Multivariate conditional entropy
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I would like to take data columns and compute the multivariate conditional entropy. For instance, suppose I have columns $A, B, C D, E$ and I want to compute the conditional entropy $H(E | A,B,C,D)$. Can someone give a little explanation of all this, pointing out the first joint variable $A,B,C,D$ vs the second variable $E$. Then please give the algorithm and math for calculating the conditional entropy.
information-theory
asked Jan 6 at 0:11
Ben SprottBen Sprott
444312
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add a comment |
$begingroup$
I would like to take data columns and compute the multivariate conditional entropy. For instance, suppose I have columns $A, B, C D, E$ and I want to compute the conditional entropy $H(E | A,B,C,D)$. Can someone give a little explanation of all this, pointing out the first joint variable $A,B,C,D$ vs the second variable $E$. Then please give the algorithm and math for calculating the conditional entropy.
information-theory
asked Jan 6 at 0:11
Ben SprottBen Sprott
444312
$endgroup$
add a comment |
$begingroup$
I would like to take data columns and compute the multivariate conditional entropy. For instance, suppose I have columns $A, B, C D, E$ and I want to compute the conditional entropy $H(E | A,B,C,D)$. Can someone give a little explanation of all this, pointing out the first joint variable $A,B,C,D$ vs the second variable $E$. Then please give the algorithm and math for calculating the conditional entropy.
information-theory
asked Jan 6 at 0:11
Ben SprottBen Sprott
444312
$endgroup$
I would like to take data columns and compute the multivariate conditional entropy. For instance, suppose I have columns $A, B, C D, E$ and I want to compute the conditional entropy $H(E | A,B,C,D)$. Can someone give a little explanation of all this, pointing out the first joint variable $A,B,C,D$ vs the second variable $E$. Then please give the algorithm and math for calculating the conditional entropy.
information-theory
information-theory
asked Jan 6 at 0:11
Ben SprottBen Sprott
444312
asked Jan 6 at 0:11
Ben SprottBen Sprott
444312
edited Jan 6 at 0:21
Ben Sprott
asked Jan 6 at 0:11
Ben SprottBen Sprott
444312
asked Jan 6 at 0:11
Ben SprottBen Sprott
444312
asked Jan 6 at 0:11
Ben SprottBen Sprott
444312
444312
add a comment |
add a comment |
1 Answer
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$begingroup$
suppose I have columns A,B,C,D,E
If by "columns" you mean random variables, for which you know the joint (five dimensional) probability function, then to compute $H(E | A,B,C,D)$ you just use the common defition of conditional entropy
$$H(X | Y) = sum_Y P(Y=y) H(X | Y=y)$$
replacing $X$ by $E$ and $Y$ by your (multivariate) variable $(A,B,C,D)$.
answered Jan 6 at 3:12
leonbloyleonbloy
40.5k645107
$endgroup$
$begingroup$
Yes, I think random variable is the same as a data column.
$endgroup$
– Ben Sprott
Jan 6 at 18:20
add a comment |
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1 Answer
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1 Answer
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$begingroup$
suppose I have columns A,B,C,D,E
If by "columns" you mean random variables, for which you know the joint (five dimensional) probability function, then to compute $H(E | A,B,C,D)$ you just use the common defition of conditional entropy
$$H(X | Y) = sum_Y P(Y=y) H(X | Y=y)$$
replacing $X$ by $E$ and $Y$ by your (multivariate) variable $(A,B,C,D)$.
answered Jan 6 at 3:12
leonbloyleonbloy
40.5k645107
$endgroup$
$begingroup$
Yes, I think random variable is the same as a data column.
$endgroup$
– Ben Sprott
Jan 6 at 18:20
add a comment |
$begingroup$
suppose I have columns A,B,C,D,E
If by "columns" you mean random variables, for which you know the joint (five dimensional) probability function, then to compute $H(E | A,B,C,D)$ you just use the common defition of conditional entropy
$$H(X | Y) = sum_Y P(Y=y) H(X | Y=y)$$
replacing $X$ by $E$ and $Y$ by your (multivariate) variable $(A,B,C,D)$.
answered Jan 6 at 3:12
leonbloyleonbloy
40.5k645107
$endgroup$
$begingroup$
Yes, I think random variable is the same as a data column.
$endgroup$
– Ben Sprott
Jan 6 at 18:20
add a comment |
$begingroup$
suppose I have columns A,B,C,D,E
If by "columns" you mean random variables, for which you know the joint (five dimensional) probability function, then to compute $H(E | A,B,C,D)$ you just use the common defition of conditional entropy
$$H(X | Y) = sum_Y P(Y=y) H(X | Y=y)$$
replacing $X$ by $E$ and $Y$ by your (multivariate) variable $(A,B,C,D)$.
answered Jan 6 at 3:12
leonbloyleonbloy
40.5k645107
$endgroup$
suppose I have columns A,B,C,D,E
If by "columns" you mean random variables, for which you know the joint (five dimensional) probability function, then to compute $H(E | A,B,C,D)$ you just use the common defition of conditional entropy
$$H(X | Y) = sum_Y P(Y=y) H(X | Y=y)$$
replacing $X$ by $E$ and $Y$ by your (multivariate) variable $(A,B,C,D)$.
answered Jan 6 at 3:12
leonbloyleonbloy
40.5k645107
answered Jan 6 at 3:12
leonbloyleonbloy
40.5k645107
answered Jan 6 at 3:12
leonbloyleonbloy
40.5k645107
answered Jan 6 at 3:12
leonbloyleonbloy
40.5k645107
40.5k645107
$begingroup$
Yes, I think random variable is the same as a data column.
$endgroup$
– Ben Sprott
Jan 6 at 18:20
add a comment |
$begingroup$
Yes, I think random variable is the same as a data column.
$endgroup$
– Ben Sprott
Jan 6 at 18:20
$begingroup$
Yes, I think random variable is the same as a data column.
$endgroup$
– Ben Sprott
Jan 6 at 18:20
$begingroup$
Yes, I think random variable is the same as a data column.
$endgroup$
– Ben Sprott
Jan 6 at 18:20
add a comment |
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