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How is the Representer theorem used in the derivation of the SVM dual form?

This is the primal form of the SVM hypothesis : $$ h _{\mathbf{\vec w}, b}(\mathbf{\vec x}^{(i)}) = \mathbf{\vec w}\cdot \mathbf{\vec x}^{(i)} + b $$ The Representer theorem as formulated here ...
Sagnik Taraphdar's user avatar
1 vote
1 answer
55 views

What is the dual function of this non-overlapping Group Lasso's penalty?

I'm trying to find the dual function of this function (non-overlapping Group Lasso's penalty function): $$ \mathfrak{h}: \mathbb{R}^p \to [0,\infty], \ a \mapsto \sum_{j=1}^{k} \left\| a_{\mathscr{A}...
Mai Khanh Truong's user avatar
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0 answers
10 views

how to solve for wasserstein duality easily in a special case when 2-Wasserstein inequality constraint is binding

I was going through this nice paper ” A Simple and General Duality Proof for Wasserstein Distributionally Robust Optimization”, and one quick qu on applying Theorem 1 to my poject: What if in my ...
numpynp's user avatar
  • 21
2 votes
1 answer
214 views

How to solve alphas (or the dual equation) after getting Lagrangian dual of SVM

I'm trying to learn SVM by myself, and I'm stuck after getting the dual of SVM. I understand getting the dual after the primal. But, I am stuck here. Please help. We assume that the hard margin case ...
dvdy's user avatar
  • 21
1 vote
0 answers
26 views

Min max formulation conversion to max min formulation. Reason?

Question is based on the screenshot attached. Based on paper here. I am not being able to understand why min max formulation (eq 4) is first converted to max min formulation (eq 5). Is it something ...
Curious's user avatar
  • 11
1 vote
1 answer
63 views

Excercise 6.1 and its solution in Bishop's PRML, Question 1

The problem comes from Exercise 6.1 of "Pattern Recognition and Machine Learning" by Christopher M. Bishop: Consider the dual formulation of the least squares linear regression problem ...
zzzhhh's user avatar
  • 333
1 vote
1 answer
364 views

Demonstration and Interpretation between a Fisher matrix and its dual space which is covariance matrix

I have a simple (maybe not) issue about the interpretation of the link between Fisher information matrix and its inverse which is the covariance matrix. How to formulate that a line of Covariance ...
user avatar
0 votes
0 answers
123 views

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 ...
user8714896's user avatar
2 votes
0 answers
78 views

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 '...
cgo's user avatar
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2 votes
1 answer
153 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}) \...
gazza89's user avatar
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1 vote
0 answers
37 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 ...
Saksin's user avatar
  • 11
3 votes
2 answers
182 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 ...
taciturno's user avatar
  • 251
3 votes
1 answer
194 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 ...
Chechy Levas's user avatar
  • 1,275
1 vote
1 answer
150 views

Primal solution exists but dual does not [closed]

I am working on the following 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 ...
Angelıque's user avatar
3 votes
1 answer
602 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 ...
Upendra01's user avatar
  • 1,956
7 votes
1 answer
3k 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 ...
www3's user avatar
  • 681