Three changes to ForecastHead and the conformal calibrator, each measured
walk-forward on real data over seven train splits.
Hedge normalised its losses by the current sample's worst loss, so on a quiet
step where every member agreed to within 0.01 C whichever happened to be worst
still took the full exp(-eta) penalty, exactly as if it had been wrong by 5 C.
The regret bound assumes a fixed loss range, not a per-sample one, and the
symptom was weights that jumped around with no relation to horizon. Normalising
by the running member MAE instead is worth 1.81% of MAE, better on 106 of 126
heads, coverage unchanged.
The residual handed to the conformal calibrator was computed after this
sample's loss had already moved the weights, so it was better than anything the
forecaster could produce and the intervals were calibrated about 2% too narrow.
Coverage survived only because ACI notices the extra misses and reopens the
band, a correction that should never have been needed. Scoring the blend with
the pre-update weights leaves MAE untouched, as it must, and widens the
intervals 2% to the honest width.
The conformal quantile refused to produce a band below 20 scores. That number
is arbitrary: the (1-alpha) empirical quantile is the ceil((k+1)(1-alpha))-th
of k order statistics, so alpha = 0.10 needs 9. The 20 became actively harmful
in the previous commit but one, because striding pairs by the horizon leaves a
long-horizon head about 13 scores per refit. Twelve of eighteen heads therefore
fell through to 1.645*sigma with sigma from an unconstrained x'Px, giving bands
of +/- 45 C and +/- 115% relative humidity on a young station. Those cover, by
being absurd, which is why the backtest never flagged them: a long walk-forward
passes 20 scores early and never looks back. After the change all eighteen
heads have a band from the first fit, +/- 3.1 C and +/- 7.7% in the same place.
Also measured and deliberately not done: adding the Kalman level variance to
the predictive spread. It moves sigma by 0.06% at the shortest horizon and
0.00% everywhere else, so the plumbing to carry it through three files buys
nothing.
Co-Authored-By: Claude Opus 5 <[email protected]>
The companion to the Kalman fix. RecursiveLeastSquares.from_dict and
AdaptiveConformal.from_dict restore lambda, delta, alpha, gamma and the
conformal window alongside their data, and load_dict replaces the
config-built heads with those, so every one of those knobs was immutable on
any station that already had state. Editing config.yaml and restarting looks
exactly like a change with no effect, which is the failure mode that cost real
time on the Kalman side of this before it was found.
Only the estimate is state now. Weights, covariances and conformal scores are
restored; tuning is re-applied from config on every load. The conformal deques
are rebuilt when the configured window changes, preserving their contents.
load_dict also skips heads for a target or horizon this build no longer has,
rather than resurrecting them from a stale file.
Found while implementing a damped-trend ensemble member, which was then
abandoned: see the following note.
Co-Authored-By: Claude Opus 5 <[email protected]>
Reported from a real station after 1.5 days: a six hour temperature forecast of
53 C in a 24 C room, and 9 C at one day, both carrying a plus or minus of 0.43.
Confidently wrong is the one failure this project is supposed to refuse.
Root cause. fit() replayed history into the live RLS on every retrain tick and
never reset, so 453 grid rows had produced 64,676 updates in a day and a half.
RLS with forgetting reads every update as fresh evidence, so the model believed
it had a hundred times the data it had: P collapsed, in-sample error looked
excellent, and the weights drifted without bound in directions the data never
excited. Measured: cond(P) 3.1e9 and ||theta|| 1680 against a median |theta| of
1.67. A refit now starts from the prior, which makes retraining idempotent.
Across 25 refits on the real data ||theta|| holds at 11.35, drifting 0.03, where
before it grew without limit.
The two largest weights were sin_doy and cos_doy at +1174 and +1191. Annual
harmonics were in the design matrix from the first sample, where they are
near-constant, near-collinear with each other and with the bias, and a
rank-deficient regressor is what RLS answers with enormous cancelling weights.
They are now held at zero until the record spans the same 120 days the
climatology fit already requires, because a day and a half of data says nothing
whatsoever about the season.
Also raised the standardiser's variance floor from 1e-8, which only caught a
bit-exactly constant column, to 1e-3. A feature that merely barely moves was
being divided by its own noise.
The conformal calibrators and Hedge weights are deliberately not reset by a
refit: those are earned from scored forecasts, not from this regression.
Backtest unchanged within noise, coverage still 89 to 91 across all 18 heads.
Four regression tests added, including that refitting the same history twice
must give the same model.
kemalandClaude Opus 5