关于scikit-learn LogisticRegressionCV最优系数计算逻辑的问询

Great question—let’s break this down clearly, since it’s a common point of confusion!

First, let’s walk through the two core steps when refit=True is enabled:

1. Identifying the optimal regularization parameter C #

• During cross-validation, every candidate C value is tested across all folds. For each C, we calculate the model’s performance score (like accuracy or ROC-AUC) on each fold’s validation set, then take the average score across all folds.
• The C with the highest average score becomes our optimal C. If multiple C values tie for the top average score, the smallest C is usually selected (since it applies stronger regularization, resulting in a simpler, more generalizable model).

2. Computing the final optimal coefficients #

Here’s where your initial assumption differs from the actual implementation:

You thought we’d take coefficients from the single fold (using the optimal C) that had the highest individual score. That’s not how refit=True works!

Instead, once the optimal C is locked in, we train a brand-new logistic regression model using your entire training dataset (all folds combined) with this optimal C value. The coefficients from this full-dataset model are the "optimal coefficients" that get returned.

Why this approach makes sense #

Using the complete training dataset maximizes the amount of information the model can learn, leading to more reliable and generalizable results. A single fold’s training subset is smaller, so its coefficients might be noisier or less representative of the overall data pattern. Cross-validation’s job is to pick the best hyperparameter (C), and refit=True leverages that hyperparameter to build the strongest possible model with all available training data.

For example, if you’re using 5-fold CV with candidate C values [0.01, 0.1, 1, 10]:

• We first evaluate each C across all 5 folds, compute average scores, and pick the top C (say, C=1).
• Then we take all your training data (not just one fold’s split) and train a logistic regression model with C=1. The coefficients from this model are your final optimal coefficients.

内容的提问来源于stack exchange，提问作者mella