VC-dimension of parity functions
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Consider the boolean hypercube ${0,1}^N$. For a set I $subseteq$ {1,2,...N}, we define the parity function $h_I$ as follows. For a binary vector x = $(x_1, x_2, ...,x_N) in {0,1}^N$,
$h_I(x) = bigg(sum_{iin I}x_ibigg)mod 2$
What is the VC-dimension of the class of all such parity functions, $H_{N-parity} = {h_I:Isubseteq {1,2,..., N}}$? [Courtesy: Shai Ben-David et al.,]
calculus statistics machine-learning
asked Dec 9 '18 at 4:02
sonali masrankarsonali masrankar
12
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add a comment |
$begingroup$
Consider the boolean hypercube ${0,1}^N$. For a set I $subseteq$ {1,2,...N}, we define the parity function $h_I$ as follows. For a binary vector x = $(x_1, x_2, ...,x_N) in {0,1}^N$,
$h_I(x) = bigg(sum_{iin I}x_ibigg)mod 2$
What is the VC-dimension of the class of all such parity functions, $H_{N-parity} = {h_I:Isubseteq {1,2,..., N}}$? [Courtesy: Shai Ben-David et al.,]
calculus statistics machine-learning
asked Dec 9 '18 at 4:02
sonali masrankarsonali masrankar
12
$endgroup$
add a comment |
$begingroup$
Consider the boolean hypercube ${0,1}^N$. For a set I $subseteq$ {1,2,...N}, we define the parity function $h_I$ as follows. For a binary vector x = $(x_1, x_2, ...,x_N) in {0,1}^N$,
$h_I(x) = bigg(sum_{iin I}x_ibigg)mod 2$
What is the VC-dimension of the class of all such parity functions, $H_{N-parity} = {h_I:Isubseteq {1,2,..., N}}$? [Courtesy: Shai Ben-David et al.,]
calculus statistics machine-learning
asked Dec 9 '18 at 4:02
sonali masrankarsonali masrankar
12
$endgroup$
Consider the boolean hypercube ${0,1}^N$. For a set I $subseteq$ {1,2,...N}, we define the parity function $h_I$ as follows. For a binary vector x = $(x_1, x_2, ...,x_N) in {0,1}^N$,
$h_I(x) = bigg(sum_{iin I}x_ibigg)mod 2$
What is the VC-dimension of the class of all such parity functions, $H_{N-parity} = {h_I:Isubseteq {1,2,..., N}}$? [Courtesy: Shai Ben-David et al.,]
calculus statistics machine-learning
calculus statistics machine-learning
asked Dec 9 '18 at 4:02
sonali masrankarsonali masrankar
12
asked Dec 9 '18 at 4:02
sonali masrankarsonali masrankar
12
asked Dec 9 '18 at 4:02
sonali masrankarsonali masrankar
12
asked Dec 9 '18 at 4:02
sonali masrankarsonali masrankar
12
asked Dec 9 '18 at 4:02
sonali masrankarsonali masrankar
12
12
add a comment |
add a comment |
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