Sequential NPE with truncated-prior proposals (TSNPE)

Multi-round NPE targeting a single observation x_obs. Single-round npe() spends its simulation budget across the whole prior; when only one observation matters, most of those simulations land in regions the posterior never visits. npe_sequential() implements truncated sequential NPE (TSNPE, Deistler et al. 2022): after each round the prior is truncated to the highest-probability region of the current posterior estimate, and the next round's parameters are drawn from that truncated prior. Because every proposal is proportional to the prior on its support, the standard NPE loss stays valid – no importance-weight or atomic correction is needed, which is what makes TSNPE the simplest correct sequential scheme.

Usage

npe_sequential(
  prior,
  simulator,
  x_obs,
  n_rounds = 2L,
  n_simulations = 1000L,
  sim_args = list(),
  density_estimator = c("maf", "mdn", "nsf", "linear_gaussian"),
  epsilon = 1e-04,
  n_truncation_samples = 5000L,
  max_proposal_batches = 200L,
  seed = NULL,
  verbose = FALSE,
  ...
)

Arguments

prior: An nsbi_prior (see prior_uniform(), prior_normal()).
simulator: A function called once per parameter set, returning one simulated observation; see nsbi_simulator.
x_obs: The observation to target, as one numeric vector, one-row matrix or one-row data frame whose width matches the simulator's output. Sequential inference concentrates simulations around the posterior for this observation.
n_rounds: Number of rounds, at least 1. Round 1 is ordinary single-round NPE.
n_simulations: Simulation budget per round; either a scalar or a vector of length n_rounds.
sim_args: Named list of extra arguments passed to every simulator call; see nsbi_simulator.
density_estimator: Passed to npe() each round.
epsilon: Mass cut for the truncation: the proposal region is the 1 - epsilon highest-probability region of the current posterior. Must be a single number strictly between 0 and 1.
n_truncation_samples: Posterior draws used to locate the truncation threshold each round.
max_proposal_batches: Cap on rejection-sampling batches per round.
seed: Optional integer seed for reproducibility.
verbose: Print per-round progress.
...: Passed to npe() (estimator and training settings). Checked before round 1 simulates, the same as the arguments above.

Value

An object of class c("nsbi_snpe", "nsbi_npe") with a rounds field recording per-round budgets, acceptance rates, and thresholds.

Details

The rounds accumulate: each round's estimator is trained on all simulations so far. The final fit is returned as an nsbi_npe (subclass nsbi_snpe) and works with posterior(), sample() and the diagnostics, but unlike single-round NPE it is not amortized: it is only trustworthy at (or very near) x_obs.

Proposal draws are obtained by rejection: prior candidates are kept when their posterior log-density clears the epsilon-quantile threshold of the current posterior's own draws. If the posterior is much narrower than the prior the acceptance rate falls; the round then stops after max_proposal_batches batches and continues with the draws it has, with a warning.

References

Deistler, Goncalves & Macke (2022), "Truncated proposals for scalable and hassle-free simulation-based inference", NeurIPS. doi:10.48550/arXiv.2210.04815

Examples

prior <- prior_normal(mean = c(mu = 0, nu = 0), sd = 1)
simulator <- function(mu, nu) c(mu, nu) + rnorm(2, sd = 0.3)
fit <- npe_sequential(prior, simulator, x_obs = c(0.5, -0.5),
                      n_rounds = 2, n_simulations = 1000,
                      density_estimator = "linear_gaussian")
post <- posterior(fit, x_obs = c(0.5, -0.5))
draws <- sample(post, 1000)