# Tag Info

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### What is the exact definition of VC dimension?

The definition of VC dimension is: if there exists a set of n points that can be shattered by the classifier and there is no set of n+1 points that can be shattered by the classifier, then the VC ...
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### How to calculate VC-dimension?

The VC dimension is an estimate for the capability of a binary classifier. If you can find a set of $n$ points, so that it can be shattered by the classifier (i.e. classify all possible $2^n$ ...
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### What is the exact definition of VC dimension?

The points should fulfil points in general condition before consider for VC dimension.
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### How to calculate VC-dimension?

The VC dimension of a classifier is determined the following way: ...
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### With regards to VC-dimension, why can you shatter 3 points with circles but not 4 points?

Given $4$ points $A,B,C,D$. If they do not lie on the boundary of a convex hull, then it is impossible to shatter the inner point from the boundary. So assume they lie on the boundary of the hull. ...
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### VC-dimension of the infinite set of convex bodies?

For a binary class of data and any number of instances, as you have an infinite number of convex bodies, you can put all instances of a class inside the body and leave others. In this way, you can ...
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• 11.6k
1 vote
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### VC dimension of half spaces over the real line

First you need to understand how to calculate the VC-dimension. There are two conditions for the VC-dimension to be $n$ (here $n=1$): You need to find one set of $n$ points that can be shattered (i.e....
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1 vote

### A question on realizable sample complexity

We want to prove: If H is PAC learnable, then $\forall \epsilon, \exists C, \forall m \geq m_2:=Clog(1/\epsilon)(m_1+1/\epsilon^2), E[L] \leq \epsilon \mbox{ (a)}$ where $m_1:=m(\epsilon/2,1/2)$ ...
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1 vote

### Why the VC dimension to this linear hypothesis equal to 3?

The VC dimension depends on the dimension of your data and on the family of functions you are evaluating. In $\mathbb R^2$, the VC dimesion of the family $h(x)$ of oriented lines is 3 beacause, with ...
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