Logistic regression is a widely used algorithm but can face convergence issues due to various factors. Proven strategies to improve convergence include:

• Feature Scaling: Standardize or normalize features to ensure consistent scales, which helps optimization algorithms converge faster.
• Learning Rate Adjustment: Use adaptive optimizers like Adam or RMSProp, and apply learning rate schedules or early stopping to prevent overshooting or slow progress.
• Regularization Tuning: Avoid overly strong L1/L2 penalties; use cross-validation to find the best regularization strength or elastic net regularization to balance model complexity.
• Multicollinearity: Reduce highly correlated features via PCA or feature selection methods to stabilize coefficient estimates.
• Class Imbalance: Use techniques like SMOTE, undersampling, or class weighting to help the model converge to better solutions.
• Outlier Treatment: Detect and transform or remove outliers to prevent gradient distortion.
• Solver-Specific Tweaks: Choose appropriate solvers (e.g., liblinear, saga), adjust tolerance and max iterations, or try stochastic solvers for large datasets.
• Advanced Feature Engineering: Apply domain-driven transformations or create interaction terms to improve model fit and convergence.

Saisuman Singamsetty

When addressing logistic regression convergence problems, several practical methods have been found effective. These solutions span solver parameter tweaks, advanced preprocessing steps, and domain-driven feature engineering strategies that can significantly improve model convergence and performance.

Common Causes and Solutions for Convergence Problems

• Data Separation Issues: Complete or quasi-complete separation in the data, where predictor variables perfectly predict the outcome, can cause the maximum likelihood estimates not to exist, leading to convergence failure. Methods such as exact logistic regression or Firth’s bias-reduced logistic regression help overcome these issues by providing penalized likelihood estimation that stabilizes coefficient estimates and ensures convergence.
• Poor Initialization and Complex Models: Using improved or alternative starting values for model parameters can help the optimization algorithm converge more reliably.
• Solver Choice and Regularization: The choice of solver and regularization parameters is crucial. For instance: The 'lbfgs' solver is effective for medium to large dense datasets. The 'liblinear' solver works well with small datasets and sparse data but is less efficient for larger datasets. The 'saga' solver supports elastic net and is suited for large-scale data.
• Adjusting regularization strength (C) and penalty type (L1, L2, or elastic net) helps control model complexity and can mitigate convergence issues.
• Increasing the maximum number of iterations (max_iter) and decreasing the optimization tolerance can allow more time for the solver to converge effectively.

Advanced Preprocessing Strategies

• Feature Scaling: Logistic regression is sensitive to feature magnitude, so applying standardization (e.g., StandardScaler) in a pipeline speeds convergence.
• Dimensionality Reduction: Applying techniques like Principal Component Analysis (PCA) can reduce multicollinearity and noise, improving stability and convergence.
• Handling Imbalanced Data: Using class weights or resampling techniques improves model training stability on skewed datasets.

Domain-Driven Feature Engineering

• Creating polynomial features and interaction terms can capture complex, nonlinear relationships that a standard logistic model might miss. This not only improves accuracy but can lead to better convergence by providing more informative predictors.
• For categorical variables, techniques beyond simple one-hot encoding like target encoding or feature hashing are useful, especially with high-cardinality variables.
• Incorporating domain knowledge to craft or select features relevant to the problem context frequently improves model behavior and convergence.

Less Common, Solver-Specific and Experimental Tweaks

• Using penalty-specific solvers tailored to the regularization type (e.g., saga for elastic net).
• Employing exact logistic regression or median unbiased estimators for separated data problems.
• Refining starting values using simpler models or heuristic adjustments before fitting the full model.
• Exploring software-specific options like alternative integration methods (Gauss-Hermite quadrature, Laplacian approximations) in mixed models as convergence aids.

Summary

To fine-tune logistic regression for better convergence, practitioners should:

These approaches, backed by research and practical experiments, represent a toolkit for improving logistic regression convergence while maximizing predictive performance in varied application domains.

Yes, one can tweak the algorithms many ways but I would first consider taking a bayesian approach to integrate domain knowledge. This is especially useful in the case of multicollinearity or imbalance, and should provide more meaningful results.