Questions tagged [duality]
9 questions
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Earth Movers Distance and Maximum Mean Discrepency
By Kantorovich-Rubinstein duality the Earth Movers Distance (EMD)/Wasserstein Metric is equivalent to Maximum Mean Discrepancy (MMD) correct? See here for a more thorough explanation. Why then does the original Kernel MMD paper compare their…
www3
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What is the intuition of a dual?
I have been hearing that the Ridge regression is the dual to the GP (Gaussian process regression). What does this mean? Can someone please give an intuition on what 'dual' is.
My impression of the 'dual' is something along the lines of being…
cgo
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How to solve MNP (minimum norm) problem in SVM?
I'm reading an article, which says that MNP (minimum norm problem) can be solved as SVM.
In the minimum norm problem, we're given a set of points in $R^d$ and need to find a point in convex hull of our points closest to the origin.
In SVM method…
taciturno
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A PCA related problem
Consider the problem of shape averaging. In particular, suppose $X_i\ (i = 1,\dots, M$) are the input matrices, $X_i\in \mathbb R^{N\times2}$, with each sampled from corresponding 2D positions of shapes (or handwritten letters). We seek a shape…
Saksin
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Quadratic programming and interpretation of dual solution (Lagrangian)
Note: this question is about a common data science problem, but I am solving it using a specific piece of software. I believe the problem is common enough that these principles will be common across all solvers, but I understand that this question…
Chechy Levas
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Primal solution exists but dual does not
I am working on the follwoing nonlinear model.
Min z=10(1-$\exp$(−3x)
)
subject to:
x $\leq$ 3
When I solve this problem on LINGO, I got the message "dual solution does not exist but primal solution will be shown". 1) Why there is no dual solution?…
Angelıque
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How to recover primal problem from its dual counterpart
I am asking this from context of optimization in machine learning. We often talk about a primal problem and how this primal problem can be solved by first converting it into a dual problem (Using Lagrange Duality concept).
However, I want to ask if…
Upendra01
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What are the Karush–Kuhn–Tucker conditions for $\min_x \frac{1}{2} ||x-u||_2^2:$ subject to $||x||_1\le c$
What are the Karush–Kuhn–Tucker conditions for $\min_x \frac{1}{2} ||x-u||_2^2:$ subject to $||x||_1\le c$
Apparently these are the conditions
but it's not all that clear how this can be applied to above function, especially the stationarity…
user8714896
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Why is the Dual Formulation a valid reparametrization of a regression model
In polynomial regression problems, in which an input vector $\underline{\phi}(\underline{x})$ is used to map a feature vector to a higher dimensional space (an example of this being $(x_{1}, x_{2}) \to (x_{1}, x_{2}, x_{1}x_{2}, x_{1}^{2},…
gazza89
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