R语言实现Stagewise regression：与第i个标准基向量相乘维度错误

Hey there! Let's work through your issues with implementing that paper's algorithm in R—first the dimension mismatch with standard basis vectors, then verifying the rest of your code.

Fixing the Standard Basis Vector Dimension Mismatch #

This is almost always an issue with whether you're using row vs. column vectors, or mismatched matrix dimensions. Here's how to address it:

• Ensure the basis vector has the right shape: If your feature matrix has p features (so your model parameters are a p×1 column vector), the i-th standard basis vector should also be a p×1 column vector. Create it like this:

  # Assume p is the number of features in your dataset
  p <- ncol(X) 
  e_i <- matrix(0, nrow = p, ncol = 1)
  e_i[i, 1] <- 1
  

• Check matrix multiplication order: Matrix multiplication requires the number of columns in the first object to match the number of rows in the second. For example, if your parameters are stored as a p×1 vector theta, then theta %*% e_i will throw an error (since p×1 × p×1 is invalid), but t(e_i) %*% theta will work (1×p × p×1 gives a scalar). Double-check the paper's notation to confirm the correct multiplication order.
• Debug with dim(): Add dim(e_i) and dim(your_matrix/vector) calls right before the multiplication to confirm their shapes match the paper's requirements.

Verifying the Rest of Your Code #

Since your code compiles but you're unsure about correctness, try these sanity checks:

• Align with paper steps line-by-line: Pull up the algorithm's pseudocode from the paper and compare each line to your R code. For example:
  • Did you initialize parameters correctly (zeros, small random values, etc.)?
  • Is your loss function calculation exactly as described in the paper?
  • Are parameter updates using the right gradient formula?
• Test with a tiny subset of data: Take 5-10 rows from the Boston housing dataset and run your algorithm. Check if:
  • The loss function decreases over iterations (if it's an iterative algorithm like gradient descent).
  • Parameter values change in a logical way (e.g., coefficients for features correlated with housing prices should have positive values).
• Compare with a known baseline: If your algorithm is a variant of linear regression, run lm(medv ~ ., data = train_data) and compare its coefficients to your algorithm's output. They shouldn't be identical (unless your algorithm is vanilla linear regression), but they should be in the same ballpark if your code is correct.

内容的提问来源于stack exchange，提问作者Majk