Spline Search and Tuning

Practical tuning guidance for crs, including search size, smoothness, knot selection, and memory-aware spline search.

Keywords

crs, spline search, knots, degree, segments, cv.df.min, smoothness

This page collects the practical tuning advice for crs: what to do when search is expensive, when the chosen spline is rougher than you expected, and how to impose a narrower search when that is scientifically warranted.

Why can the search take time?

crs is often searching over:

spline degree,
knot or segment structure,
basis type,
categorical handling.

So if a run feels slow, the first question is not “is something broken?” but rather “how large is the search space I asked for?”

If the search still feels long

Current crs releases use compact single-line status I/O during NOMAD search, so the usual next step is not to change optimizer display settings. If progress is slow, first assume the requested search space is large and reduce the problem before concluding anything more dramatic.

The controls below are the practical levers to reach for first.

CRS NOMAD budget controls

Current crs releases choose route-specific defaults for NOMAD black-box evaluation budgets after the search route is known. Continuous-only searches and kernel/categorical searches therefore no longer have to share one blunt default.

If you need to override the defaults, use the public budget controls directly:

## Override CRS NOMAD budgets only when the default search is not appropriate
model <- crs(y ~ x1 + x2,
  max.bb.eval = 10000,
  max.eval = 1000)

max.bb.eval controls the black-box evaluation budget, while max.eval controls repeated NOMAD point-lookup budgets. Summaries now report elapsed time and cache diagnostics more clearly, so inspect the fitted object before loosening a search globally.

Memory control during search

If the spline basis can become very large, one practical control is to restrict the minimum degrees of freedom the search is allowed to approach.

In crs, that means looking at cv.df.min.

The practical interpretation is simple: if the unrestricted search can wander into absurdly large bases, use cv.df.min to keep the search in a region that is computationally defensible.

Reduce the search space deliberately

If you need a smaller problem first, the usual levers are:

lower degree.max,
lower segments.max,
use complexity = "degree" or another narrower search,
use basis = "additive" when additivity is a defensible restriction.

That last option can reduce the combinatorics materially, but of course it changes the model class, so it should be a modeling decision and not just a computational trick.

What if the fitted spline is not smooth enough?

Cross-validation can legitimately choose a rougher spline than you expected. That is not a bug. It is the optimizer doing what the criterion asked for.

If you want a smoother object, one honest way to do it is to impose a minimum degree:

## Impose a minimum spline degree when you want a smoother fitted object
model <- crs(y ~ x1 + x2, degree.min = 3)

That is cleaner than pretending the cross-validated solution was wrong while silently using a different one.

Can `crs` mimic a cubic smoothing-spline style search?

Yes. If you want to hold degree fixed and optimize knot structure instead, a practical route is:

## Hold the degree fixed and let the knot search do the work
model <- crs(y ~ x1, complexity = "knots", degree = 3)
summary(model)

That is not identical to every smoothing-spline implementation, but it is the natural crs analogue when you want to hold degree fixed and let the knot search do the work.

Can `crs` recover linear regression?

Yes. This is worth remembering because it clarifies the model family.

## Recover the linear-regression-style special case inside crs
model_crs <- crs(y ~ x1 + x2 + z1 + z2,
  cv = "none",
  kernel = FALSE,
  degree = rep(1, 2),
  segments = rep(1, 2))

This is the simple linear-regression-style special case already highlighted on Splines.

Quantile regression splines

If you want a conditional quantile rather than a conditional mean, use tau.

## Use tau to target a conditional quantile rather than a conditional mean
model_q <- crs(y ~ x1 + x2, tau = 0.5)

That gives the conditional median when tau = 0.5, or any other conditional quantile for tau in (0, 1).

Retrieving knots

Once a model is fit, the practical route to the knot locations depends on whether uniform or quantile knots were used. The key quantity to inspect is the selected number of segments for each predictor.

For a single predictor x1, the old FAQ’s practical rule was:

## Recover uniform knot locations from the selected segment count
seq(min(x1), max(x1), length = model$segments[1] + 1)

for uniform spacing, or

## Recover quantile knot locations from the selected segment count
quantile(x1, probs = seq(0, 1, length = model$segments[1] + 1))

for quantile spacing.

Compare against a parametric baseline when useful

If you want to compare a parametric model and a spline model on a common predictive criterion, compare the cross-validation score rather than only the fitted curves.

That is often a more honest question than “which summary table looks nicer?”