72 research outputs found
An Efficient Parallel Solver for SDD Linear Systems
We present the first parallel algorithm for solving systems of linear
equations in symmetric, diagonally dominant (SDD) matrices that runs in
polylogarithmic time and nearly-linear work. The heart of our algorithm is a
construction of a sparse approximate inverse chain for the input matrix: a
sequence of sparse matrices whose product approximates its inverse. Whereas
other fast algorithms for solving systems of equations in SDD matrices exploit
low-stretch spanning trees, our algorithm only requires spectral graph
sparsifiers
On the Impossibility of Convex Inference in Human Computation
Human computation or crowdsourcing involves joint inference of the
ground-truth-answers and the worker-abilities by optimizing an objective
function, for instance, by maximizing the data likelihood based on an assumed
underlying model. A variety of methods have been proposed in the literature to
address this inference problem. As far as we know, none of the objective
functions in existing methods is convex. In machine learning and applied
statistics, a convex function such as the objective function of support vector
machines (SVMs) is generally preferred, since it can leverage the
high-performance algorithms and rigorous guarantees established in the
extensive literature on convex optimization. One may thus wonder if there
exists a meaningful convex objective function for the inference problem in
human computation. In this paper, we investigate this convexity issue for human
computation. We take an axiomatic approach by formulating a set of axioms that
impose two mild and natural assumptions on the objective function for the
inference. Under these axioms, we show that it is unfortunately impossible to
ensure convexity of the inference problem. On the other hand, we show that
interestingly, in the absence of a requirement to model "spammers", one can
construct reasonable objective functions for crowdsourcing that guarantee
convex inference.Comment: AAAI 201
- …