Package 'mlr3inferr'

Description

Confidence interval and resampling methods for inference on the generalization error.

Author(s)

Maintainer: Sebastian Fischer [email protected] (ORCID)

Authors:

• Hannah Schulz-Kümpel [email protected] (ORCID)

See Also

Useful links:

• https://mlr3inferr.mlr-org.com

• https://github.com/mlr-org/mlr3inferr

• Report bugs at https://github.com/mlr-org/mlr3inferr/issues

Description

Base class for confidence interval measures. See section Inheriting on how to add a new method.

Details

The aggregator of the wrapped measure is ignored, as the inheriting CI dictates how the point estimate is constructed. If a measure for which to calculate a CI has ⁠$obs_loss⁠ but also a ⁠$trafo⁠, (such as RMSE), the delta method is used to obtain confidence intervals.

Parameters

• alpha :: numeric(1)
  The desired alpha level. This is initialized to $0.05$.

• within_range :: logical(1)
  Whether to restrict the confidence interval within the range of possible values. This is initialized to TRUE.

Inheriting

To define a new CI method, inherit from the abstract base class and implement the private method: ⁠ci: function(tbl: data.table, rr: ResampleResult, param_vals: named ⁠list()⁠) -> numeric(3)⁠ If requires_obs_loss is set to TRUE, tbl contains the columns loss, row_id and iteration, which are the pointwise loss, Otherwise, tbl contains the result of rr$score() with the name of the loss column set to "loss". the identifier of the observation and the resampling iteration. It should return a vector containing the estimate, lower and upper boundary in that order.

In case the confidence interval is not of the form ⁠(estimate, estimate - z * se, estimate + z * se)⁠ it is also necessary to implement the private method: ⁠.trafo: function(ci: numeric(3), measure: Measure) -> numeric(3)⁠ Which receives a confidence interval for a pointwise loss (e.g. squared-error) and transforms it according to the transformation measure$trafo (e.g. sqrt to go from mse to rmse).

Super class

mlr3::Measure -> MeasureAbstractCi

Public fields

Methods

Public methods

• MeasureAbstractCi$new()

• MeasureAbstractCi$aggregate()

• MeasureAbstractCi$clone()

Method new()

Creates a new instance of this R6 class.

Usage

MeasureAbstractCi$new(
  measure = NULL,
  param_set = ps(),
  packages = character(),
  resamplings,
  label,
  delta_method = FALSE,
  requires_obs_loss = TRUE,
  man = NA
)

Arguments

Method aggregate()

Obtain a point estimate, as well as lower and upper CI boundary.

Usage

MeasureAbstractCi$aggregate(rr)

Arguments

Returns

named numeric(3)

Method clone()

The objects of this class are cloneable with this method.

Usage

MeasureAbstractCi$clone(deep = FALSE)

Arguments

Description

For certain resampling methods, there are default confidence interval methods. See mlr3::mlr_reflections$default_ci_methods for a selection. This measure will select the appropriate CI method depending on the class of the used Resampling.

Parameters

Only those from MeasureAbstractCi.

Super classes

mlr3::Measure -> mlr3inferr::MeasureAbstractCi -> Measure

Methods

Public methods

• MeasureCi$new()

• MeasureCi$aggregate()

• MeasureCi$clone()

Method new()

Creates a new instance of this R6 class.

Usage

MeasureCi$new(measure)

Arguments

Method aggregate()

Obtain a point estimate, as well as lower and upper CI boundary.

Usage

MeasureCi$aggregate(rr)

Arguments

Returns

named numeric(3)

Method clone()

The objects of this class are cloneable with this method.

Usage

MeasureCi$clone(deep = FALSE)

Arguments

Examples

rr = resample(tsk("sonar"), lrn("classif.featureless"), rsmp("holdout"))
rr$aggregate(msr("ci", "classif.acc"))
# is the same as:
rr$aggregate(msr("ci.holdout", "classif.acc"))

Description

The conservative-z confidence intervals based on the ResamplingPairedSubsampling. Because the variance estimate is obtained using only n / 2 observations, it tends to be conservative. This inference method can also be applied to non-decomposable losses.

Point Estimation

For the point estimation, only the first repeats_out resampling iterations will be used, as the other resampling iterations are only used to estimate the variance. This is respected when calling ⁠$aggregate()⁠ using a standard (non-CI) measure.

Parameters

Only those from MeasureAbstractCi.

Super classes

mlr3::Measure -> mlr3inferr::MeasureAbstractCi -> MeasureCiConZ

Methods

Public methods

• MeasureCiConZ$new()

• MeasureCiConZ$clone()

Method new()

Creates a new instance of this R6 class.

Usage

MeasureCiConZ$new(measure)

Arguments

Method clone()

The objects of this class are cloneable with this method.

Usage

MeasureCiConZ$clone(deep = FALSE)

Arguments

References

Nadeau, Claude, Bengio, Yoshua (1999). “Inference for the generalization error.” Advances in neural information processing systems, 12.

Examples

ci_conz = msr("ci.con_z", "classif.acc")
ci_conz

Description

Corrected-T confidence intervals based on ResamplingSubsampling. A heuristic factor is applied to correct for the dependence between the iterations. The confidence intervals tend to be liberal. This inference method can also be applied to non-decomposable losses.

Parameters

Only those from MeasureAbstractCi.

Super classes

mlr3::Measure -> mlr3inferr::MeasureAbstractCi -> MeasureCiCorrectedT

Methods

Public methods

• MeasureCiCorrectedT$new()

• MeasureCiCorrectedT$clone()

Method new()

Creates a new instance of this R6 class.

Usage

MeasureCiCorrectedT$new(measure)

Arguments

Method clone()

The objects of this class are cloneable with this method.

Usage

MeasureCiCorrectedT$clone(deep = FALSE)

Arguments

References

Nadeau, Claude, Bengio, Yoshua (1999). “Inference for the generalization error.” Advances in neural information processing systems, 12.

Examples

m_cort = msr("ci.cor_t", "classif.acc")
m_cort
rr = resample(
  tsk("sonar"),
  lrn("classif.featureless"),
  rsmp("subsampling", repeats = 10)
)
rr$aggregate(m_cort)

Description

Standard holdout CI. This inference method can only be applied to decomposable losses.

Parameters

Only those from MeasureAbstractCi.

Super classes

mlr3::Measure -> mlr3inferr::MeasureAbstractCi -> MeasureCiHoldout

Methods

Public methods

• MeasureCiHoldout$new()

• MeasureCiHoldout$clone()

Method new()

Creates a new instance of this R6 class.

Usage

MeasureCiHoldout$new(measure)

Arguments

Method clone()

The objects of this class are cloneable with this method.

Usage

MeasureCiHoldout$clone(deep = FALSE)

Arguments

Examples

ci_ho = msr("ci.holdout", "classif.acc")
ci_ho
rr = resample(tsk("sonar"), lrn("classif.featureless"), rsmp("holdout"))
rr$aggregate(ci_ho)

Description

Confidence Intervals based on ResamplingNestedCV, including bias-correction. This inference method can only be applied to decomposable losses.

Point Estimation

The point estimate uses a bias correction term as described in Bates et al. (2024). Therefore, the results of directly applying a measure ⁠$aggregate(msr(<key>))⁠ will be different from the point estimate of ⁠$aggregate(msr("ci", <key>))⁠, where the point estimate is obtained by averaging over the outer CV results.

Parameters

Those from MeasureAbstractCi, as well as:

• bias :: logical(1)
  Whether to do bias correction. This is initialized to TRUE. If FALSE, the outer iterations are used for the point estimate and no bias correction is applied.

Super classes

mlr3::Measure -> mlr3inferr::MeasureAbstractCi -> MeasureCiNestedCV

Methods

Public methods

• MeasureCiNestedCV$new()

• MeasureCiNestedCV$clone()

Method new()

Creates a new instance of this R6 class.

Usage

MeasureCiNestedCV$new(measure)

Arguments

Method clone()

The objects of this class are cloneable with this method.

Usage

MeasureCiNestedCV$clone(deep = FALSE)

Arguments

References

Bates, Stephen, Hastie, Trevor, Tibshirani, Robert (2024). “Cross-validation: what does it estimate and how well does it do it?” Journal of the American Statistical Association, 119(546), 1434–1445.

Examples

ci_ncv = msr("ci.ncv", "classif.acc")
ci_ncv

Description

Confidence intervals for cross-validation. The method is asymptotically exact for the so called Test Error as defined by Bayle et al. (2020). For the (expected) risk, the confidence intervals tend to be too liberal. This inference method can only be applied to decomposable losses.

Parameters

Those from MeasureAbstractCi, as well as:

• variance :: "all-pairs" or "within-fold"
  How to estimate the variance. The results tend to be very similar.

Super classes

mlr3::Measure -> mlr3inferr::MeasureAbstractCi -> MeasureCiWaldCV

Methods

Public methods

• MeasureCiWaldCV$new()

• MeasureCiWaldCV$clone()

Method new()

Creates a new instance of this R6 class.

Usage

MeasureCiWaldCV$new(measure)

Arguments

Method clone()

The objects of this class are cloneable with this method.

Usage

MeasureCiWaldCV$clone(deep = FALSE)

Arguments

References

Bayle, Pierre, Bayle, Alexandre, Janson, Lucas, Mackey, Lester (2020). “Cross-validation confidence intervals for test error.” Advances in Neural Information Processing Systems, 33, 16339–16350.

Examples

m_waldcv = msr("ci.wald_cv", "classif.ce")
m_waldcv
rr = resample(tsk("sonar"), lrn("classif.featureless"), rsmp("cv"))
rr$aggregate(m_waldcv)

Description

This implements the Nested CV resampling procedure by Bates et al. (2024).

Point Estimation

When calling ⁠$aggregate()⁠ on a resample result obtained using this resampling method, only the outer resampling iterations will be used, as they have a smaller bias. See section "Point Estimation" of MeasureCiNestedCV.

Parameters

• folds :: integer(1)
  The number of folds. This is initialized to 5.

• repeats :: integer(1)
  The number of repetitions. THis is initialized to 10.

Super class

mlr3::Resampling -> ResamplingNestedCV

Active bindings

Methods

Public methods

• ResamplingNestedCV$new()

• ResamplingNestedCV$unflatten()

• ResamplingNestedCV$clone()

Method new()

Creates a new instance of this R6 class.

Usage

ResamplingNestedCV$new()

Method unflatten()

Convert a resampling iteration to a more useful representation. For outer resampling iterations, inner is NA.

Usage

ResamplingNestedCV$unflatten(iter)

Arguments

Returns

list(rep, outer, inner)

Method clone()

The objects of this class are cloneable with this method.

Usage

ResamplingNestedCV$clone(deep = FALSE)

Arguments

References

Bates, Stephen, Hastie, Trevor, Tibshirani, Robert (2024). “Cross-validation: what does it estimate and how well does it do it?” Journal of the American Statistical Association, 119(546), 1434–1445.

Examples

ncv = rsmp("ncv", folds = 3, repeats = 10L)
ncv
rr = resample(tsk("mtcars"), lrn("regr.featureless"), ncv)

Description

Paired Subsampling to enable inference on the generalization error.

Details

The first repeats_in iterations are a standard ResamplingSubsampling and should be used to obtain a point estimate of the generalization error. The remaining iterations should be used to estimate the standard error. Here, the data is divided repeats_out times into two equally sized disjunct subsets, to each of which subsampling which, a subsampling with repeats_in repetitions is applied. See the ⁠$unflatten(iter)⁠ method to map the iterations to this nested structure.

Point Estimation

When calling ⁠$aggregate()⁠ on a resample result obtained using this resampling method, only the first repeats_out iterations will be used. See section "Point Estimation" of MeasureCiConZ.

Parameters

• repeats_in :: integer(1)
  The inner repetitions.

• repeats_out :: integer(1)
  The outer repetitions.

• ratio :: numeric(1)
  The proportion of data to use for training.

Super class

mlr3::Resampling -> ResamplingPairedSubsampling

Active bindings

Methods

Public methods

• ResamplingPairedSubsampling$new()

• ResamplingPairedSubsampling$unflatten()

• ResamplingPairedSubsampling$clone()

Method new()

Creates a new instance of this R6 class.

Usage

ResamplingPairedSubsampling$new()

Method unflatten()

Unflatten the resampling iteration into a more informative representation:

• inner: The subsampling iteration

• outer: NA for the first repeats_in iterations. Otherwise it indicates the outer iteration of the paired subsamplings.

• partition: NA for the first repeats_in iterations. Otherwise it indicates whether the subsampling is applied to the first or second partition Of the two disjoint halfs.

Usage

ResamplingPairedSubsampling$unflatten(iter)

Arguments

Returns

list(outer, partition, inner)

Method clone()

The objects of this class are cloneable with this method.

Usage

ResamplingPairedSubsampling$clone(deep = FALSE)

Arguments

References

Nadeau, Claude, Bengio, Yoshua (1999). “Inference for the generalization error.” Advances in neural information processing systems, 12.

Examples

pw_subs = rsmp("paired_subsampling")
pw_subs