Talk:Basis pursuit denoising

Corrected edit Nov 4, reverting $$\lambda \rightarrow \infty$$ to $$\lambda \rightarrow 0$$. When $$\lambda = \infty$$, the solution is always the 0 vector.

Cheers, Patrick Gill (talk) 19:19, 7 November 2011 (UTC)!


 * $$\lambda \rightarrow 0$$ cannot be correct either. For $$\lambda = 0$$, the problem becomes
 * $$\min_x \frac{1}{2}\|y-Ax\|^2_2\text{,}$$
 * which is certainly not basis pursuit. --77.187.199.142 (talk) 10:20, 8 June 2017 (UTC)

Fastest solver
Patrick, since you're the author of the In-Crowd algorithm, I think it is inappropriate to claim that the In-Crowd algorithm is the fastest. Your paper shows evidence suggesting that it is fast, but when the problem is *very* sparse (and if the matrix correlation is low, then SPGL1 is just as good). So just saying "large sparse" problems is pushing the boundary here. Furthermore, you didn't test against all possible algorithms, and you didn't test on a standard problem set (SPARCO). Also, you test matrices drawn from a Gaussian ensemble.

I am not trying to denigrate your algorithm in any way. I just thing your wording here sounds like "fighting words". You don't read the authors of an algorithm like BFGS claim that they have "the fastest" algorithm for unconstrained optimization; rather, they let their results speak for themselves. Lavaka (talk) 09:49, 29 February 2012 (UTC)

Reply
Hi Stephen, I like the changes you made, and the removal of "fighting words" is an improvement and a step towards the neutral point of view that Wikipedia enshrines. I admit that part of my motive was to needle experienced researchers to add their expertise to this page; I suppose it worked.

One minor correction to the above: In-Crowd is still a factor of 5 or so faster than SPGL1 on matrices with low correlation.

On another note, it would be great if the work you've done on your personal wiki to list various sparse and low-rank algorithms were brought to Wikipedia. Compressed sensing is a rapidly growing field, and newcomers might be more attracted to it if the Wikipedia literature were more complete. A lot of work, I know, but probably still worth doing.

All the best! Patrick Gill (talk) 15:06, 5 March 2012 (UTC)

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