fisher-scoring 2.0.4

A Python implementation of the Fisher Scoring algorithm for classification and incidence rate tasks.

Fisher Scoring with Python

Author: xRiskLab
Version: v2.0.4
License: MIT License (2025)

This repository contains optimized Python implementations of the Fisher Scoring algorithm for various logistic regression models. With version 2.0, the core algorithms are now significantly faster due to optimized matrix operations and reduced memory usage, providing faster convergence for larger datasets.

%pip install fisher-scoring
from fisher_scoring import LogisticRegression

# Initialize and fit model
model = LogisticRegression()
model.fit(X_train, y_train)

# Make predictions
predictions = model.predict(X_test)
probabilities = model.predict_proba(X_test)

Overview

Introduction

This repository contains a Python package with scikit-learn compatible implementations of the Fisher Scoring algorithm for various modeling problems.

The packages provides implementations of logistic regression (MLE for binary, multiclass, and binary imbalanced) for proportions (risk or prevalence) and Poisson and Negative Binomial regression for log-linear regression for incidence rates.

1. Binary classification problems: Logistic Regression.
2. Multi-class classification problems: Multinomial Logistic Regression.
3. Imbalanced classification problems: Focal Loss Logistic Regression.
4. Count modeling problems: Poisson Regression and Negative Binomial Regression.

Fisher Scoring Algorithm

The Fisher Scoring algorithm is an iterative optimization technique that estimates maximum likelihood estimates by leveraging the expected or observed Fisher information matrix. This second-order optimization method allows to avoid the use of learning rates and provides more stable convergence compared to gradient descent.

There are two types of information matrices used in the Fisher Scoring algorithm:

• Expected Information Matrix: Relies on predicted probabilities, providing an efficient approximation for the information matrix.
• Empirical Information Matrix: Uses ground truth labels to calculate the information matrix, often resulting in more reliable inference metrics.

These information matrices are used to derive standard errors of estimates to calculate detailed model statistics, including Wald statistics, p-values, and confidence intervals at a chosen level.

Source: Limitations of the Empirical Fisher Approximation for Natural Gradient Descent.

Implementation Notes

• Multinomial Logistic Regression
  The MultinomialLogisticRegression model differs from standard statistical multinomial logistic regression by using all classes rather than $K - 1$. This approach allows multi-class classification problems to be converted to binary problems by calculating $1 - P_{Class=1}$.

• Focal Loss Regression
  The FocalLossRegression class employs a non-standard focal log-likelihood function in its optimization process leveraging $\gamma$ to focus on difficult-to-classify examples. The focal loss function, originally developed for object detection, prioritizes difficult-to-classify examples—often the minority class—by reducing the contribution of easy-to-classify samples. It introduces a focusing parameter, gamma, which down-weights the influence of easily classified instances, thereby concentrating learning on challenging cases.

  Source: Focal Loss for Dense Object Detection.

Models

Logistic Regression

The LogisticRegression class is a custom implementation of logistic regression using the Fisher scoring algorithm. It provides methods for fitting the model, making predictions, and computing model statistics, including standard errors, Wald statistics, p-values, and confidence intervals.

Parameters:

• epsilon: Convergence threshold for the algorithm.
• max_iter: Maximum number of iterations for the algorithm.
• information: Type of information matrix to use ('expected' or 'empirical').
• use_bias: Include a bias term in the model.
• significance: Significance level for computing confidence intervals.

Methods:

• fit(X, y): Fit the model to the data.
• predict(X): Predict target labels for input data.
• predict_proba(X): Predict class probabilities for input data.
• predict_ci(X): Predict class probabilities with confidence intervals.
• get_params(): Get model parameters.
• set_params(**params): Set model parameters.
• summary(): Get a summary of model parameters, standard errors, p-values, and confidence intervals.
• display_summary(): Display a summary of model parameters, standard errors, p-values, and confidence intervals.

Multinomial Logistic Regression

The MultinomialLogisticRegression class implements the Fisher Scoring algorithm for multinomial logistic regression, suitable for multi-class classification tasks.

Parameters:

• epsilon: Convergence threshold for the algorithm.
• max_iter: Maximum number of iterations for the algorithm.
• information: Type of information matrix to use ('expected' or 'empirical').
• use_bias: Include a bias term in the model.
• significance: Significance level for computing confidence intervals.
• verbose: Enable verbose output.

Methods:

• fit(X, y): Fit the model to the data.
• predict(X): Predict target labels for input data.
• predict_proba(X): Predict class probabilities for input data.
• predict_ci(X): Predict class probabilities with confidence intervals.
• summary(class_idx): Get a summary of model parameters, standard errors, p-values, and confidence intervals for a specific class.
• display_summary(class_idx): Display a summary of model parameters, standard errors, p-values, and confidence intervals for a specific class.

The algorithm is in a beta version and may require further testing and optimization to speed up matrix operations.

Focal Loss Regression

The FocalLossRegression class implements the Fisher Scoring algorithm with focal loss, designed for imbalanced classification problems where the positive class is rare.

Parameters:

• gamma: Focusing parameter for focal loss.
• epsilon: Convergence threshold for the algorithm.
• max_iter: Maximum number of iterations for the algorithm.
• information: Type of information matrix to use ('expected' or 'empirical').
• use_bias: Include a bias term in the model.
• verbose: Enable verbose output.

Methods:

• fit(X, y): Fit the model to the data.
• predict(X): Predict target labels for input data.
• predict_proba(X): Predict class probabilities for input data.
• predict_ci(X): Predict class probabilities with confidence intervals.
• get_params(): Get model parameters.
• set_params(**params): Set model parameters.
• summary(): Get a summary of model parameters, standard errors, p-values, and confidence intervals.
• display_summary(): Display a summary of model parameters, standard errors, p-values, and confidence intervals.

Poisson Regression

The PoissonRegression class implements the Fisher Scoring algorithm for Poisson regression, suitable for modeling count data.

Parameters:

• max_iter: Maximum number of iterations for optimization.
• epsilon: Convergence tolerance.
• use_bias: Whether to include an intercept term.

Methods:

• fit(X, y): Fit the model to the data.
• predict(X): Predict mean values for the Poisson model.
• calculate_st_errors(X): Calculate standard errors for the coefficients.

Negative Binomial Regression

The NegativeBinomialRegression class implements the Fisher Scoring algorithm for Negative Binomial regression, suitable for overdispersed count data.

Parameters:

• max_iter: Maximum number of iterations for optimization.
• epsilon: Convergence tolerance.
• use_bias: Whether to include an intercept term.
• alpha: Fixed dispersion parameter (overdispersion adjustment for Negative Binomial).
• phi: Constant scale parameter.
• offset: Offset term for the linear predictor.

Methods:

• fit(X, y): Fit the model to the data.
• predict(X): Predict mean values for the Negative Binomial model.
• calculate_st_errors(X): Calculate standard errors for the coefficients.

Utilities

Visualization

The package includes a utility function for visualizing observed vs predicted probabilities for count data, which can be useful for users working with Poisson and Negative Binomial models.

Function:

• plot_observed_vs_predicted(y, mu, max_count=15, alpha=None, title="Observed vs Predicted Probabilities", model_name="Model", ax=None, plot_params=None): Plot observed vs predicted probabilities for count data.

Parameters:

• y: Observed count data.
• mu: Predicted mean values from the model.
• max_count: Maximum count to consider for probabilities.
• alpha: Overdispersion parameter for Negative Binomial. If None, assumes Poisson (alpha=0).
• title: Title for the plot.
• model_name: Name of the model for labeling.
• ax: Matplotlib axis to plot on.

Change Log

• v2.0.4

  • Added a beta version of Poisson and Negative Binomial regression using Fisher Scoring.
  • Changed naming conventions for simplicity and consistency.
  • Changed poetry to uv for packaging.

• v2.0.3

  • Added a new functionality of inference of mean responses with confidence intervals for all algorithms.
  • Focal logistic regression now supports all model statistics, including standard errors, Wald statistics, p-values, and confidence intervals.

• v2.0.2

  • Bug Fixes: Fixed the MultinomialLogisticRegression class to have flexible NumPy data types.

• v2.0.1

  • Bug Fixes: Removed the debug print statement from the LogisticRegression class.

• v2.0

  • Performance Improvements: Performance Enhancements: Optimized matrix calculations for substantial speed and memory efficiency improvements across all models. Leveraging streamlined operations, this version achieves up to 290x faster convergence. Performance gains per model:
    • Multinomial Logistic Regression: Training time reduced from 125.10s to 0.43s (~290x speedup).
    • Logistic Regression: Training time reduced from 0.24s to 0.05s (~5x speedup).
    • Focal Loss Logistic Regression: Training time reduced from 0.26s to 0.01s (~26x speedup).
  • Bug Fixes: verbose parameter in Focal Loss Logistic Regression now functions as expected, providing accurate logging during training.

• v0.1.4

  • Updated log likelihood for Multinomial Regression and minor changes to Logistic Regression for integration with scikit-learn.

• v0.1.3

  • Added coefficients, standard errors, p-values, and confidence intervals for Multinomial Regression.

• v0.1.2

  • Updated NumPy dependency.

• v0.1.1

  • Added support for Python 3.9+ 🐍.

• v0.1.0

  • Initial release of Fisher Scoring Logistic, Multinomial, and Focal Loss Regression.