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Perform Grid Search with Warm Start #1

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AlexGibberd opened this issue Mar 23, 2017 · 0 comments
Open

Perform Grid Search with Warm Start #1

AlexGibberd opened this issue Mar 23, 2017 · 0 comments

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@AlexGibberd
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We need to give people the ability to quickly try many settings of lambda out when fitting GFGL/IFGL.

Typically with these algorithms this is achieved by simply running the optimiser over a grid of
lambda1, lambda2 values.

To start with it might be iteresting to fix lambda1 and then look at the warm start method only applied in the lambda2 direction.

The paper below is very interesting in that it proposes a slightly more advanced method to optimise along this grid of lambdas.

https://arxiv.org/pdf/1504.06637.pdf

We will not need to implement their full method yet, but we want to have something which is the equivalent of Algorithm 1 (pages 9-10). In particular, take note of the initialisation settings for the grid, it should search from lambda2=0 to some arbitrary, but quite large lambda2max. Log-spacing may be used to specify the grid points.

The paper may hold much promise for finding paths of solutions, they suggest that they can find the full path (i.e. grid-search) solutions in not much more time than finding one single solution. However, I don't really know how their method should be applied to the GFGL problem other than for section 1.2. Let's keep it simple for now.

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