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The trivial answer is that yes, it is possible. Consider standard Gaussian data and a generator sampling points $1/n$ with $n \rightarrow \infty$. Since you never see points beyond $(0,1]$, you are unlikely to learn the parameters of the distribution. More generally, and for a supervised problem with data $X,Y$, if your data generator covers a subset of the ...


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I can say "Stable Learning" of a supervised machine learner is as follows: A stable learning algorithm is one for which the prediction does not change much when the training data is modified slightly. You can follow this link to know more in details about how can we measure the stability in the context of computational learning theory.


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The measure that you are talking about actually has a name. It is called the "Popper dimension" -- it was introduced by Karl Popper in his "Logic of scientific discovery". Popper's idea of falsifiability was, as Vladimir Vapnik himself admits, the inspiration behind their work on the VC dimension. The VC dimension of the hypothesis set $\...


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I would say, that meaning of VC dimension is at least a possibility to implement any function on the given number of points for some case, not an express any function on $n$ points. Yes, you are right, that this definition, unfortunately, is not very useful in practice. Say, family of functions $\text{sign}(\sin(ax))$ has infinite $\text{VC}$ dimension. ...


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