Questions tagged [duality]

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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 '...
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1answer
32 views

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}) \...
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0answers
32 views

A PCA related problem [closed]

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 ...
2
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2answers
34 views

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 ...
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0answers
12 views

Is penalized logistic regression convex? [duplicate]

Is logistic regression problem penalized by elastic net penalty convex optimization problem? More specifically, I want to find out whether it is suitable for dual formulation such that the duality gap ...
1
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1answer
14 views

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 ...
1
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0answers
21 views

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 ...
1
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1answer
117 views

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 ...
3
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1answer
631 views

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 ...