Caffe CNN多变量回归：输出值范围差异大的技术问题咨询

Hey there, let's tackle your three questions about regression with Caffe CNN, based on practical experience with such tasks:

Q1: Will predicting raw y values interfere with model learning? Why? #

Absolutely, this can definitely interfere with your model's performance—even if your initial experiment showed "acceptable but not great" results. Here's the breakdown:

• Scale imbalance dominates loss: Euclidean loss (L2) penalizes errors proportionally to the square of the difference. For your targets, a 1-unit error in yₙ (0-15) contributes 1 to the loss, while a 0.1-unit error in y₁ (0.1-0.2) contributes only 0.01. The model will naturally prioritize minimizing errors for large-scale targets, ignoring smaller ones, leading to uneven prediction accuracy across your y variables.
• Gradient update bias: Gradients calculated from large-scale targets are much larger than those from small-scale ones. This means parameter updates are driven primarily by the large y values, while the small y's gradient signals get drowned out, making training unstable for the smaller targets.

Q2: Can we normalize y to [0,1] by setting sum(yₛ)=1? #

It depends entirely on the meaning of your target variables:

• If your y₁, y₂,...yₙ represent proportional quantities (e.g., percentage contributions of different components, or multi-dimensional probability distributions), this normalization makes sense—it aligns with how models like Softmax output valid distributions.
• However, if your targets are independent regression values (each yₛ represents a separate, unrelated quantity), this approach will break their original numerical relationships. For example, y₂ (originally 1-5) would be compressed to a tiny range once summed to 1 with yₙ (0-15), making it nearly impossible for the model to learn meaningful patterns for y₂.

A better alternative for independent targets is to normalize each yₛ individually:

• Use min-max scaling per variable: y_scaled = (y - min(y)) / (max(y) - min(y)) to map each to [0,1].
• Or standardize to zero mean and unit variance: y_standardized = (y - mean(y)) / std(y).
  This way, all targets are on a comparable scale, so the model can learn each one fairly.

Q3: Can we use losses like Softmax or Logistic instead of Euclidean loss? #

Let's break down each option and other alternatives:

• Softmax loss: This is designed for multi-class classification, where outputs represent class probabilities that sum to 1. It's not a standard regression loss unless your task inherently requires outputs to form a valid probability distribution (e.g., predicting proportional contributions). Forcing it on independent regression targets will artificially constrain outputs to sum to 1, hurting performance.
• Logistic loss (binary cross-entropy): This works for outputs in the [0,1] range, typically for binary classification or regression tasks where targets are probabilities. If you first normalize each yₛ to [0,1], you can use Logistic loss—it's more robust to outliers than Euclidean loss in some cases. But note it's only suitable if your normalized targets make sense as "probability-like" values.

Beyond these, consider other regression losses tailored to your scale-imbalanced targets:

• L1 loss: Less sensitive to outliers than L2, as it penalizes absolute error instead of squared error.
• Huber loss: Combines the best of L1 and L2—uses squared error for small errors, absolute error for large ones, balancing robustness and smoothness.
• Weighted Euclidean loss: Assign higher weights to small-scale targets (e.g., weight y₁ by 100, yₙ by 1) so their errors contribute equally to the total loss, forcing the model to pay attention to all targets.

内容的提问来源于stack exchange，提问作者Nima