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How are singular values related to minimum mean squared error?
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When I read the Sergio Verdu's tutorial on Eigenvalues and Singular Values of Random Matrices: A Tutorial Introduction, I found a very interesting conclusion on Slide 5-7, which says that, for a linear system:
$$
y = Hx + n
$$
where $n$ denotes the noise term, $x$ and $y$ are input/output vectors, and $H$ is (probably, I guess) a random matrix, then we have:
$$
minimum MSE = dfrac1Ksum_i^Kdfrac11+SNRlambda_i(H^TH)
$$
where $K$ is the dimension of $x$.
Could anyone help explain what's happening here?
random-matrices
asked Jul 27 at 14:50
Haohan Wang
213110
add a comment |Â
up vote
1
down vote
favorite
When I read the Sergio Verdu's tutorial on Eigenvalues and Singular Values of Random Matrices: A Tutorial Introduction, I found a very interesting conclusion on Slide 5-7, which says that, for a linear system:
$$
y = Hx + n
$$
where $n$ denotes the noise term, $x$ and $y$ are input/output vectors, and $H$ is (probably, I guess) a random matrix, then we have:
$$
minimum MSE = dfrac1Ksum_i^Kdfrac11+SNRlambda_i(H^TH)
$$
where $K$ is the dimension of $x$.
Could anyone help explain what's happening here?
random-matrices
asked Jul 27 at 14:50
Haohan Wang
213110
add a comment |Â
up vote
1
down vote
favorite
up vote
1
down vote
favorite
When I read the Sergio Verdu's tutorial on Eigenvalues and Singular Values of Random Matrices: A Tutorial Introduction, I found a very interesting conclusion on Slide 5-7, which says that, for a linear system:
$$
y = Hx + n
$$
where $n$ denotes the noise term, $x$ and $y$ are input/output vectors, and $H$ is (probably, I guess) a random matrix, then we have:
$$
minimum MSE = dfrac1Ksum_i^Kdfrac11+SNRlambda_i(H^TH)
$$
where $K$ is the dimension of $x$.
Could anyone help explain what's happening here?
random-matrices
asked Jul 27 at 14:50
Haohan Wang
213110
When I read the Sergio Verdu's tutorial on Eigenvalues and Singular Values of Random Matrices: A Tutorial Introduction, I found a very interesting conclusion on Slide 5-7, which says that, for a linear system:
$$
y = Hx + n
$$
where $n$ denotes the noise term, $x$ and $y$ are input/output vectors, and $H$ is (probably, I guess) a random matrix, then we have:
$$
minimum MSE = dfrac1Ksum_i^Kdfrac11+SNRlambda_i(H^TH)
$$
where $K$ is the dimension of $x$.
Could anyone help explain what's happening here?
random-matrices
asked Jul 27 at 14:50
Haohan Wang
213110
asked Jul 27 at 14:50
Haohan Wang
213110
asked Jul 27 at 14:50
Haohan Wang
213110
asked Jul 27 at 14:50
Haohan Wang
213110
213110
add a comment |Â
add a comment |Â
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