#1




The trap of local minimum/maximum for linear regression
Hi,
I refer to the method of minimizing the Ein, as explained in the Lecture 3, slide 15. When choosing the minimum as the point where the derivative (gradient) is zero, how can we be sure that we don't run over a local minimum, or worse, a local maximum? Does the quadratic form of the error measure ensures Ein does not have such local maxima and minima, just one global minimum? Indeed, it seems that grad(Ein) = 0 has only one solution. Is this really the case? If it really is the case, than choosing another error measure could yield such local minima/maxima. How can we avoid getting stuck into one of those points? 
#2




Re: The trap of local minimum/maximum for linear regression
Quote:
Other error measures may result in local minima and often no closedform solution, and the situation is tackled with methods like gradient descent and heuristcs to reduce the impact of local minima. Finding the global minimum is a general problem in optimization that is unlikely to have an exact, tractable solution since it is NPhard in the general case.
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