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Old 08-22-2012, 12:16 PM
tadworthington tadworthington is offline
Join Date: Jun 2012
Location: Chicago, IL
Posts: 32
Default What happens when error cannot be computed (is infinite) with leave-one-out CV?

I thought of this while working on the homework for the class. Let's say I have three points: (-1,0), (1,0), and (1,1). I want to use a linear model (h(x) = mx + b) to do the fitting, and I use LOO to check my cross validation error. The problem becomes apparent right away:

Leave out (-1,0), and fit (1,0), (1,1).  Fitting gives a vertical line, x = 1.
Of course, I am now unable to compute the squared error for the point (-1,0) that was left out - the error will be infinite.

Is the solution that I can't choose a vertical line (x = k, for some k) when fitting the data?
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