Visualization and calculation of posterior function

[IGB-leonhardt]

Hello together,

I tried to call (and visualize) the posterior function of an already fitted model in order to describe my experimental data over the whole range of the search space.

Unfortunately, with this code, I only managed to call mean and variance of candidates:

meassurements = campaign.measurements
posterior = campaign.posterior(candidates=meassurements)
print(posterior)
mean = posterior.mean
variance = posterior.variance
print("Mean:\n", mean)
print("Variance:\n", variance)

Is there a way to get the mean and variance function of the fitted model?

[AdrianSosic]

Hi @IGB-leonhardt, the answer is probably "yes" but I'm not entirely sure if I understand the question right. Note: Computationally, you can always only ever evaluate statistics on a finite number of points – so I'm not 100% clear what exactly you refer to when you say mean and variance of the fitted model. If you restrict this question to a finite number of query points --> yes.

Consequently, in a discrete search space, there is a simple answer because you can just evaluate the entire search space via

campaign.posterior(campaign.searchspace.discrete.exp_rep)

However, as soon as you go to continuous or mixed spaces, it is no longer clear how to interpret the question in the first place. Maybe you can clarify what you mean? For example, one thing you can do is to subsample your space and then do the evaluation on that subset of points, just like you did above.

Does this help you?

[IGB-leonhardt]

Thank you, for your fast answer!

For clarification: Ideally, I would like to get a continuous function, that describes (predicts) mean and variance depending on the parameters. The aim is to receive an empirical representation on how parameter A...E are influencing the outcome of target F.

[AdrianSosic]

Ok, I see. But that has little to do with BayBE itself and is just a matter of wrapping the call appropriately into a function with the signature of your choice. So for example:

import pandas as pd

from baybe import Campaign
from baybe.parameters import NumericalContinuousParameter
from baybe.targets import NumericalTarget
from baybe.utils.dataframe import create_fake_input

searchspace = NumericalContinuousParameter("p", (0, 1)).to_searchspace()
objective = NumericalTarget("t", "MAX").to_objective()
measurements = create_fake_input(searchspace.parameters, objective.targets, 10)

campaign = Campaign(searchspace, objective)
campaign.add_measurements(measurements)

# Here is your continuous function
f = lambda df: campaign.posterior_stats(df)

mean_and_std = f(pd.DataFrame({"p": [0.44523, 0.64352, 0.12345]}))
print(mean_and_std)

Note that you can completely customize how the interface of that function should look like (without having to touch any BayBE code itself) by simply adjusting the wrapper, e.g. instead of using a lambda, you can also define a def with the interface you like to have.

Is this what you are looking for?

[Scienfitz]

Hi @IGB-leonhardt ,
its a bit unclear to me what exactly do you need in addition of the code from above?

You can change candidates to be any set of points that you want to visualize over, how to get the mean and var of those predicitons is already in your code. For instance if you have a continous search space you can create a grid first and then evaluate this on the grid. Can you elaborate what else do you need?

Note that we already implemented another convenience function called Campaign.posterior_stats which provides the ability to access other statistics. This is not released yet but you can find it on main (and the doc link is ent you links to latest not stable. The release of this is schedules for tomorrow or soon afterwards.