The fourth and final day of SPARS 2011 served up two plenaries by two prodigious reserarchers: Joel Tropp and Stephen Wright. At the beginning of his talk, Tropp asked who in the room knows how MATLAB computes the SVD. Only a few out of about 200 raised their hand, and a few more gestured that they kind of knew.
The problem is that the methods we use today are treated as black boxes, but are based on extremely optimized classical methods that are incapable of working with massive matrices (billions by billions and up). So, we need better tools. He presented his work in SVD by a randomized algorithm … which at first sounds scarily inaccurate, but proves to be extremely effective at a much reduced computational cost.
In the last plenary, Wright presented a lot of work in state of the art methods for regularized optimization. At the beginning, he showed some fantastic pictures that he called an “Atlas of the Null Space,” which showed where solutions to min l1 are the same as min l0.
His talked centered around the message that though we talk a lot of exact solutions, or sparsest representations, most applications in the real world only need good algorithms that give the correct support before the whole solution. The trick is to determine when to stop an algorithm, and post-process the results to find the better solution.
In between these talks, there were plenty others, discussing various items of interest with dictionary learning, audio inpainting (Po’D coming soon), and several posters, one of which is by CRISSP reader Graham Coleman. He presented his novel work applying l1 minimization of sound feature mixtures to drive concatenative sound synthesis, or musaicing. (I have discussed an earlier version of this work here.) Coleman’s approach appears to be the next generation of concatenative synthesis.
All in all, this workshop was an excellent use of my time and money. Its duration was just perfect that after the last session I really felt as if my fuel tank was completely full. The organizers did an extremely nice job of selecting plenary speakers, assembling a wide range of quality work, and finding an accommodating venue with helpful staff. I even heard that the committee was able to raise enough funds so that many of the student participants had their accommodations paid for.
I am really looking forward to the 2013 edition of SPARS (or CoSPARS).