Use SBI to generate synthetic data

[dirknbr]

There is some data D that generates metrics M (corr matrix, model coefficients, quantiles, etc). I cannot observe D but only M. I want to generate a synthetic copy D' which generates metrics M' which have a small distance with M. 
I was wondering how I would use SBI to find parameters P (eg mu and cov matrix) that generate D' so to minimise the distance between M and M'. 

My function f(P) that generates the data could be the simulator function in SBI.

[michaeldeistler]

Hi there,

Yes, you can absolutely use sbi for this. A few clarifications:

• indeed, as you suggesst, f(P) would be the simulator.
• sbi focuses on stochastic simulators. It is a bit unclear to me whether the mapping D->M is stochastic in your case. If it is not, then I would suggest to add Gaussian noise with: D->M + eps
• To find those P which minimize distance (as compared to getting the full posterior over P, I would recommend to compute the MAP of the posterior, which you can do with posterior.map() in sbi.

Does this make sense?
Michael

[dirknbr]

I have now approached this like as follows.

My sim_t_3 function translates P into a cov matrix, it then generates D (stochastic), then I estimate M given D.

However I find that the posterior P is very close to the prior given M_obs. I don't find posterior P close to the ground truth.

# ground truth M
P = torch.reshape(torch.tensor([1, .6, .5, 1, .5, 1]), (1, 6))
M_obs = sim_t_3(P)
print(M_obs)

# set prior
P_prior = torch.randn(1000, 6) * .12 + torch.tensor([.8, .4, .4, .7, .4, .8])
M = sim_t_3(P_prior)

inference = NPE()
inference.append_simulations(P_prior, M).train()

posterior = inference.build_posterior()
# infer P posterior samples
samples = posterior.sample((1000,), x=M_obs)
samples = np.array(samples)
print(samples.mean(axis=0))

[michaeldeistler]

It's hard to debug this without knowing what sim_t_3 looks like. Generally, 1k simulations is still quite little, I recommend to try with at least 10k simulations. See here for an overview of published sbi applications: many use >1M simulations.