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Finite-lag divergence table

Source: R/aci-assimilation.R
lag_table.Rd

Builds the table of finite-lag divergences consumed by the causal influence range estimators. A lag table uses the complete online Theorem 3 smoother as its reference. That reference costs O(N) time-point work; table construction then costs work proportional to the retained lag cells, with O(N^2) cells for a full table in the worst case.

Usage

lag_table(
  model,
  obs,
  mode = c("forward", "full"),
  tol = getOption("aci.default_tol", 1e-08),
  window = 3L,
  max_lag = Inf,
  filter = NULL,
  smoother = NULL,
  conditional = NULL,
  init = NULL,
  stepper = "explicit",
  nsub = 1L,
  regularize = NULL,
  ...
)

Arguments

model

A cgns_model object.

obs

An observed trajectory, or anything as_obs() accepts.

mode

Either "forward" or "full", selecting which cells are retained.

tol

Positive tolerance below which a row is frozen by the adaptive storage rule.

window

Number of consecutive steps a row must stay below tol before it is frozen.

max_lag

Maximum positive lag retained, or Inf for no cap.

filter

Optional precomputed filter path.

smoother

Optional precomputed smoother path.

conditional

Optional aci_conditional_spec; see aci_conditional().

init

Optional list with the initial hidden mean and cov.

stepper

Either "explicit" or "implicit".

nsub

Positive whole number of sub-steps taken per observation.

regularize

Covariance policy for this call; see aci_filter(). One record covers the filter, the Theorem 3 reference smoother and every relative-entropy denominator the table forms, and is returned in meta$regularization.

...

Must be empty; unused arguments are an error.

Value

An object of class lag_table.

References

Andreou, M. and Chen, N. (2026). Bridging prediction and attribution: identifying forward and backward causal influence ranges using assimilative causal inference. arXiv:2510.21889v2, 4 August 2026. doi:10.48550/arXiv.2510.21889

Andreou, M., Chen, N. and Li, Y. (2026). An adaptive online smoother with closed-form solutions and information-theoretic lag selection for conditional Gaussian nonlinear systems. Journal of Nonlinear Science 36(4), 71. doi:10.1007/s00332-026-10271-x

See also

aci_range(), lt_row()

Examples

m <- aci_dyad_model()
sim <- simulate(m, seed = 1, t_end = 2, dt = 0.01)
ob <- as_obs(sim)
lag_table(m, ob, mode = "forward")
#> Warning: No init$cov supplied; using a diffuse prior. Discard an initial burn-in window when interpreting results.
#> <lag_table> mode = forward, N+1 = 201, tol = 1e-08
#>   mean retained lag: 100.0 steps; max heuristic tail estimate: 0.00e+00