Statistical inference of time-dependent data
Suhas Gundimeda
10.25394/PGS.12276527.v1
https://hammer.figshare.com/articles/thesis/Statistical_inference_of_time-dependent_data/12276527
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>
2020-05-11 16:27:41
tree distribution
tree approximation
time series
structure inference
expectation maximization algorithm
Baum Welch
mixtures of trees
mixtures of time dependent trees