How to retrieve latent state over time for DynamicLinearRegression

[Sigrid Keydana]

Hi,

I'm preparing a post on DLMs with TFP and would like to showcase an example of dynamic linear regression. However, I don't see how to access the state over time - I only seem to be able to draw samples for drift_scale independent of time?

Can you please let me know what I'm missing?

Thanks!

Cheers,

Sigrid

[Dave Moore]

Hi Sigrid,

You can get out the means and covariances over the model's latent state using the `posterior_marginals` method of a LinearGaussianStateSpaceModel instance:

```

ssm = model.make_state_space_model(num_timesteps, param_vals=q_samples_)

latent_means, latent_covs = ssm.posterior_marginals(observed_time_series)

```

where 

`model = tfp.sts.Sum([..., tfp.sts.DynamicLinearRegression(...), ...], ...)` 

is an STS model instance, and

`q_samples_ = {k: q.sample(50) for k, q in variational_distributions.items()}`

are posterior model params sampled from a fitted variational distribution (as in the example notebook

https://github.com/tensorflow/probability/blob/master/tensorflow_probability/examples/jupyter_notebooks/Structural_Time_Series_Modeling_Case_Studies_Atmospheric_CO2_and_Electricity_Demand.ipynb)

If your model is a `tfp.sts.Sum` of multiple components, then `np.cumsum([c.latent_size for c in model.components])` will give you the start and end indices of all the model components in the latent state, which might be useful if you want to slice out just the dynamic regression part.

Dave

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[Sigrid Keydana]

Thanks Dave, awesome! This was exactly the missing link I needed ... :-)

[Sigrid Keydana]

Hi Dave,

thanks again, this looks promising! One terminological question, the way this is implemented, is it more appropriate to call these filtered or smoothed estimates, in normal DLM lingo?

Thanks!

[Dave Moore]

You're welcome! The distributions from `ssm.posterior_marginals(observed_time_series)` are smoothed, i.e., they're the marginals of the posterior conditioned on the entire time series (from the forward-backward algorithm). If you just need the forward pass, `ssm.forward_filter(observed_time_series)` will give you the filtered marginals.

Dave

[Sigrid Keydana]

Awesome, thanks! (Actually I see now it's all there in linear_gaussian_ssm.py, could just have looked there ... :-))

And forward_filter returns the intermediate calculations too, that's nice!