12,653 research outputs found
Maximum-a-posteriori estimation with Bayesian confidence regions
Solutions to inverse problems that are ill-conditioned or ill-posed may have
significant intrinsic uncertainty. Unfortunately, analysing and quantifying
this uncertainty is very challenging, particularly in high-dimensional
problems. As a result, while most modern mathematical imaging methods produce
impressive point estimation results, they are generally unable to quantify the
uncertainty in the solutions delivered. This paper presents a new general
methodology for approximating Bayesian high-posterior-density credibility
regions in inverse problems that are convex and potentially very
high-dimensional. The approximations are derived by using recent concentration
of measure results related to information theory for log-concave random
vectors. A remarkable property of the approximations is that they can be
computed very efficiently, even in large-scale problems, by using standard
convex optimisation techniques. In particular, they are available as a
by-product in problems solved by maximum-a-posteriori estimation. The
approximations also have favourable theoretical properties, namely they
outer-bound the true high-posterior-density credibility regions, and they are
stable with respect to model dimension. The proposed methodology is illustrated
on two high-dimensional imaging inverse problems related to tomographic
reconstruction and sparse deconvolution, where the approximations are used to
perform Bayesian hypothesis tests and explore the uncertainty about the
solutions, and where proximal Markov chain Monte Carlo algorithms are used as
benchmark to compute exact credible regions and measure the approximation
error
Kinematic calibration of Orthoglide-type mechanisms from observation of parallel leg motions
The paper proposes a new calibration method for parallel manipulators that
allows efficient identification of the joint offsets using observations of the
manipulator leg parallelism with respect to the base surface. The method
employs a simple and low-cost measuring system, which evaluates deviation of
the leg location during motions that are assumed to preserve the leg
parallelism for the nominal values of the manipulator parameters. Using the
measured deviations, the developed algorithm estimates the joint offsets that
are treated as the most essential parameters to be identified. The validity of
the proposed calibration method and efficiency of the developed numerical
algorithms are confirmed by experimental results. The sensitivity of the
measurement methods and the calibration accuracy are also studied
Fast algorithms for large scale generalized distance weighted discrimination
High dimension low sample size statistical analysis is important in a wide
range of applications. In such situations, the highly appealing discrimination
method, support vector machine, can be improved to alleviate data piling at the
margin. This leads naturally to the development of distance weighted
discrimination (DWD), which can be modeled as a second-order cone programming
problem and solved by interior-point methods when the scale (in sample size and
feature dimension) of the data is moderate. Here, we design a scalable and
robust algorithm for solving large scale generalized DWD problems. Numerical
experiments on real data sets from the UCI repository demonstrate that our
algorithm is highly efficient in solving large scale problems, and sometimes
even more efficient than the highly optimized LIBLINEAR and LIBSVM for solving
the corresponding SVM problems
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