Implementation:Scikit learn Scikit learn LinkFunctions

Knowledge Sources	Scikit_learn Scikit-learn Docs
Domains	Machine Learning, Statistical Modeling
Last Updated	2026-02-08 15:00 GMT

Overview

Concrete tool for defining invertible and differentiable link functions used in generalized linear models, provided by scikit-learn.

Description

This module contains classes for invertible (and differentiable) link functions. It defines an abstract base class BaseLink along with concrete implementations such as IdentityLink, LogLink, LogitLink, and MultinomialLogit. It also includes the Interval dataclass for validating value ranges and a helper function _inclusive_low_high for testing purposes.

Usage

Use link functions when working with generalized linear models (GLMs) to transform between the linear predictor space and the predicted mean space. These are primarily used internally by scikit-learn's loss functions and GLM estimators.

Code Reference

Source Location

• Repository: scikit-learn
• File: sklearn/_loss/link.py

Signature

@dataclass
class Interval:
    low: float
    high: float
    low_inclusive: bool
    high_inclusive: bool

class BaseLink(ABC):
    is_multiclass = False
    interval_y_pred = Interval(-np.inf, np.inf, False, False)

Import

from sklearn._loss.link import BaseLink, Interval

I/O Contract

Inputs

Name	Type	Required	Description
raw_prediction	ndarray	Yes	Raw prediction values (linear predictor) to be transformed via inverse link
y_pred	ndarray	Yes	Predicted values to be transformed via the link function

Outputs

Name	Type	Description
raw_prediction	ndarray	Result of applying the link function g(y_pred)
y_pred	ndarray	Result of applying the inverse link h(raw_prediction)

Usage Examples

Basic Usage

import numpy as np
from sklearn._loss.link import LogitLink

link = LogitLink()
y_pred = np.array([0.2, 0.5, 0.8])
raw = link.link(y_pred)
y_back = link.inverse(raw)
print(y_back)  # array([0.2, 0.5, 0.8])

Related Pages

• Principle:Scikit_learn_Scikit_learn_Generalized_Linear_Models