Quant Library · The machine layer · Any

Hedge Expert Mixture

Combine forecasters online, with a bound on how far behind the best one you can end up.

Exponential weights over any set of probabilistic forecasters, with the regret bound that makes the weights worth trusting.

Read the specification (PDF) Run it on the API The the machine layer family · £1,199

Inputs

What it takes

Name	Type	Units	Where it comes from
experts	list of names	-	your forecasters: a model, a market, a base rate
forecasts	dict per match of expert -> probabilities	probability	-
results	list	-	what happened
eta optional	float	-	learning rate; 0.5 is the platform's

Outputs

What it gives back

Name	Type	Units
weights	dict	-
mixture	probabilities per match	probability
regret_bound	float	nats

Method

How it works

Start uniform. After each result multiply every expert's weight by exp(−η ℓ), where ℓ is its log loss on that result, then renormalise.
2 further steps in the licensed specification

Assumptions

Losses are bounded, which log loss is not unless probabilities are clipped. The implementation clips at 1e-9 and says so.

Limits

It converges on the best single expert, and cannot beat it by much. If one of your experts is a closing line, expect the mixture to become that line.
1 further limits in the licensed specification

Validation

What it was measured at

Four experts per league: a base rate, the goals model, the shots blend and the closing line.

Leagues	1
Weight the mixture gives the closing line	0.97 to 0.97	it learns what the Trust tab already says
Mixture loss minus the best expert's	+0.0037 to +0.0037	nats per match; the bound guarantees this stays small
Regret bound	ln N / η + η T / 8	worst case over any sequence, not an average

In the package

The full specification: inputs, method, assumptions and limits
The validation panel as measured on the day of purchase
A reference implementation extracted from the running source
Perpetual commercial use for one entity

Reference modules:

1 module(s), named in the licensed specification and shipped in the package

Read this before you buy. The platform's own walk-forward tests say the closing line forecasts football better than these models do. What they give you is a coherent price for every market and match, before the market opens, with the band and the working attached. Any model here that has been beaten by something simpler says so in its limits, and the validation panel above is generated from the platform's result files rather than typed in.