Laplace Algorithm Empirical Results

One tiny, fast, online model against heavy machinery, on their respective home turf. As Malcolm Fraser once said, life wasn’t meant to be easy.

Strengths by regime

Five regimes plus a price/returns axis, one score each: how often a challenger beats laplace per series, ties split, scaled so a 50/50 draw is 1.0. The dashed ring is laplace itself; outside the ring the challenger is winning that regime, inside it is losing. Soft vs hard waveforms are the two halves of M4-Hourly (noisy daily cycles vs nearly deterministic ones; see the TBATS bout). Price/returns is the one axis laplace is not built for, and GARCH-t wins it decisively (~1.8x on 2500 return series). Pick up to six challengers — GARCH-t, Prophet, the foundation models and more. Entries marked (sandwiched) are drawn dashed: those models run inside laplace's own coordinates and beat it by construction, so they are collaboration, not a head-to-head win (see collaborative use). The default view includes the PyMC–laplace sandwich, which finishes ahead across the whole universe when run this way — the clearest case of cooperation beating competition.

Should you use something else?

Quite possibly. laplace is one small, fast, online forecaster; the methods below range from classical workhorses to 200M-parameter foundation models, and several do their best work on particular ground: GARCH on price and return series, Viole's NNS on strongly seasonal data, TBATS where a soft daily cycle wants smoothing. The record below marks each of those corners where we found them, in its own row rather than averaged away. What laplace is for, and what it deliberately is not, is set out on the scope page, and the whole record is written up in the papers.

Should you use laplace with something else?

Very possibly — and it is the more interesting question. skaters cooperates as well as it competes: sandwiched in laplace's coordinates a challenger keeps its own strengths but inherits laplace's calibration and manufactured stationarity, and usually improves dramatically (the sandwich). PyMC, new but already strong, finishes ahead across the whole universe once sandwiched (+0.04 nats median on 65% of series) — it is the dashed entry in the star map above. Prophet, which wins only 4 of 921 pre-registered series raw, changes character entirely in these coordinates. So a bare horserace can mislead: these pages look for the series and regimes where each method does its best work, alone or sandwiched.

Featured bouts

The above caveats notwithstanding, Laplace does seem to outperform as a practical generalist model: fast, light, and with no dependencies.

The record

Numbers are per-series win-rates for laplace, log-likelihood first, CRPS second. Everyone is converted to the same Dist and scored by the same code on the same held-out points. Every row links its tape.

Challengers that earn a full treatment get a bout page: TimesFM, TabFM, and PYMC-Forecast so far. The next candidates are the native-density foundation models, Moirai and Lag-Llama, which came closest. Rematch conditions for TimesFM are tracked in skaters#97.

Send a challenger

The protocol is packaged and copyable: the benchmark-against-laplace skill for any distributional forecaster, and the timesfm-study skill for foundation models specifically. Same Dist, same code, same held-out points, both metrics, splits disclosed. Run it, and if your method wins, open an issue with the tape; the table takes new rows in either direction.

New bouts are pre-registered: the protocol, parameters and analysis plan are committed to benchmarks/preregistrations before the results are read, with everything already observed at filing disclosed. The first filed statement is the TabFM bout.