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Generate a v0 ladder for exploring sparsity levels

make_v0_ladder.Rd

Creates a decreasing sequence of spike variance values (v0) for use with ssjgl. This is primarily useful for exploring how sparsity changes across v0 values, for diagnostics, or for replicating the full dynamic posterior exploration strategy of Li et al. (2019).

Usage

make_v0_ladder(
  lambda1,
  n_steps = 10,
  min_ratio = 5,
  max_ratio = 500,
  start_sparse = TRUE
)

Arguments

lambda1

Numeric scalar; the off-diagonal penalty used in ssjgl. The v0 ladder is scaled to this value.

n_steps

Integer number of v0 values in the ladder. Default 10.

min_ratio

Numeric minimum effective penalty ratio lambda1/v0 at the first (densest) step. Default 5.

max_ratio

Numeric maximum effective penalty ratio lambda1/v0 at the last (sparsest) step. Default 500.

start_sparse

Logical. If TRUE (default), the first v0 is the largest (weakest penalty) and the sequence is decreasing, which is the correct direction for warm-starting. If FALSE, returns an increasing sequence.

Value

A numeric vector of length n_steps with v0 values, decreasing by default.

Details

For routine use, a short ladder like v0s = c(0.1, 0.03, 0.01) is recommended (see ssjgl defaults and vignette("parameter-exploration") for details).

The effective penalty for edge sparsity is lambda1/v0. This function creates a log-spaced ladder of v0 values such that the effective penalty ranges from min_ratio to max_ratio. Log-spacing concentrates more steps in the sparse (small v0) end where the model is most sensitive.

Interpreting v0: The spike standard deviation sqrt(v0) sets the scale below which partial correlations are treated as noise. For normalized data where partial correlations live in -1, 1:

  • v0 = 0.1 (spike SD = 0.32): weak sparsity, broad spike

  • v0 = 0.01 (spike SD = 0.10): moderate sparsity, good default

  • v0 = 0.001 (spike SD = 0.03): aggressive sparsity

  • v0 = 0.0001 (spike SD = 0.01): very aggressive, may over-sparsify

See also

ssjgl(), plot_stability()

Examples

# Exploration ladder for lambda1 = 0.5
v0s <- make_v0_ladder(lambda1 = 0.5, n_steps = 10)
data.frame(v0 = v0s, spike_sd = sqrt(v0s),
           eff_penalty = 0.5 / v0s)
#>             v0   spike_sd eff_penalty
#> 1  0.100000000 0.31622777    5.000000
#> 2  0.059948425 0.24484367    8.340503
#> 3  0.035938137 0.18957357   13.912797
#> 4  0.021544347 0.14677993   23.207944
#> 5  0.012915497 0.11364637   38.713184
#> 6  0.007742637 0.08799225   64.577483
#> 7  0.004641589 0.06812921  107.721735
#> 8  0.002782559 0.05274997  179.690683
#> 9  0.001668101 0.04084239  299.742125
#> 10 0.001000000 0.03162278  500.000000