Question-13

Which of the following is the loss for a single training example \((\mathbf{x}, y)\) for a linear regression model with weight vector \(\mathbf{w}\)? Assume the most common scenario.

• \(\mathbf{w}^T \mathbf{x} - y\)

• \((\mathbf{w}^T \mathbf{x} - y)^2\)

• \(|(\mathbf{w}^T \mathbf{x} - y)|\)

• \(-y \log(\mathbf{w}^T\mathbf{x})\)

Answer

• \(\mathbf{w}^T \mathbf{x} - y\)

• \((\mathbf{w}^T \mathbf{x} - y)^2\)

• \(|(\mathbf{w}^T \mathbf{x} - y)|\)

• \(-y \log(\mathbf{w}^T\mathbf{x})\)

Solution

The loss function for linear regression is usually the squared error.