Is class of multivariate sign functions VC-class?
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For $theta inmathbb{R}^n$ define $f_{theta}:mathbb{R}^nrightarrow mathbb{R}$ as $f_{theta}(x)=frac{theta'x}{|x|_2}$ if $xneq 0$ and $f_{theta}(0)=0$. Is the collection of functions $mathcal{C}=left{f_{theta}(cdot-eta)|theta,etainmathbb{R}^nright}$ a VC-class?
machine-learning empirical-processes
asked Nov 22 at 12:58
John_Wick
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up vote
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For $theta inmathbb{R}^n$ define $f_{theta}:mathbb{R}^nrightarrow mathbb{R}$ as $f_{theta}(x)=frac{theta'x}{|x|_2}$ if $xneq 0$ and $f_{theta}(0)=0$. Is the collection of functions $mathcal{C}=left{f_{theta}(cdot-eta)|theta,etainmathbb{R}^nright}$ a VC-class?
machine-learning empirical-processes
asked Nov 22 at 12:58
John_Wick
1,134111
what have you tried?
– Viktor Glombik
Nov 22 at 13:05
I have been trying using the definition of VC class of a class of functions, ie, trying to show the class of subgraphs for the functions $mathcal{D}=left{{(x,t),t<f_{theta}(x-eta)}:theta,etainmathbb{R}^nright}$ to be VC class, but I could do it only for $n=1$, for $n>1$ I didn't have that much luck.
– John_Wick
Nov 22 at 14:02
add a comment |
up vote
-1
down vote
favorite
up vote
-1
down vote
favorite
For $theta inmathbb{R}^n$ define $f_{theta}:mathbb{R}^nrightarrow mathbb{R}$ as $f_{theta}(x)=frac{theta'x}{|x|_2}$ if $xneq 0$ and $f_{theta}(0)=0$. Is the collection of functions $mathcal{C}=left{f_{theta}(cdot-eta)|theta,etainmathbb{R}^nright}$ a VC-class?
machine-learning empirical-processes
asked Nov 22 at 12:58
John_Wick
1,134111
For $theta inmathbb{R}^n$ define $f_{theta}:mathbb{R}^nrightarrow mathbb{R}$ as $f_{theta}(x)=frac{theta'x}{|x|_2}$ if $xneq 0$ and $f_{theta}(0)=0$. Is the collection of functions $mathcal{C}=left{f_{theta}(cdot-eta)|theta,etainmathbb{R}^nright}$ a VC-class?
machine-learning empirical-processes
machine-learning empirical-processes
asked Nov 22 at 12:58
John_Wick
1,134111
asked Nov 22 at 12:58
John_Wick
1,134111
asked Nov 22 at 12:58
John_Wick
1,134111
asked Nov 22 at 12:58
John_Wick
1,134111
asked Nov 22 at 12:58
John_Wick
1,134111
1,134111
what have you tried?
– Viktor Glombik
Nov 22 at 13:05
I have been trying using the definition of VC class of a class of functions, ie, trying to show the class of subgraphs for the functions $mathcal{D}=left{{(x,t),t<f_{theta}(x-eta)}:theta,etainmathbb{R}^nright}$ to be VC class, but I could do it only for $n=1$, for $n>1$ I didn't have that much luck.
– John_Wick
Nov 22 at 14:02
add a comment |
what have you tried?
– Viktor Glombik
Nov 22 at 13:05
I have been trying using the definition of VC class of a class of functions, ie, trying to show the class of subgraphs for the functions $mathcal{D}=left{{(x,t),t<f_{theta}(x-eta)}:theta,etainmathbb{R}^nright}$ to be VC class, but I could do it only for $n=1$, for $n>1$ I didn't have that much luck.
– John_Wick
Nov 22 at 14:02
what have you tried?
– Viktor Glombik
Nov 22 at 13:05
what have you tried?
– Viktor Glombik
Nov 22 at 13:05
I have been trying using the definition of VC class of a class of functions, ie, trying to show the class of subgraphs for the functions $mathcal{D}=left{{(x,t),t<f_{theta}(x-eta)}:theta,etainmathbb{R}^nright}$ to be VC class, but I could do it only for $n=1$, for $n>1$ I didn't have that much luck.
– John_Wick
Nov 22 at 14:02
I have been trying using the definition of VC class of a class of functions, ie, trying to show the class of subgraphs for the functions $mathcal{D}=left{{(x,t),t<f_{theta}(x-eta)}:theta,etainmathbb{R}^nright}$ to be VC class, but I could do it only for $n=1$, for $n>1$ I didn't have that much luck.
– John_Wick
Nov 22 at 14:02
add a comment |
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what have you tried?
– Viktor Glombik
Nov 22 at 13:05
I have been trying using the definition of VC class of a class of functions, ie, trying to show the class of subgraphs for the functions $mathcal{D}=left{{(x,t),t<f_{theta}(x-eta)}:theta,etainmathbb{R}^nright}$ to be VC class, but I could do it only for $n=1$, for $n>1$ I didn't have that much luck.
– John_Wick
Nov 22 at 14:02