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The context is this - I'm considering doing a part time PhD in statistical learning and today I've met up with a prospective supervisor who suggested that I think about causality in machine learning as (in his words) a lot of people are doing deep learning/neural network stuff and less so in time series learning and causality inference. Causality inference is less developed in machine learning and it's an area I could contribute to.

So I've spent some time googling and thinking and I came away with these elements that I would ideally like to see in a learning algorithm.

  • Can handle multi-dimensional time series data
  • Online learning
  • Time varying relationships
  • Can use regularisation
  • Allows causality inference (actually, this may overlap with regularisation in some way to prevent overfitting)

This to me sounded like a state-space/dynamic model of some sort. As an example, I could extend the Kalman filter in some way to include the above. Any idea on more specific algorithms I should have a look at?

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If you're thinking about extending the Kalman filter you may be interested in these publications as a starting point. They check most of the boxes except the causality, but that is where you come in:

  1. Särkkä, S. (2013). Bayesian filtering and smoothing (Vol. 3). Cambridge University Press. Online version.

  2. Van Vaerenbergh, S., Lázaro-Gredilla, M., & Santamaría, I. (2012). Kernel recursive least-squares tracker for time-varying regression. IEEE transactions on neural networks and learning systems, 23(8), 1313-1326. Online version.

[Disclaimer: I'm author of the second one.]

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