# Interesting Papers at SODA 2009

Several talks seem potentially interesting to ML folks at this year’s SODA.

1. Maria-Florina Balcan, Avrim Blum, and Anupam Gupta, Approximate Clustering without the Approximation. This paper gives reasonable algorithms with provable approximation guarantees for k-median and other notions of clustering. It’s conceptually interesting, because it’s the second example I’ve seen where NP hardness is subverted by changing the problem definition subtle but reasonable way. Essentially, they show that if any near-approximation to an optimal solution is good, then it’s computationally easy to find a near-optimal solution. This subtle shift bears serious thought. A similar one occurred in our ranking paper with respect to minimum feedback arcset. With two known examples, it suggests that many more NP-complete problems might be finessed into irrelevance in this style.
2. Yury Lifshits and Shengyu Zhang, Combinatorial Algorithms for Nearest Neighbors, Near-Duplicates, and Small-World Design. The basic idea of this paper is that actually creating a metric with a valid triangle inequality inequality is hard for real-world problems, so it’s desirable to have a datastructure which works with a relaxed notion of triangle inequality. The precise relaxation is more extreme than you might imagine, implying the associated algorithms give substantial potential speedups in incomparable applications. Yuri tells me that a cover tree style “true O(n) space” algorithm is possible. If worked out and implemented, I could imagine substantial use.
3. Elad Hazan and Satyen Kale Better Algorithms for Benign Bandits. The basic idea of this paper is that in real-world applications, an adversary is less powerful than is commonly supposed, so carefully taking into account the observed variance can yield an algorithm which works much better in practice, without sacrificing the worst case performance.
4. Kevin Matulef, Ryan O’Donnell, Ronitt Rubinfeld, Rocco Servedio, Testing Halfspaces. The basic point of this paper is that testing halfspaces is qualitatively easier than finding a good half space with respect to 0/1 loss. Although the analysis is laughably far from practical, the result is striking, and it’s plausible that the algorithm works much better than the analysis. The core algorithm is at least conceptually simple: test that two correlated random points have the same sign, with “yes” being evidence of a halfspace and “no” not.
5. I also particularly liked Yuval Peres‘s invited talk The Unreasonable Effectiveness of Martingales. Martingale’s are endemic to learning, especially online learning, and I suspect we can tighten and clarify several arguments using some of the techniques discussed.