DerivedRankBasedMetric
- class DerivedRankBasedMetric(base_cls=None, **kwargs)[source]
Bases:
RankBasedMetric
,ABC
A derived rank-based metric.
The derivation is based on an affine transformation of the metric, where scale and bias may depend on the number of candidates. Since the transformation 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. Moreover, we can obtain closed form solutions for expected value and variance.
Let \(\alpha, \beta\) denote the scale and offset of the affine transformation, i.e.,
\[M^* = \alpha \cdot M + \beta\]Then we have for the expectation
\[\mathbb{E}[M^*] = \mathbb{E}[\alpha \cdot M + \beta] = \alpha \cdot \mathbb{E}[M] + \beta\]and for the variance
\[\mathbb{V}[M^*] = \mathbb{V}[\alpha \cdot M + \beta] = \alpha^2 \cdot \mathbb{V}[M]\]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
The rank-based metric class that this derived metric extends
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
Return the key for use in metric result dictionaries.
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
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.
Generate the extra repr, cf.
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.
Iterate over the components of the
extra_repr()
.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
- base_cls: ClassVar[Type[RankBasedMetric] | None] = None
The rank-based metric class that this derived metric extends
- closed_expectation: ClassVar[bool] = False
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']]] = ('optimistic', 'realistic', 'pessimistic')
the supported rank types. Most of the time equal to all rank types
- synonyms: ClassVar[Collection[str]] = ()
synonyms for this metric
Methods Documentation
- adjust(base_metric_result, num_candidates, weights=None)[source]
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)[source]
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()
.
- extra_repr()
Generate the extra repr, cf. :meth`torch.nn.Module.extra_repr`.
- abstract get_coefficients(num_candidates, weights=None)[source]
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
- iter_extra_repr()
Iterate over the components of the
extra_repr()
.This method is typically overridden. A common pattern would be
def iter_extra_repr(self) -> Iterable[str]: yield from super().iter_extra_repr() yield "<key1>=<value1>" yield "<key2>=<value2>"
- Return type:
- Returns:
an iterable over individual components of the
extra_repr()
- 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)[source]
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()
.