Metrics tweediedeviance

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TweedieDeviance

The deviance of a generalised linear model, which is what a squared error becomes when the target is not normally distributed. One type with a power, because the reference is one function with a power: the Poisson and the gamma deviances are this at 1 and 2, and PoissonDeviance and GammaDeviance exist only so a caller need not know that.

The power picks a distribution, and each has its own domain

The deviance's formula and the inputs it will accept both change with the power. This is the whole content of the family, and every boundary below is measured against scikit-learn 1.9.0 rather than inferred:

power	distribution	yTrue	yPred
below 0	stable, positive support	any real	strictly positive
0	normal — the squared error	any real	any real
(0, 1)	none — refused	—	—
1	Poisson	non-negative	strictly positive
(1, 2)	compound Poisson-gamma	non-negative	strictly positive
2	gamma	strictly positive	strictly positive
above 2	inverse gaussian and beyond	strictly positive	strictly positive

There is no distribution between the normal and the Poisson. A power in the open interval (0, 1) is refused with ArgumentOutOfRangeException, where scikit-learn raises InvalidParameterError saying the parameter "must be a float in the range (-inf, 0.0] or a float in the range [1.0, inf)". Everything else in the table is an ArgumentException carrying scikit-learn's own sentence.

The one boundary worth remembering: a zero truth is legal from 1 up to but not including 2, and illegal from 2 on. Measured, y_true = [0, 2, 3] against y_pred = [1, 2, 3] scores 0.6666… at power 1 and 1.3333… at power 1.5, and is refused at power 2.

At power 0 it is the mean squared error

Not approximately — the same number. That regime's deviance is (y − ŷ)², so TweedieDeviance.Score at the default power and MeanSquaredError.Score agree, and so do D2Tweedie and R2. It is worth knowing which of the two you are reading in a table.

Members

Member	What it does
TweedieDeviance.Score	The mean deviance at the given power.