机器学习算法输入归一化：训练测试集及目标变量相关疑问

Great questions—these are some of the most frequent pitfalls folks run into when setting up pipelines for neural networks and logistic regression. Let’s unpack each one clearly:

问题1：是否需要对全部预测变量（训练集和测试集数据）进行归一化？ #

Short answer: Yes, but with a critical caveat—you must use the statistics (mean, standard deviation for z-score; min/max values for min-max scaling) calculated only from the training set to normalize both the training and test sets.

Here’s why this matters:

• Your test set is supposed to mimic "unseen" real-world data. If you calculate separate stats for the test set, you’re leaking information about the test distribution into your preprocessing step, which will make your model’s performance look better than it actually is (this is called data leakage).
• Algorithms like neural networks are extremely sensitive to feature scales. For example, if one feature ranges from 0-1000 and another from 0-1, the model will prioritize the larger feature during training simply because its gradients are bigger. Logistic regression, especially when trained with gradient descent, will also converge much faster and more reliably when features are on similar scales.

Practical example for z-score normalization:

1. Compute train_mean = mean(training_features) and train_std = std(training_features)
2. Normalize training set: train_normalized = (training_features - train_mean) / train_std
3. Normalize test set using the same values: test_normalized = (test_features - train_mean) / train_std

Never compute test_mean or test_std to normalize the test set—this is a classic mistake that invalidates your model’s evaluation.

问题2：是否需要对被预测变量y进行归一化？ #

This depends entirely on your task type:

回归任务（预测连续值，比如房价、销售额） #

• Yes, usually a good idea, especially for neural networks. When y has a large range (e.g., 0 to 100,000), the loss function (like MSE) will produce very large gradients during training, which can make the model unstable or slow to converge. Normalizing y (e.g., to 0-1 or -1 to 1) keeps the gradient scales balanced with your normalized features, leading to faster, more stable training.
• Important note: After making predictions with your trained model, you’ll need to reverse the normalization (using the training set’s y stats) to get back the actual, interpretable values.

分类任务（预测离散类别，比如二分类的0/1，多分类的类别标签） #

• No, don’t normalize y. For logistic regression (a binary classification algorithm), y represents class labels (0 or 1)—normalizing these values serves no purpose, since the model outputs probabilities that map directly to these discrete labels. For multi-class tasks, you might use one-hot encoding for y, but that’s a categorical encoding step, not normalization.

内容的提问来源于stack exchange，提问作者Niccola Tartaglia