基于多维度输入的多品类果汁采购量预测：问题类型判定与适用机器学习算法咨询

Hey there, let's break this down clearly for you:

First off, this is definitely a regression problem, not a classification problem. Here's why:

• Classification tasks predict discrete, categorical labels (like "will buy orange juice" or "won't"), but your goal is to predict continuous numerical values (the exact number of bottles for each juice flavor).
• Since we're forecasting specific quantities (non-negative integers, treated as continuous for modeling), regression is the right fit.

Your task has two critical constraints:

1. Sum of the three predicted quantities must equal the given total purchase volume
2. Each predicted quantity must be non-negative

Here are the best approaches to handle this, ordered by practicality:

Option 1: Predict Proportions (Most Elegant) #

Instead of predicting raw quantities directly, predict the proportion of total volume each flavor should take. Then multiply each proportion by the total purchase volume to get the final quantity. This naturally handles the "sum to total" constraint, and we just need to ensure proportions are non-negative and sum to 1.

• Dirichlet Regression: This is tailor-made for this scenario. It models compositional data (multiple non-negative variables that sum to 1). The model outputs three proportions that inherently satisfy the sum-to-1 and non-negative constraints. You can implement this using libraries like statsmodels or custom extensions in scikit-learn.
• Adapted Softmax Regression: Treat flavor proportions as a pseudo-probability distribution. The softmax activation ensures outputs sum to 1 and are non-negative. Train the model to minimize the MSE between predicted quantities (proportion × total) and actual quantities in your historical data.

Option 2: Direct Quantity Prediction (With Constraint Enforcement) #

If you prefer predicting quantities directly, you'll need to add logic to enforce constraints:

• Constrained Linear/Ridge/Lasso Regression: Use a multi-output regression model to predict the three quantities. After getting raw predictions:
  1. Clip any negative values to 0
  2. Rescale the three values so their sum equals the total purchase volume (e.g., if predicted sum is 45 but total is 50, multiply each value by 50/45)
     Note: This post-hoc correction works but can introduce minor bias, so it's less ideal than the proportion approach.
• Neural Network with Custom Loss Function: Build a simple feedforward network with three output nodes. Define a loss function that:
  1. Penalizes negative predictions (e.g., add a large penalty term for any prediction < 0)
  2. Penalizes deviations from the total sum (e.g., add MSE between predicted sum and actual total)
  3. Uses standard regression loss (like MSE) between predicted and actual quantities
     This way, the model learns to respect constraints during training, rather than fixing predictions after the fact.

Don't forget to preprocess your input features first:

• Categorical features (season, weather, group type) need encoding (one-hot encoding is a safe, straightforward choice)
• Numerical features (temperature) should be normalized/standardized to help models converge faster

内容的提问来源于stack exchange，提问作者Stephen Chey