Jacobian of Matrix Loss Function
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I am attempting to perform a convex optimization that requires the Jacobian of the loss function w.r.t to the parameters to be estimated.
The loss function of my system has the form:
$$f(beta) = sum_{i=0}^n (left|A^{-1}B_iCD_i - A^{-1}Eright|)$$
where the parameter vector $beta$, has size 18, and its elements are found in the matrices A, B, C, E. There are n data points as inputs.
The norm is a frobenius norm. I also recognize that minimizing over the squared frobenius norm $left|...right|^2$ would acheive the same result ultimately, so i am open to that approach.
How can i break this down and find $frac{df(beta)}{dbeta}$ = [$frac{df(beta)}{dbeta_1}$, ... , $frac{df(beta)}{dbeta_k}$], where k = 18
Thank you,
calculus linear-algebra matrices multivariable-calculus
asked Dec 10 '18 at 17:58
Jad TawilJad Tawil
11
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add a comment |
$begingroup$
I am attempting to perform a convex optimization that requires the Jacobian of the loss function w.r.t to the parameters to be estimated.
The loss function of my system has the form:
$$f(beta) = sum_{i=0}^n (left|A^{-1}B_iCD_i - A^{-1}Eright|)$$
where the parameter vector $beta$, has size 18, and its elements are found in the matrices A, B, C, E. There are n data points as inputs.
The norm is a frobenius norm. I also recognize that minimizing over the squared frobenius norm $left|...right|^2$ would acheive the same result ultimately, so i am open to that approach.
How can i break this down and find $frac{df(beta)}{dbeta}$ = [$frac{df(beta)}{dbeta_1}$, ... , $frac{df(beta)}{dbeta_k}$], where k = 18
Thank you,
calculus linear-algebra matrices multivariable-calculus
asked Dec 10 '18 at 17:58
Jad TawilJad Tawil
11
$endgroup$
add a comment |
$begingroup$
I am attempting to perform a convex optimization that requires the Jacobian of the loss function w.r.t to the parameters to be estimated.
The loss function of my system has the form:
$$f(beta) = sum_{i=0}^n (left|A^{-1}B_iCD_i - A^{-1}Eright|)$$
where the parameter vector $beta$, has size 18, and its elements are found in the matrices A, B, C, E. There are n data points as inputs.
The norm is a frobenius norm. I also recognize that minimizing over the squared frobenius norm $left|...right|^2$ would acheive the same result ultimately, so i am open to that approach.
How can i break this down and find $frac{df(beta)}{dbeta}$ = [$frac{df(beta)}{dbeta_1}$, ... , $frac{df(beta)}{dbeta_k}$], where k = 18
Thank you,
calculus linear-algebra matrices multivariable-calculus
asked Dec 10 '18 at 17:58
Jad TawilJad Tawil
11
$endgroup$
I am attempting to perform a convex optimization that requires the Jacobian of the loss function w.r.t to the parameters to be estimated.
The loss function of my system has the form:
$$f(beta) = sum_{i=0}^n (left|A^{-1}B_iCD_i - A^{-1}Eright|)$$
where the parameter vector $beta$, has size 18, and its elements are found in the matrices A, B, C, E. There are n data points as inputs.
The norm is a frobenius norm. I also recognize that minimizing over the squared frobenius norm $left|...right|^2$ would acheive the same result ultimately, so i am open to that approach.
How can i break this down and find $frac{df(beta)}{dbeta}$ = [$frac{df(beta)}{dbeta_1}$, ... , $frac{df(beta)}{dbeta_k}$], where k = 18
Thank you,
calculus linear-algebra matrices multivariable-calculus
calculus linear-algebra matrices multivariable-calculus
asked Dec 10 '18 at 17:58
Jad TawilJad Tawil
11
asked Dec 10 '18 at 17:58
Jad TawilJad Tawil
11
asked Dec 10 '18 at 17:58
Jad TawilJad Tawil
11
asked Dec 10 '18 at 17:58
Jad TawilJad Tawil
11
asked Dec 10 '18 at 17:58
Jad TawilJad Tawil
11
11
add a comment |
add a comment |
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