skaters

The sandwich

Run any model in laplace's coordinates, map back exactly. Everyone improves.

z = Φ⁻¹(Fₜ(y)) the laplace transform lettuce: a near-i.i.d. N(0,1) stream, drift and volatility removed any model: Prophet · ETS · AutoARIMA · GARCH · TabFM cheese: its z-space density, whatever shape it likes log f₁(y) = log f₂(z) + log fₜ(y) − log φ(z) exact inverse
Featured sandwich of the day: Prophet. Raw, it trails laplace by 0.76 nats median across 921 series (4.6 family-weighted). Sandwiched, 0.02. That is 97% of its density gap closed without retraining anything, calendar machinery intact, via pip install prophet-laplace.

laplace defines a causal bijection on paths: the Rosenblatt transform of each observation under the predictive issued for it. Feed the resulting z stream to any model, map its output back through the exact Jacobian, and the model operates on a stationarised, unit-scale stream instead of raw data. No retraining, no approximation in the accounting. The skill has the recipe; prophet-laplace is the drop-in package for Prophet.

Forecasters, one-step log-likelihood vs plain laplace

modeluniverserawsandwiched
ETSFRED-30−2.03+0.01
AutoARIMAFRED-30−2.03+0.05
GARCH(1,1)FRED-30−1.94+0.03
ProphetFRED-30−2.04+0.03
Prophet921 series, pre-registered−0.76 (−4.6 family-weighted)−0.02
TabFM (regressor)226 series−0.75−0.02
TabFM (x100 classifier)921 series, pre-registered−0.15+0.87 family-weighted; +1.99 on repeat-heavy series

Numbers are median nats per observation relative to laplace alone (FRED-30 rows are means relative to laplace's 3.674). The pattern: raw models trail by whole nats; sandwiched, they converge to laplace plus or minus a small epsilon, and the epsilon measures conditional structure laplace missed. The one large positive epsilon is the discrete TabFM head on repeat-heavy series, which found real structure and became a library work item.

Detectors

detectormeasurerawsandwiched
DSPOT (EVT thresholding)UCR accuracy, 250 series0.1200.232
DSPOTalarm rate at nominal 1e-3 (FRED, median)2.3e-32.5e-3, and best-in-table deep-tail behavior
RRCF (random cut forest)UCR accuracy0.2440.236 (a wash; carries its own normalizer)
left-discord matrix profileUCR accuracy, 150 series0.5870.427 (hurt; z whitens its templates)

The detector rows locate the boundary: the sandwich lifts methods whose theorems want a stationary, calibrated input, does little for weak structural methods, and hurts template matchers. It transfers the forecaster's competence, in both directions.

Full protocols, statements filed before results, and every table's source: the challengers page, the paper's sandwich section, and benchmarks/anomaly/RESULTS.md in the repository.

Every study here is reproducible from the harnesses committed under benchmarks/, each beside the results it produced.