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Jax SSM Library

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in KF and EKF, there probably is a better name than `filter` for the functions. because `filter` is a python built-in https://docs.python.org/3/library/functions.html#filter

Hello Dr. @murphyk, The following line is not working with latest blackjax version https://github.com/probml/JSL/blob/4227d05203c8d868cd665e0a75e5d5254dcd32c5/jsl/demos/logreg_biclusters.py#L11 ![image](https://user-images.githubusercontent.com/76422222/176196169-72079eb0-6b14-47c8-aa61-c1a07f943318.png)

Old figure new one is different https://github.com/probml/JSL/blob/main/jsl/demos/hmm_casino.py

bug

Verify that the JSL kalman filter / smoother code returns the same marginal means, covariances and log marginal likelihood as when using [tfd.LinearGaussianModel](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/LinearGaussianStateSpaceModel), similar to the 1d test used in...

enhancement

The `ekf_vs_ukf_mlp.py` demo doesn't properly fit the data when fitting using UKF. ## UKF result ## EKF result Compare previous result to EKF's output

In https://github.com/probml/JSL/blob/main/jsl/demos/hmm_lillypad.py we use ``` hmm = HMM(trans_dist=distrax.Categorical(probs=A), init_dist=distrax.Categorical(probs=initial_probs), obs_dist=distrax.as_distribution( tfp.substrates.jax.distributions.MultivariateNormalFullCovariance(loc=mu_collection, covariance_matrix=cov_collection))) ``` but it fails when I switch to ``` hmm = HMM(trans_dist=distrax.Categorical(probs=A), init_dist=distrax.Categorical(probs=initial_probs), obs_dist=distrax.MultivariateNormalFullCovariance( loc=mu_collection, covariance_matrix=cov_collection)) ``` Why?

bug

Calling KF on a dataset returns a tuple; using EKF returns a dictionary. Refactor KF so that - [ ] Calling KF on a dataset returns a dictionary of results...

enhancement

Section 9.3 of Särkkä's book. > Särkkä, S. (2013). Bayesian Filtering and Smoothing (Institute of Mathematical Statistics Textbooks). Cambridge: Cambridge University Press. doi:10.1017/CBO9781139344203

Implementation

Section 9.2 of Särkkä's book. > Särkkä, S. (2013). Bayesian Filtering and Smoothing (Institute of Mathematical Statistics Textbooks). Cambridge: Cambridge University Press. doi:10.1017/CBO9781139344203

Implementation

Section 5.4 of Särkkä's book. > Särkkä, S. (2013). Bayesian Filtering and Smoothing (Institute of Mathematical Statistics Textbooks). Cambridge: Cambridge University Press. doi:10.1017/CBO9781139344203

help wanted
Implementation