com:article/12276527 |
| Date | 11 May 2020 |
| Creators | Suhas Gundimeda (5930648) |
| Source Sets | Purdue University |
| Detected Language | English |
| Type | Text, Thesis |
| Rights | CC BY-NC-SA 4.0 |
| Relation | https://figshare.com/articles/Statistical_inference_of_time-dependent_data/12276527 |
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