39,449 research outputs found
Interactive Submodular Set Cover
We introduce a natural generalization of submodular set cover and exact
active learning with a finite hypothesis class (query learning). We call this
new problem interactive submodular set cover. Applications include advertising
in social networks with hidden information. We give an approximation guarantee
for a novel greedy algorithm and give a hardness of approximation result which
matches up to constant factors. We also discuss negative results for simpler
approaches and present encouraging early experimental results.Comment: 15 pages, 1 figur
Fast B-spline Curve Fitting by L-BFGS
We propose a novel method for fitting planar B-spline curves to unorganized
data points. In traditional methods, optimization of control points and foot
points are performed in two very time-consuming steps in each iteration: 1)
control points are updated by setting up and solving a linear system of
equations; and 2) foot points are computed by projecting each data point onto a
B-spline curve. Our method uses the L-BFGS optimization method to optimize
control points and foot points simultaneously and therefore it does not need to
perform either matrix computation or foot point projection in every iteration.
As a result, our method is much faster than existing methods
Opt: A Domain Specific Language for Non-linear Least Squares Optimization in Graphics and Imaging
Many graphics and vision problems can be expressed as non-linear least
squares optimizations of objective functions over visual data, such as images
and meshes. The mathematical descriptions of these functions are extremely
concise, but their implementation in real code is tedious, especially when
optimized for real-time performance on modern GPUs in interactive applications.
In this work, we propose a new language, Opt (available under
http://optlang.org), for writing these objective functions over image- or
graph-structured unknowns concisely and at a high level. Our compiler
automatically transforms these specifications into state-of-the-art GPU solvers
based on Gauss-Newton or Levenberg-Marquardt methods. Opt can generate
different variations of the solver, so users can easily explore tradeoffs in
numerical precision, matrix-free methods, and solver approaches. In our
results, we implement a variety of real-world graphics and vision applications.
Their energy functions are expressible in tens of lines of code, and produce
highly-optimized GPU solver implementations. These solver have performance
competitive with the best published hand-tuned, application-specific GPU
solvers, and orders of magnitude beyond a general-purpose auto-generated
solver
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