Add tutorial for training interface

[michaeldeistler]

from sbi.neural_nets.flow import build_nsf
from sbi.neural_nets.density_estimators.flow import NFlowsFlow
from sbi.inference.posteriors import MCMCPosterior
from sbi.inference.potentials import likelihood_estimator_based_potential


# Build neural density estimator.
net = build_nsf(x, theta)
de = NFlowsFlow(net, condition_shape=(theta.shape[1],))

# Train the density estimator.
opt = Adam(list(de.parameters()), lr=5e-4)
for _ in range(100):
    opt.zero_grad()
    log_probs = de.log_prob(x, condition=theta)
    loss = -torch.mean(log_probs)
    loss.backward()
    opt.step()

# Build posterior and sample with MCMC.
potential, tf = likelihood_estimator_based_potential(de.net, prior, x_o)
posterior = MCMCPosterior(
    potential,
    proposal=prior,
    theta_transform=tf,
    num_chains=100,
    method="slice_np_vectorized"
)
samples = posterior.sample((1000,), x=x_o)
_ = pairplot(samples, limits=[[-3, 3], [-3, 3]], figsize=(3, 3))

TODO:

• have an abstraction that avoids two lines for the density estimator (not sure about this one...)
• Make the DirectPosterior and all potentials use the DensityEstimator abstraction
• Make it easier to use NRE by having an abstraction for the loss

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 77.01%. Comparing base (afbd5e7) to head (d8db78c).

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- Coverage   85.08%   77.01%   -8.07%     
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  Files          90       90              
  Lines        6643     6643              
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- Hits         5652     5116     -536     
- Misses        991     1527     +536     

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