Kalman Smoothing google
The optimal fixed-interval smoother provides the optimal estimate using the measurements from a fixed interval z_1 to z_n. This is also called ‘Kalman Smoothing’. There are several smoothing algorithms in common use.
“Kalman Filter”


Gradient Boosting Machine google
Gradient boosting machines are a family of powerful machine-learning techniques that have shown considerable success in a wide range of practical applications. They are highly customizable to the particular needs of the application, like being learned with respect to different loss functions. This article gives a tutorial introduction into the methodology of gradient boosting methods with a strong focus on machine learning aspects of modeling. A theoretical information is complemented with descriptive examples and illustrations which cover all the stages of the gradient boosting model design. Considerations on handling the model complexity are discussed. Three practical examples of gradient boosting applications are presented and comprehensively analyzed. …

Hawkes Graph google
This paper introduces the Hawkes skeleton and the Hawkes graph. These notions summarize the branching structure of a multivariate Hawkes point process in a compact and fertile way. In particular, we explain how the graph view is useful for the specification and estimation of Hawkes models from large, multitype event streams. Based on earlier work, we give a nonparametric statistical procedure to estimate the Hawkes skeleton and the Hawkes graph from data. We show how the graph estimation may then be used for choosing and fitting parametric Hawkes models. Our method avoids the a priori assumptions on the model from a straighforward MLE-approach and it is numerically more flexible than the latter. A simulation study confirms that the presented procedure works as desired. We give special attention to computational issues in the implementation. This makes our results applicable to high-dimensional event-stream data, such as dozens of event streams and thousands of events per component. …

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