# DerivedRankBasedMetric¶

class DerivedRankBasedMetric(base_cls=None, **kwargs)[source]

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:

Attributes Summary

 base_cls The rank-based metric class that this derived metric extends binarize whether the metric needs binarized scores closed_expectation whether there is a closed-form solution of the expectation closed_variance whether there is a closed-form solution of the variance key Return the key for use in metric result dictionaries. needs_candidates whether the metric requires the number of candidates for each ranking task supported_rank_types the supported rank types. supports_weights whether the metric supports weights synonyms 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 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

binarize: ClassVar[bool] = False

whether the metric needs binarized scores

closed_expectation: ClassVar[bool] = False

whether there is a closed-form solution of the expectation

closed_variance: ClassVar[bool] = False

whether there is a closed-form solution of the variance

key

Return the key for use in metric result dictionaries.

Return type:

str

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

supports_weights: ClassVar[bool] = False

whether the metric supports weights

synonyms: ClassVar[Collection[str]] = ()

synonyms for this metric

Methods Documentation

__call__(ranks, num_candidates=None, weights=None)[source]

Evaluate the metric.

Parameters:
Return type:

float

Adjust base metric results based on the number of candidates.

Parameters:
Return type:

float

Returns:

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:
Return type:

float

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. :methtorch.nn.Module.extra_repr.

Return type:

str

Returns:

the extra part of the repr()

abstract get_coefficients(num_candidates, weights=None)[source]

Compute the scaling coefficients.

Parameters:
Return type:

AffineTransformationParameters

Returns:

a tuple (scale, offset)

classmethod get_description()

Get the description.

Return type:

str

Get the link from the docdata.

Return type:

str

classmethod get_range()

Get the math notation for the range of this metric.

Return type:

str

get_sampled_values(num_candidates, num_samples, weights=None, generator=None, memory_intense=True)

Calculate the metric on sampled rank arrays.

Parameters:
Return type:

ndarray

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:

float

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:

ndarray

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:

float

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:

ndarray

std(num_candidates, num_samples=None, weights=None, **kwargs)

Compute the standard deviation.

Parameters:
Return type:

float

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:
Return type:

float

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().