Why do we square the error in cost function?

A squared-error cost function is designed to reflect a penalty for an error in our estimate that increases with the square of the difference between our estimate and the actual value.

What is the reason we square the error mean square error in the cost function calculation in regression problem?

It does this by taking the distances from the points to the regression line (these distances are the “errors”) and squaring them. The squaring is necessary to remove any negative signs. It also gives more weight to larger differences. It’s called the mean squared error as you’re finding the average of a set of errors.

Why do we divide the cost function by 2?

It is because when you take the derivative of the cost function, that is used in updating the parameters during gradient descent, that 2 in the power get cancelled with the 12 multiplier, thus the derivation is cleaner.

Why is the squared error loss function more convenient than the norm function?

The squared error is everywhere differentiable, while the absolute error is not (its derivative is undefined at 0). This makes the squared error more amenable to the techniques of mathematical optimization.

Why do we care about the squared error?

The main reason is that squared error allows to decompose each observed value into the sum of orthogonal components such that the sum of observed squared values is equal to the sum of squared components.

Why is half mean squared error?

The half mean squared error evaluates how well the network predictions correspond to the target values. Create the input predictions as a single observation of random values with a height and width of six and a single channel. Compute the half mean squared error between the predictions and the targets.

What mean squared error is good?

There are no acceptable limits for MSE except that the lower the MSE the higher the accuracy of prediction as there would be excellent match between the actual and predicted data set. But it should be noted that it is possible that R2 is as close to 1, But MSE or RMSE is not an acceptable value.