Any differences in cvxpy library between l2 norm and sum_of_square?
I am trying to use cvxpy lib to solve a very simple least square problem. But I found that cvxpy gave me very different results when I use sum_squares and norm(x,2) as loss functions.
The same happens when I try the l1 norm and sum of absolute values.
Does these differences come from mathematically the optimization problem definition, or the implementation of the library?
Here is my code example:
s = cvx.Variable(n)
constrains = [cvx.sum(s)==1 , s>=0, s<=1]
prob = cvx.Problem(cvx.Minimize(cvx.sum_squares(A * s - y)), constrains)
prob = cvx.Problem(cvx.Minimize(cvx.norm(A*s - y ,2)), constrains)
Both y and s are vectors representing histograms. y is the histogram of randomized data, and s is the original histogram that I want to recover. A is a n*m "transition" matrix of probabilities how s is randomized to y.
The following are the histograms of variable s:
Using sum_of_square
Using norm2
convex-optimization cvxpy norm
asked Dec 27 '18 at 18:06
skinfaxi
11
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I am trying to use cvxpy lib to solve a very simple least square problem. But I found that cvxpy gave me very different results when I use sum_squares and norm(x,2) as loss functions.
The same happens when I try the l1 norm and sum of absolute values.
Does these differences come from mathematically the optimization problem definition, or the implementation of the library?
Here is my code example:
s = cvx.Variable(n)
constrains = [cvx.sum(s)==1 , s>=0, s<=1]
prob = cvx.Problem(cvx.Minimize(cvx.sum_squares(A * s - y)), constrains)
prob = cvx.Problem(cvx.Minimize(cvx.norm(A*s - y ,2)), constrains)
Both y and s are vectors representing histograms. y is the histogram of randomized data, and s is the original histogram that I want to recover. A is a n*m "transition" matrix of probabilities how s is randomized to y.
The following are the histograms of variable s:
Using sum_of_square
Using norm2
convex-optimization cvxpy norm
asked Dec 27 '18 at 18:06
skinfaxi
11
New contributor
skinfaxi is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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it would help if you share the results that you are getting along with the expected results.
– noobcode
Dec 27 '18 at 18:24
@noocode I just updated the question. Do you have any clue of how this happens?
– skinfaxi
Dec 27 '18 at 19:16
Add some reproducible example and check the solver state. Hard to reason about your problem. But in the core sum of squares and norm are two very different things. E.g. qp vs. Socp optimization problem. Depending on what cvxpy does, in some extreme case it might even chose a different solver (as different opt problems) although i doubt it does. I would expect the norm-prob to be the better/more stable formulation.
– sascha
Dec 27 '18 at 21:07
I'm not sure but CVXR has some interesting material on the subject: cvxr.com/cvx/doc/advanced.html#eliminating-quadratic-forms I'd be interested if someone can interpret that into an answer.
– Jacques Kvam
Dec 29 '18 at 22:50
add a comment |
I am trying to use cvxpy lib to solve a very simple least square problem. But I found that cvxpy gave me very different results when I use sum_squares and norm(x,2) as loss functions.
The same happens when I try the l1 norm and sum of absolute values.
Does these differences come from mathematically the optimization problem definition, or the implementation of the library?
Here is my code example:
s = cvx.Variable(n)
constrains = [cvx.sum(s)==1 , s>=0, s<=1]
prob = cvx.Problem(cvx.Minimize(cvx.sum_squares(A * s - y)), constrains)
prob = cvx.Problem(cvx.Minimize(cvx.norm(A*s - y ,2)), constrains)
Both y and s are vectors representing histograms. y is the histogram of randomized data, and s is the original histogram that I want to recover. A is a n*m "transition" matrix of probabilities how s is randomized to y.
The following are the histograms of variable s:
Using sum_of_square
Using norm2
convex-optimization cvxpy norm
asked Dec 27 '18 at 18:06
skinfaxi
11
New contributor
skinfaxi is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
I am trying to use cvxpy lib to solve a very simple least square problem. But I found that cvxpy gave me very different results when I use sum_squares and norm(x,2) as loss functions.
The same happens when I try the l1 norm and sum of absolute values.
Does these differences come from mathematically the optimization problem definition, or the implementation of the library?
Here is my code example:
s = cvx.Variable(n)
constrains = [cvx.sum(s)==1 , s>=0, s<=1]
prob = cvx.Problem(cvx.Minimize(cvx.sum_squares(A * s - y)), constrains)
prob = cvx.Problem(cvx.Minimize(cvx.norm(A*s - y ,2)), constrains)
Both y and s are vectors representing histograms. y is the histogram of randomized data, and s is the original histogram that I want to recover. A is a n*m "transition" matrix of probabilities how s is randomized to y.
The following are the histograms of variable s:
Using sum_of_square
Using norm2
convex-optimization cvxpy norm
convex-optimization cvxpy norm
asked Dec 27 '18 at 18:06
skinfaxi
11
New contributor
skinfaxi is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Dec 27 '18 at 18:06
skinfaxi
11
New contributor
skinfaxi is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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edited Dec 27 '18 at 19:14
asked Dec 27 '18 at 18:06
skinfaxi
11
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skinfaxi is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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asked Dec 27 '18 at 18:06
skinfaxi
11
asked Dec 27 '18 at 18:06
skinfaxi
11
11
New contributor
skinfaxi is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
skinfaxi is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
skinfaxi is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
it would help if you share the results that you are getting along with the expected results.
– noobcode
Dec 27 '18 at 18:24
@noocode I just updated the question. Do you have any clue of how this happens?
– skinfaxi
Dec 27 '18 at 19:16
Add some reproducible example and check the solver state. Hard to reason about your problem. But in the core sum of squares and norm are two very different things. E.g. qp vs. Socp optimization problem. Depending on what cvxpy does, in some extreme case it might even chose a different solver (as different opt problems) although i doubt it does. I would expect the norm-prob to be the better/more stable formulation.
– sascha
Dec 27 '18 at 21:07
I'm not sure but CVXR has some interesting material on the subject: cvxr.com/cvx/doc/advanced.html#eliminating-quadratic-forms I'd be interested if someone can interpret that into an answer.
– Jacques Kvam
Dec 29 '18 at 22:50
add a comment |
it would help if you share the results that you are getting along with the expected results.
– noobcode
Dec 27 '18 at 18:24
@noocode I just updated the question. Do you have any clue of how this happens?
– skinfaxi
Dec 27 '18 at 19:16
Add some reproducible example and check the solver state. Hard to reason about your problem. But in the core sum of squares and norm are two very different things. E.g. qp vs. Socp optimization problem. Depending on what cvxpy does, in some extreme case it might even chose a different solver (as different opt problems) although i doubt it does. I would expect the norm-prob to be the better/more stable formulation.
– sascha
Dec 27 '18 at 21:07
I'm not sure but CVXR has some interesting material on the subject: cvxr.com/cvx/doc/advanced.html#eliminating-quadratic-forms I'd be interested if someone can interpret that into an answer.
– Jacques Kvam
Dec 29 '18 at 22:50
it would help if you share the results that you are getting along with the expected results.
– noobcode
Dec 27 '18 at 18:24
it would help if you share the results that you are getting along with the expected results.
– noobcode
Dec 27 '18 at 18:24
@noocode I just updated the question. Do you have any clue of how this happens?
– skinfaxi
Dec 27 '18 at 19:16
@noocode I just updated the question. Do you have any clue of how this happens?
– skinfaxi
Dec 27 '18 at 19:16
Add some reproducible example and check the solver state. Hard to reason about your problem. But in the core sum of squares and norm are two very different things. E.g. qp vs. Socp optimization problem. Depending on what cvxpy does, in some extreme case it might even chose a different solver (as different opt problems) although i doubt it does. I would expect the norm-prob to be the better/more stable formulation.
– sascha
Dec 27 '18 at 21:07
Add some reproducible example and check the solver state. Hard to reason about your problem. But in the core sum of squares and norm are two very different things. E.g. qp vs. Socp optimization problem. Depending on what cvxpy does, in some extreme case it might even chose a different solver (as different opt problems) although i doubt it does. I would expect the norm-prob to be the better/more stable formulation.
– sascha
Dec 27 '18 at 21:07
I'm not sure but CVXR has some interesting material on the subject: cvxr.com/cvx/doc/advanced.html#eliminating-quadratic-forms I'd be interested if someone can interpret that into an answer.
– Jacques Kvam
Dec 29 '18 at 22:50
I'm not sure but CVXR has some interesting material on the subject: cvxr.com/cvx/doc/advanced.html#eliminating-quadratic-forms I'd be interested if someone can interpret that into an answer.
– Jacques Kvam
Dec 29 '18 at 22:50
add a comment |
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it would help if you share the results that you are getting along with the expected results.
– noobcode
Dec 27 '18 at 18:24
@noocode I just updated the question. Do you have any clue of how this happens?
– skinfaxi
Dec 27 '18 at 19:16
Add some reproducible example and check the solver state. Hard to reason about your problem. But in the core sum of squares and norm are two very different things. E.g. qp vs. Socp optimization problem. Depending on what cvxpy does, in some extreme case it might even chose a different solver (as different opt problems) although i doubt it does. I would expect the norm-prob to be the better/more stable formulation.
– sascha
Dec 27 '18 at 21:07
I'm not sure but CVXR has some interesting material on the subject: cvxr.com/cvx/doc/advanced.html#eliminating-quadratic-forms I'd be interested if someone can interpret that into an answer.
– Jacques Kvam
Dec 29 '18 at 22:50