MinCost

class empulse.metrics.MinCost(integration_method='auto', n_mc_samples_exp=16, random_state=None, alpha=1.0)

Strategy for the Minimum Cost metric.

The cost phrasing of MaxProfit: it locates the same optimal threshold and reports the value there negated, as a cost to minimize rather than a profit to maximize. Which of the two you use is a presentation choice – models train identically on either, because they optimize _loss, which removes the sign difference.

See also

MaxProfit : The profit phrasing of the same metric.

Parameters:

integration_method{‘auto’, ‘quad’, ‘monte-carlo’, ‘quasi-monte-carlo’}, default=’auto’

The integration method to use when the metric has stochastic variables. See MaxProfit for the meaning of each value.

n_mc_samples_expint, default=16

2**n_mc_samples_exp is the number of (Quasi-) Monte Carlo samples to use. See MaxProfit.

random_stateint, np.random.Generator or None, default=None

The random state used by the Monte Carlo integration methods. See MaxProfit.

alphafloat, default=1.0

Temperature of the smooth sigmoid approximation used by the gradient objectives. See MaxProfit.

build(tp_benefit, tn_benefit, fp_cost, fn_cost)

Build the metric strategy.

property capabilities

The set of Capability members this strategy supports.

LOGIT_OBJECTIVE and BOOST_OBJECTIVE are only present once build has run and picked a deterministic or BasePositiveDistribution stochastic score function – the same condition logit_objective and gradient_boost_objective check before raising NotImplementedError. Before build, or for any other stochastic distribution, neither is present.

gradient_boost_objective(y_true, y_score, **parameters)

Compute gradient and hessian for boosting with MaxProfit.

Automatically handles deterministic and stochastic piecewise integrals.

logit_objective(features, y_true, C, l1_ratio, fit_intercept, **parameters)

Build the prepared logit-gradient objective for the current metric configuration.

Uses the Envelope Theorem combined with a smooth sigmoid approximation of the ROC curve to derive an analytically differentiable proxy for the Expected Maximum Profit.

Only supported for deterministic metrics or metrics with one stochastic variable following a distribution with positive support.

Parameters:

featuresNDArray of shape (n_samples, n_features)

The features of the samples.

y_trueNDArray of shape (n_samples,)

The ground truth labels.

Cfloat

Regularization strength parameter. Smaller values specify stronger regularization.

l1_ratiofloat

The Elastic-Net mixing parameter, with range 0 <= l1_ratio <= 1. l1_ratio=0 corresponds to L2 penalty, l1_ratio=1 to L1 penalty.

fit_interceptbool

Specifies if an intercept should be included in the model.

**parametersfloat or NDArray of shape (n_samples,)

The parameter values for the costs and benefits defined in the metric. If any parameter is a stochastic variable, you should pass values for their distribution parameters. You can set the parameter values for either the symbol names or their aliases.

• If float, the value is used as-is (class-dependent).

• If array-like, the mean of the values is used: this strategy does not take instance-dependent costs/benefits into account (see the class docstring), so passing an array gives the same result as passing that array’s mean directly.

Returns:

logistic_objectiveCallable[[NDArray], tuple[float, NDArray]]

A function that takes logistic regression weights as input and returns the negated metric value and its gradient (negated for minimization). The function signature is: logistic_objective(weights) -> (value, gradient).

Raises:

NotImplementedError

If the metric is neither purely deterministic nor a BasePositiveDistribution stochastic variant.

optimal_rate(y_true, y_score, **parameters)

Compute the predicted positive rate to optimize the metric value.

Parameters:

y_truearray-like of shape (n_samples,)

The ground truth labels.

y_scorearray-like of shape (n_samples,)

The predicted labels, probabilities, or decision scores (based on the chosen metric).

**parametersfloat or array-like of shape (n_samples,)

The parameter values for the costs and benefits defined in the metric. If any parameter is a stochastic variable, you should pass values for their distribution parameters. You can set the parameter values for either the symbol names or their aliases.

• If float, the value is used as-is (class-dependent).

• If array-like, the mean of the values is used: this strategy does not take instance-dependent costs/benefits into account (see the class docstring), so passing an array gives the same result as passing that array’s mean directly.

Returns:

optimal_ratefloat

The optimal predicted positive rate.

optimal_threshold(y_true, y_score, **parameters)

Compute the classification threshold(s) to optimize the metric value.

i.e., the score threshold at which an observation should be classified as positive to optimize the metric. For instance-dependent costs and benefits, this will return an array of thresholds, one for each sample. For class-dependent costs and benefits, this will return a single threshold value.

Parameters:

y_truearray-like of shape (n_samples,)

The ground truth labels.

y_scorearray-like of shape (n_samples,)

The predicted labels, probabilities, or decision scores (based on the chosen metric).

**parametersfloat or array-like of shape (n_samples,)

The parameter values for the costs and benefits defined in the metric. If any parameter is a stochastic variable, you should pass values for their distribution parameters. You can set the parameter values for either the symbol names or their aliases.

• If float, the value is used as-is (class-dependent).

• If array-like, the mean of the values is used: this strategy does not take instance-dependent costs/benefits into account (see the class docstring), so passing an array gives the same result as passing that array’s mean directly.

Returns:

optimal_thresholdfloat | FloatNDArray

The optimal classification threshold(s).

prepare_boost_objective(y_true, **parameters)

Compute the gradient’s constant term of the metric wrt gradient boost.

Parameters:

y_trueNDArray of shape (n_samples,)

The ground truth labels.

**parametersfloat or NDArray of shape (n_samples,)

The parameter values for the costs and benefits defined in the metric. If any parameter is a stochastic variable, you should pass values for their distribution parameters. You can set the parameter values for either the symbol names or their aliases.

• If float, the same value is used for all samples (class-dependent).

• If array-like, the values are used for each sample (instance-dependent).

Returns:

gradient_constNDArray of shape (n_samples, n_features)

The constant term of the gradient.

property requires_dynamic_boost_objective

Whether gradients must be recomputed from the metric each boosting round.

Deprecated since version Use: Capability.PRECOMPUTED_BOOST_OBJECTIVE not in strategy.capabilities instead.

True for strategies whose per-sample loss is not linear in the predicted probability (e.g. LogCost) or that need the current round’s scores to locate a threshold (e.g. MaxProfit); such strategies cannot use the precomputed constant returned by prepare_boost_objective.

score(y_true, y_score, **parameters)

Compute the minimum cost score.

Parameters:

y_truearray-like of shape (n_samples,)

The ground truth labels.

y_scorearray-like of shape (n_samples,)

The predicted labels, probabilities, or decision scores (based on the chosen metric).

**parametersfloat or array-like of shape (n_samples,)

The parameter values for the costs and benefits defined in the metric. If any parameter is a stochastic variable, you should pass values for their distribution parameters. You can set the parameter values for either the symbol names or their aliases.

• If float, the value is used as-is (class-dependent).

• If array-like, the mean of the values is used: like MaxProfit, this strategy does not take instance-dependent costs/benefits into account, so passing an array gives the same result as passing that array’s mean directly.

Returns:

scorefloat

The minimum cost score.

to_latex(tp_benefit, tn_benefit, fp_cost, fn_cost)

Return the LaTeX representation of the metric.