Adam D. Bull
Adaptive confidence sets in L^{2}.
Thu, 11/24/2011 - 15:01 — SomNambulAuthors: Richard Nickl, Adam D. Bull
Subjects: Statistics
AbstractThe problem of constructing nonparametric confidence sets that are adaptive
in L^{2}-loss over a continuous scale of Sobolev classes is considered.
Adaptation holds, where possible, with respect to both the radius of the
Sobolev ball and its smoothness degree, and over maximal parameter spaces for
which adaptation is possible. Two key regimes of parameter constellations are
identified: one where full adaptation is possible, and one where adaptation
requires critical regions be removed. The phase transition between these
regimes is analysed separately.- Read more
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Convergence Rates of Efficient Global Optimization Algorithms.
Wed, 01/19/2011 - 16:01 — SomNambulAuthors: Adam D. Bull
Subjects: Machine Learning
AbstractEfficient global optimization is the problem of minimizing an unknown
function f, using as few evaluations f(x) as possible. It can be considered as
a continuum-armed bandit problem, with noiseless data and simple regret.
Expected improvement is perhaps the most popular method for solving this
problem; the algorithm performs well in experiments, but little is known about
its theoretical properties. Implementing expected improvement requires a choice
of Gaussian process prior, which determines an associated space of functions,
its reproducing-kernel Hilbert space (RKHS).
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