AdjustedArithmeticMeanRank
- class AdjustedArithmeticMeanRank(base_cls=None, **kwargs)[source]
Bases:
pykeen.metrics.ranking.ExpectationNormalizedMetric
The adjusted arithmetic mean rank (AMR).
The adjusted (arithmetic) mean rank (AMR) was introduced by [berrendorf2020]. It is defined as the ratio of the mean rank to the expected mean rank. It lies on the open interval \((0, 2)\) where lower is better.
Initialize the derived metric.
- Parameters
base_cls (
Union
[str
,RankBasedMetric
,Type
[RankBasedMetric
],None
]) – the base class, or a hint thereof. If None, use the class-attributekwargs – additional keyword-based parameters used to instantiate the base metric
Attributes Summary
whether the metric needs binarized scores
whether there is a closed-form solution of the expectation
whether there is a closed-form solution of the variance
whether it is increasing, i.e., larger values are better
Return the key for use in metric result dictionaries.
The name of the metric
whether the metric requires the number of candidates for each ranking task
the supported rank types.
whether the metric supports weights
synonyms for this metric
the value range
Methods Summary
__call__
(ranks[, num_candidates, weights])Evaluate the metric.
adjust
(base_metric_result, num_candidates[, ...])Adjust base metric results based on the number of candidates.
expected_value
(num_candidates[, ...])Compute expected metric value.
get_coefficients
(num_candidates[, weights])Compute the scaling coefficients.
Get the description.
get_link
()Get the link from the docdata.
Get the math notation for the range of this metric.
get_sampled_values
(num_candidates, num_samples)Calculate the metric on sampled rank arrays.
numeric_expected_value
(**kwargs)Compute expected metric value by summation.
numeric_expected_value_with_ci
(**kwargs)Estimate expected value with confidence intervals.
numeric_variance
(**kwargs)Compute variance by summation.
numeric_variance_with_ci
(**kwargs)Estimate variance with confidence intervals.
std
(num_candidates[, num_samples, weights])Compute the standard deviation.
variance
(num_candidates[, num_samples, weights])Compute variance.
Attributes Documentation
- closed_expectation: ClassVar[bool] = True
whether there is a closed-form solution of the expectation
- needs_candidates: ClassVar[bool] = True
whether the metric requires the number of candidates for each ranking task
- supported_rank_types: ClassVar[Collection[Literal['optimistic', 'realistic', 'pessimistic']]] = ('realistic',)
the supported rank types. Most of the time equal to all rank types
- synonyms: ClassVar[Collection[str]] = ('adjusted_mean_rank', 'amr', 'aamr')
synonyms for this metric
- value_range: ClassVar[pykeen.metrics.utils.ValueRange] = ValueRange(lower=0, lower_inclusive=True, upper=2, upper_inclusive=False)
the value range
Methods Documentation
- __call__(ranks, num_candidates=None, weights=None)
Evaluate the metric.
- adjust(base_metric_result, num_candidates, weights=None)
Adjust base metric results based on the number of candidates.
- Parameters
- Return type
- Returns
the adjusted metric
Note
since the adjustment only depends on the number of candidates, but not the ranks of the predictions, this method can also be used to adjust published results without access to the trained models.
- expected_value(num_candidates, num_samples=None, weights=None, **kwargs)
Compute expected metric value.
The expectation is computed under the assumption that each individual rank follows a discrete uniform distribution \(\mathcal{U}\left(1, N_i\right)\), where \(N_i\) denotes the number of candidates for ranking task \(r_i\).
- Parameters
num_candidates (
ndarray
) – the number of candidates for each individual rank computationnum_samples (
Optional
[int
]) – the number of samples to use for simulation, if no closed form expected value is implementedweights (
Optional
[ndarray
]) – shape: s the weights for the individual ranking taskskwargs – additional keyword-based parameters passed to
get_sampled_values()
, if no closed form solution is available
- Return type
- Returns
the expected value of this metric
- Raises
NoClosedFormError – raised if a closed form expectation has not been implemented and no number of samples are given
Note
Prefers analytical solution, if available, but falls back to numeric estimation via summation, cf.
RankBasedMetric.numeric_expected_value()
.
- get_coefficients(num_candidates, weights=None)
Compute the scaling coefficients.
- Parameters
- Return type
- Returns
a tuple (scale, offset)
- get_sampled_values(num_candidates, num_samples, weights=None, generator=None, memory_intense=True)
Calculate the metric on sampled rank arrays.
- Parameters
num_candidates (
ndarray
) – shape: s the number of candidates for each ranking tasknum_samples (
int
) – the number of samplesweights (
Optional
[ndarray
]) – shape: s the weights for the individual ranking tasksgenerator (
Optional
[Generator
]) – a random state for reproducibilitymemory_intense (
bool
) – whether to use a more memory-intense, but more time-efficient variant
- Return type
- Returns
shape: (num_samples,) the metric evaluated on num_samples sampled rank arrays
- numeric_expected_value(**kwargs)
Compute expected metric value by summation.
The expectation is computed under the assumption that each individual rank follows a discrete uniform distribution \(\mathcal{U}\left(1, N_i\right)\), where \(N_i\) denotes the number of candidates for ranking task \(r_i\).
- Parameters
kwargs – keyword-based parameters passed to
get_sampled_values()
- Return type
- Returns
The estimated expected value of this metric
Warning
Depending on the metric, the estimate may not be very accurate and converge slowly, cf. https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_discrete.expect.html
- numeric_expected_value_with_ci(**kwargs)
Estimate expected value with confidence intervals.
- Return type
- numeric_variance(**kwargs)
Compute variance by summation.
The variance is computed under the assumption that each individual rank follows a discrete uniform distribution \(\mathcal{U}\left(1, N_i\right)\), where \(N_i\) denotes the number of candidates for ranking task \(r_i\).
- Parameters
kwargs – keyword-based parameters passed to
get_sampled_values()
- Return type
- Returns
The estimated variance of this metric
Warning
Depending on the metric, the estimate may not be very accurate and converge slowly, cf. https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_discrete.expect.html
- numeric_variance_with_ci(**kwargs)
Estimate variance with confidence intervals.
- Return type
- std(num_candidates, num_samples=None, weights=None, **kwargs)
Compute the standard deviation.
- Parameters
num_candidates (
ndarray
) – the number of candidates for each individual rank computationnum_samples (
Optional
[int
]) – the number of samples to use for simulation, if no closed form expected value is implementedweights (
Optional
[ndarray
]) – shape: s the weights for the individual ranking taskskwargs – additional keyword-based parameters passed to
variance()
,
- Return type
- Returns
The standard deviation (i.e. the square root of the variance) of this metric
For a detailed explanation, cf.
RankBasedMetric.variance()
.
- variance(num_candidates, num_samples=None, weights=None, **kwargs)
Compute variance.
The variance is computed under the assumption that each individual rank follows a discrete uniform distribution \(\mathcal{U}\left(1, N_i\right)\), where \(N_i\) denotes the number of candidates for ranking task \(r_i\).
- Parameters
num_candidates (
ndarray
) – the number of candidates for each individual rank computationnum_samples (
Optional
[int
]) – the number of samples to use for simulation, if no closed form expected value is implementedweights (
Optional
[ndarray
]) – shape: s the weights for the individual ranking taskskwargs – additional keyword-based parameters passed to
get_sampled_values()
, if no closed form solution is available
- Return type
- Returns
The variance of this metric
- Raises
NoClosedFormError – Raised if a closed form variance has not been implemented and no number of samples are given
Note
Prefers analytical solution, if available, but falls back to numeric estimation via summation, cf.
RankBasedMetric.numeric_variance()
.