
Limit of $\\frac{x^c-c^x}{x^x-c^c}$ as $x \\rightarrow c$
2018年3月13日 · My question is: Show that $\lim_{x \rightarrow c} \frac{x^c-c^x}{x^x-c^c}$ exists and find its value. Because the limit is 0/0 I've tried using L'Hopital's rule, but every time I differentiate it I
combinatorics - Prove there is a formula $\phi(x,z)$ of VC …
2020年4月16日 · However, this suggests that $\mathcal{P}_{\leq 2^\kappa}(U)$ might be an example of a set system with VC dimension $2^\kappa$ and dual VC dimension $\kappa$. This is equivalent to what you asked for, by dualizing. In fact, this system has dual VC …
probability - The Variance Rule of $V(cX) = c^2V(X)
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real analysis - VC dimension of union and intersection
2020年4月24日 · What is this VC dimension of a set of "classifiers"? Well, basically a classifier on a set is like a rule : if an element is part of the classifying set, then it satisfies that rule, otherwise it does not.
Properties of VC dimension - Mathematics Stack Exchange
The VC dimension of a classification machine is larger or equal to n if at least an arrangement of n points exists that can be classified without errors for any labeling of the n points. It is equal to n if the sentence I have just written holds for every k from 2 to n but not for k = n+1.
machine learning - How to calculate Vapnik-Chervonenkis …
The VC dimension of a hypothesis class, H is the cardinality of the largest set which can be shattered by a H.The requirement is you should be able to find at least one such set of points for which you can find a H that shatters (or you can always find a member of H that can classify every possible labelling of a ) particular set.
VC dimension of linear decision surface - Mathematics Stack …
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A question about VC dimension. 2D Axis aligned rectangles
2017年9月10日 · But I still have some doubts with the definition of VC dimension. If we consider a set of given 4 points, what happens if I have $$\{x_1,x_2,x_3,x_4\} = +,-,+,-$$ aligned in order over the x axis? This is not realizable, thus VC dimension of rectangle is not $\geq 4$. However, its VC dimensino is 4. $\endgroup$ –
What is the VC dimension of a d-dimensional quadratic function?
2019年4月5日 · In fact, if the inputs are the tuples (x,y,M,u), then the VC dimension is 0 because we are just talking about the VC dimension of the "sign" function, which can't shatter any set of points. $\endgroup$
VC dimension of a circle - Mathematics Stack Exchange
2019年12月16日 · Consider the points $(1/4,0),$ $(-1/4,0),$ and $(0,2).$ It is is obvious that we can find circles that classify all three points positive (some big circle containing all three), all three negative (some tiny circle far away from the origin), and each individually positive (just take a tiny circle around that point), so the only subsets we need to worry about are the pairs.