Getting Started with Multivariate Gaussian Processes (vector autoregression)

Questions v5
,
1

Hello there,

I’m currently trying to apply Gaussian processes to vector autoregression. Specifically in the case where n>3 an example might be here:(https://arxiv.org/pdf/2112.01995)

While I find a lot of the pymc examples really helpful-I’m a little confused how to define a Multi response GP in pymc (still learning the ins and outs!). Even trying to write a row and column parameter matrix in the definition of a MGP is a bit in the confusing side for me

I want to be active in responses and not just ask for example code, so please let me know if I can be more specific. Thank you!

2

This example might help you. It’s a bit slow so it might be worth seeing if you can use HSGP to speed things up. Here are some example notebooks: basic usage, advanced usage. I think Example 2 in the advanced notebook is probably what you are looking for.

1 Like
3

thank you! i’ll try it out :slight_smile:

4

Hi, sorry for the lapse in reply, i’ve been shoring up my linear algebra and some of the theory in rassumussen to help with some development

i have what probably amounts to a silly question, but in Gaussian Processes: HSGP Advanced Usage — PyMC example gallery, this sequence of code confuses me

f_true = (
    pm.draw(pm.MvNormal.dist(mu=np.zeros(n_gps * n_t), cov=K), random_seed=rng)
    .reshape(n_gps, n_t)
    .T
)

# Additive gaussian noise
sigma_noise = 0.5
noise_dist = pm.Normal.dist(mu=0.0, sigma=sigma_noise)

y_obs = f_true + pm.draw(noise_dist, draws=n_t * n_gps, random_seed=rng).reshape(n_t, n_gps)

As I understand, f_true should be a mvG(3000,3000^2). So this draw should just be a sample in R^3000. I do not understand the reshape call right here, the only thing I can think of is that reshaping in this manner just allows us to more easily store the (time, process) index for numerical efficiency.