Why could this be an issue for the linear least squares regression model?
It could cause the backpropagation algorithm to fail during training
It could create a singular matrix during optimization, which fails to define a unique solution
It could modify the loss function during optimization, causing it to fail during training
It could introduce non-linear dependencies within the data, which could invalidate the linear assumptions of the model
Explanations:
The backpropagation algorithm is generally used in neural networks, not directly in linear least squares regression. The issue here is related to matrix operations, not backpropagation.
When two features are perfectly linearly dependent, it creates a situation where the matrix of features is singular (i.e., non-invertible). This prevents the optimization from defining a unique solution, causing failure in solving the linear system.
The loss function itself is not modified by feature linear dependencies. The issue is more related to the inability to compute a unique solution during optimization due to a singular matrix.
Perfectly linear dependencies between features do not introduce non-linear dependencies, nor do they invalidate the linear assumptions of the model. The problem is with the matrix rank and the optimization process.