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Science Forum Index » Statistics - Math Forum » compare Gaussian probability in different dimensions
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| zl2k |
 Posted: Tue Apr 15, 2008 2:25 am |
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Guest
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hi, there
Suppose I have a data set, each element is of d_0 dimension. I have 2
Gaussian pdf (G_1 and G_2).
G_1 dimension is d_1, (mu_1, sigma_1) with transform matrix m_1 of
projection from d_0 to d_1.
G_2 dimension is d_2, (mu_2, sigma_2) with transform matrix m_2 of
projection from d_0 to d_2.
d_1 < d_0 and d_2 < d_0 and d_1 > d_2.
My question is: given a data of d_0 dimension, how can I reasonably
compare the probability of its belong to G_1 and G_2?
Since d_2 < d_1, can I project G_1 to the same space of G_2 and then
do the comparison? (How can I do that if possible for the mu and
sigma?)
Thanks for help.
zl2k |
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| Ray Koopman |
| Posted: Tue Apr 15, 2008 7:35 am |
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Guest
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On Apr 15, 5:25 am, zl2k <kdsfin...@gmail.com> wrote:
Quote: hi, there
Suppose I have a data set, each element is of d_0 dimension. I have 2
Gaussian pdf (G_1 and G_2).
G_1 dimension is d_1, (mu_1, sigma_1) with transform matrix m_1 of
projection from d_0 to d_1.
G_2 dimension is d_2, (mu_2, sigma_2) with transform matrix m_2 of
projection from d_0 to d_2.
d_1 < d_0 and d_2 < d_0 and d_1 > d_2.
My question is: given a data of d_0 dimension, how can I reasonably
compare the probability of its belong to G_1 and G_2?
Since d_2 < d_1, can I project G_1 to the same space of G_2 and then
do the comparison? (How can I do that if possible for the mu and
sigma?)
Thanks for help.
zl2k
What do you mean by "the probability of its belong to G_1 and G_2"?
In general, such probabilities are zero. |
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| Guest |
| Posted: Tue Apr 15, 2008 9:46 am |
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On Apr 15, 7:25 am, zl2k <kdsfin...@gmail.com> wrote:
Quote: hi, there
Suppose I have a data set, each element is of d_0 dimension. I have 2
Gaussian pdf (G_1 and G_2).
G_1 dimension is d_1, (mu_1, sigma_1) with transform matrix m_1 of
projection from d_0 to d_1.
G_2 dimension is d_2, (mu_2, sigma_2) with transform matrix m_2 of
projection from d_0 to d_2.
d_1 < d_0 and d_2 < d_0 and d_1 > d_2.
My question is: given a data of d_0 dimension, how can I reasonably
compare the probability of its belong to G_1 and G_2?
Since d_2 < d_1, can I project G_1 to the same space of G_2 and then
do the comparison? (How can I do that if possible for the mu and
sigma?)
Thanks for help.
zl2k
At the risk of thinking this too obvious of an answer, since you have
the projection matrices from d_0 -> d_1 and d_0 -> d_2, why not just
evaluate the density of the projected point?
N( m_2 * x_0; mu_2, sigma_2) < N( m_1 * x_0; mu_1, sigma_1 )
Or is there some other reason why you need to transform the data into
the same space? |
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