# Questions tagged [vc-theory]

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### VC-dimension of the class of hypotheses that assign label $1$ to exactly $k$ points of some finite domain $\mathcal{X}$

Let $\mathcal{X}$ be a finite domain and $k$ a number such that $k\leq|\mathcal{X}|$. Consider the hypothesis class $\mathcal{H}:=\big\{h:|\{\mathbf{x}\in\mathcal{X}:h(\mathbf{x})=1\}|=k\bigr\}$; that ...
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### How is PCA applied in CV with multiple channels?

I am currently working with a CNN with a physical magnitude dataset. The goal is to downscaling one of them based on the others, but previously I would like to do dimensionality reduction. If I have ...
74 views

### VC- dimension calculate

Let X = {1, 2, 3, ... , 100}. Let H be the class of all subsets of X that contain at least 20 and at most 80 elements. What is the VC-dimension of H?
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### VC Dimension of a Countably Infinite Class

I know that there are many examples of classes where the VC Dimension is finite/infinite even though the size of the class is Uncountably Infinite. However, I could not argue if the VC Dimension of a ...
34 views

### Finite hypothesis with maximal VC dimension

The VCdim of a finite hypothesis class $H$ cannot be larger than $\log_2(H)$. But was is an example of a hypothesis class that has VCdim exactly equal to that quantity? For a reference, this is a ...
1 vote
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### calculate the VC-dimension [closed]

I have a question about VC-dimension. I have this claim and I need to find out what its VC-dimension is $H\subseteq\{0,1\}^n$ collection of Boolean functions over n In my opinion the answer should ...
• 121
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### VC Dimensions in Machine Learning

Hello I'm learning about VC dimensions in machine learning. The class of classifiers $H$ where $h \in H$ if $h \in \mathbb{R} \rightarrow \{0,1\}$ is what I believe is simply binary classifiers (with ...
• 21
1 vote
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### VC-dimension of the infinite set of convex bodies?

I try to find and prove the VC-dimension of the infinite set of (uni-directional) convex bodies. From intuition, it's clear to me that it goes to infinity, but I don't know the correct way to prove it ...
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### Find VC dimension

I'm studying theoretical machine learning at university, and I have this problem in textbook, that I have no Idea how to start. In space $X=R^2$ are given two models $H_1$ (rectangle with sides ...
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