As stated by Dr. Kilian Weinberger, that you mentioned in your question, you can never beat this error. And the formula for this error is different from the one you mentioned.

The optimal classifier gives you the mean of the distribution of all the data P, which you can never get. If you want to detect a car, for example, P has to contain all pictures of cars ever exists.

But if you do find P, there will still some points that vary from its mean. This variation is the noise that cannot be omitted.

According to the lecture: error (noise) = E(x,y) = [(y¯(x)−y)^2]). y¯(x) is the label you would expect to obtain from the whole distribution P, given a feature vector x; y is the label that you are testing.

P.S. excuse me for the bad equation, I am new to the platform...

As stated by Dr. Kilian Weinberger, that you mentioned in your question, you can never beat this error.

The optimal classifier gives you the mean of the distribution of all the data P, which you can never get. If you want to detect a car, for example, P has to contain all pictures of cars ever exists.

But if you do find P, there will still some points that vary from its mean. This variation is the noise that cannot be omitted. It defers from one distribution to another.

According to the lecture: error (noise) = E(x,y) = [(y¯(x)−y)^2]). y¯(x) is the label you would expect to obtain from the whole distribution P, given a feature vector x; y is the label that you are testing.

P.S. excuse me for the bad equation, I am new to the platform...