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The rejected splits

Description

The third component of effector's report: the REJECTED SPLITS table. Every split that was considered and refused, with the reason. The report shows its work.

Reading time

Approx. 4' to read.

What you see

In report.show(), right under the explained variance ledger:

  REJECTED SPLITS                                            min gain 1.0%
  ────────────────────────────────────────────────────────────────────────
    feature      split on                 solo     ΔR²    reason
    ──────────────────────────────────────────────────────────────────────
  ✗ temp         hr, hum                 +1.7%   +0.9%    below threshold
  ✗ yr           hr, hum                 +1.5%   -0.1%    redundant
  ✗ workingday   hr, yr                  +4.9%   -4.3%    redundant

    ✗ redundant: it would explain variance on its own (see solo),
      but the accepted splits already account for it.

On the HTML page the same rows appear dimmed inside the decision sequence table, one rejected · <feature> (on ...) row each, with the candidate's region count and its heterogeneity before → after.

The section exists only when something was rejected; a run where every candidate is accepted (or none is proposed) prints nothing here.

Why show refusals at all

Because "why is workingday not split?" deserves a row, not a shrug. The selection is greedy and it stops; everything it left behind is listed with the number that condemned it. Nothing is silently dropped, so the report can be audited, not just believed.

The two reasons

Both columns come from the same round: the moment the selection stopped, every remaining candidate was measured once more, on top of everything already accepted.

  • below threshold: the split still adds real variance (ΔR² positive), just less than min gain (the header repeats the cut: min gain 1.0%, from min_r2_gain=0.01). Lower the threshold and these are the rows that would enter the ledger next.
  • redundant: the split adds nothing, or even hurts (ΔR² zero or negative), because the accepted splits already explain its variance.
Read solo against ΔR²

workingday would have been worth +4.9% on its own: the second strongest split in the model. But once hr is split (and hr's split already conditions on workingday), it adds −4.3%. It is not useless; it is redundant. The solo column is what separates the two verdicts, and it is why the column exists.

How can ΔR² be negative?

Two splits explaining the same variance double count it: the summed surrogate moves twice for one underlying pattern, and its R² drops. A negative ΔR² is the selection catching that overlap, not a numerical accident.

Rejected does not mean fake

Every rejected split is a real split: find_regions proposed it because it genuinely reduces its feature's heterogeneity. The lesson of this table is that a heterogeneity drop and an explained-variance gain are different currencies: a split can resolve real spread inside its own feature while adding nothing to what the accepted splits already explain of the model.

In the regional analysis section of the HTML page, a rejected feature stays global, with a note pointing back at this table; its found partition is not drawn as if it had been accepted.

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