Add particle filter exercise notebook

[lucianopaz]

This tries to add a particle filter as per my comment from #24

I ran into a bunch of problems though.

1. I can't seem to be able to use RandomStream objects inside of scan, so that makes it hard for me to use rng.some_method as I would like to have been able to do.
2. I can't make scan behave as a while loop, which is what I really need to happen in the systematic_resample
3. There are some times in which closure python variables would have been nicer to use than the pytensor counterparts, but I couldn't get those to work properly.
4. The systematic_resample loop is a mess. I need to update some indices, but I'm clearly botching the indexing or the sharing or the updates. Any guidance there would be great.
5. Since I haven't gotten the filter to work, I can't guarantee that the plotting code at the end is correct.

TODO:

• Setup
• emphasize that instead of normal_logpdf you could have an arbitrary probability model (including a PyMC model one!)
• Convert into exercise
• Start with simpler dumb multinomial resampling
• Get rid of outer scan, and just call update function in a loop (make it interactive so we can see the robot moving over-time and the function updating online)

[review-notebook-app]

Check out this pull request on 

See visual diffs & provide feedback on Jupyter Notebooks.

---

Powered by ReviewNB

[lucianopaz]

As a side note. The code copies a SIR particle filter from here, and the resampling algorithm is copied from here.

One last thing. I would really love for the particle filter to work on some kind of streaming data, but I have no idea how to get that to work in pytensor.

[lucianopaz]

I got it work now!

The particle filter tracks the position of a robot that has noisy sensors and noisy controls. I think that it can still be greatly improved. One thing that I think can be better is to ditch the RandomStream and send a shared random generator that can be provided to the random variable creators. Another thing that would be nice, would be to get the particle replacement operation scan to not use what I feel are mostly patches around shared variables and python integers.

[ricardoV94]

Line #68.        i = pytensor.shared(np.array([0]))

why are you creating shared variables for i, j? Sounds like they should be recurrent outputs that get updated?

In general the only time you need shared variables is to handle RNGs in Scan (scan limitation) or to have implicit inputs / share inputs across functions

Reply via ReviewNB

[ricardoV94]

Line #142.        [particles, weights], _ = pytensor.scan(

if you have updates in the inner functions (which you will have with rng.foo(), plus your other use of updates for indices (which I don't think you want), you need to forward the updates to the outmost pytensor function, otherwise they won't work

Reply via ReviewNB

[ricardoV94]

• I can't seem to be able to use RandomStream objects inside of scan, so that makes it hard for me to use rng.some_method as I would like to have been able to do.

What do you mean, they should definitely work. Maybe you defining custom updates is messing PyTensor identification of the default randomstream updates. You do need to forward all updates from nested functions to the final compiled pytensor function.

• I can't make scan behave as a while loop, which is what I really need to happen in the systematic_resample

Why can't you? Perhaps because of the odd use of shared variables?

• There are some times in which closure python variables would have been nicer to use than the pytensor counterparts, but I couldn't get those to work properly.

What do you mean?

• The systematic_resample loop is a mess. I need to update some indices, but I'm clearly botching the indexing or the sharing or the updates. Any guidance there would be great.

indices should be regular non shared variables that are recursed (so parts of outputs_info)

[ricardoV94]

Bigger picture, how do you suggest we turn this into an exercise notebook? One concern is just to give enough intro content and break it in incremental parts, that should be a no biggie.

The other is the use of Scan which is a bit advanced, and I wasn't sure I wanted to touch in the workshop. We will need to give a bit of scaffolding for it. Specially with the use of rngs inside which requires explicitly handling updates.

[ricardoV94]

https://pytensor.readthedocs.io/en/latest/library/scan.html#using-shared-variables-gibbs-sampling

[ricardoV94]

One last thing. I would really love for the particle filter to work on some kind of streaming data, but I have no idea how to get that to work in pytensor.

You just update the data in subsequent calls to pytensor, or you mean something more fancy?

[ricardoV94]

Line #3.        particles = rng.normal(loc=mean, scale=std, size=(n_particles, 3))

normal will do the implicit broadcast of loc and scale

Reply via ReviewNB

[ricardoV94]

Line #16.        particles = pt.set_subtensor(particles[:, 2], particles[:, 2] % (2 * np.pi))

what is this line doing?

Reply via ReviewNB

[ricardoV94]

Line #3.    func = pytensor.function([], [estimate_mean, estimate_std, particles, log_weights])

this will need some updates=updates that are collected (for the RNGs in the scan). IIRC even with the default updates of RandomStreams you need them manually for the scan

Reply via ReviewNB