10,118 research outputs found
An informational approach to the global optimization of expensive-to-evaluate functions
In many global optimization problems motivated by engineering applications,
the number of function evaluations is severely limited by time or cost. To
ensure that each evaluation contributes to the localization of good candidates
for the role of global minimizer, a sequential choice of evaluation points is
usually carried out. In particular, when Kriging is used to interpolate past
evaluations, the uncertainty associated with the lack of information on the
function can be expressed and used to compute a number of criteria accounting
for the interest of an additional evaluation at any given point. This paper
introduces minimizer entropy as a new Kriging-based criterion for the
sequential choice of points at which the function should be evaluated. Based on
\emph{stepwise uncertainty reduction}, it accounts for the informational gain
on the minimizer expected from a new evaluation. The criterion is approximated
using conditional simulations of the Gaussian process model behind Kriging, and
then inserted into an algorithm similar in spirit to the \emph{Efficient Global
Optimization} (EGO) algorithm. An empirical comparison is carried out between
our criterion and \emph{expected improvement}, one of the reference criteria in
the literature. Experimental results indicate major evaluation savings over
EGO. Finally, the method, which we call IAGO (for Informational Approach to
Global Optimization) is extended to robust optimization problems, where both
the factors to be tuned and the function evaluations are corrupted by noise.Comment: Accepted for publication in the Journal of Global Optimization (This
is the revised version, with additional details on computational problems,
and some grammatical changes
The Kalai-Smorodinski solution for many-objective Bayesian optimization
An ongoing aim of research in multiobjective Bayesian optimization is to
extend its applicability to a large number of objectives. While coping with a
limited budget of evaluations, recovering the set of optimal compromise
solutions generally requires numerous observations and is less interpretable
since this set tends to grow larger with the number of objectives. We thus
propose to focus on a specific solution originating from game theory, the
Kalai-Smorodinsky solution, which possesses attractive properties. In
particular, it ensures equal marginal gains over all objectives. We further
make it insensitive to a monotonic transformation of the objectives by
considering the objectives in the copula space. A novel tailored algorithm is
proposed to search for the solution, in the form of a Bayesian optimization
algorithm: sequential sampling decisions are made based on acquisition
functions that derive from an instrumental Gaussian process prior. Our approach
is tested on four problems with respectively four, six, eight, and nine
objectives. The method is available in the Rpackage GPGame available on CRAN at
https://cran.r-project.org/package=GPGame
A Bayesian approach to constrained single- and multi-objective optimization
This article addresses the problem of derivative-free (single- or
multi-objective) optimization subject to multiple inequality constraints. Both
the objective and constraint functions are assumed to be smooth, non-linear and
expensive to evaluate. As a consequence, the number of evaluations that can be
used to carry out the optimization is very limited, as in complex industrial
design optimization problems. The method we propose to overcome this difficulty
has its roots in both the Bayesian and the multi-objective optimization
literatures. More specifically, an extended domination rule is used to handle
objectives and constraints in a unified way, and a corresponding expected
hyper-volume improvement sampling criterion is proposed. This new criterion is
naturally adapted to the search of a feasible point when none is available, and
reduces to existing Bayesian sampling criteria---the classical Expected
Improvement (EI) criterion and some of its constrained/multi-objective
extensions---as soon as at least one feasible point is available. The
calculation and optimization of the criterion are performed using Sequential
Monte Carlo techniques. In particular, an algorithm similar to the subset
simulation method, which is well known in the field of structural reliability,
is used to estimate the criterion. The method, which we call BMOO (for Bayesian
Multi-Objective Optimization), is compared to state-of-the-art algorithms for
single- and multi-objective constrained optimization
Polynomial Response Surface Approximations for the Multidisciplinary Design Optimization of a High Speed Civil Transport
Surrogate functions have become an important tool in multidisciplinary design optimization to deal with noisy functions, high computational cost, and the practical difficulty of integrating legacy disciplinary computer codes. A combination of mathematical, statistical, and engineering techniques, well known in other contexts, have made polynomial surrogate functions viable for MDO. Despite the obvious limitations imposed by sparse high fidelity data in high dimensions and the locality of low order polynomial approximations, the success of the panoply of techniques based on polynomial response surface approximations for MDO shows that the implementation details are more important than the underlying approximation method (polynomial, spline, DACE, kernel regression, etc.). This paper surveys some of the ancillary techniques—statistics, global search, parallel computing, variable complexity modeling—that augment the construction and use of polynomial surrogates
Sequential Design for Ranking Response Surfaces
We propose and analyze sequential design methods for the problem of ranking
several response surfaces. Namely, given response surfaces over a
continuous input space , the aim is to efficiently find the index of
the minimal response across the entire . The response surfaces are not
known and have to be noisily sampled one-at-a-time. This setting is motivated
by stochastic control applications and requires joint experimental design both
in space and response-index dimensions. To generate sequential design
heuristics we investigate stepwise uncertainty reduction approaches, as well as
sampling based on posterior classification complexity. We also make connections
between our continuous-input formulation and the discrete framework of pure
regret in multi-armed bandits. To model the response surfaces we utilize
kriging surrogates. Several numerical examples using both synthetic data and an
epidemics control problem are provided to illustrate our approach and the
efficacy of respective adaptive designs.Comment: 26 pages, 7 figures (updated several sections and figures
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The robust selection of predictive genes via a simple classifier
Identifying genes that direct the mechanism of a disease from expression data is extremely useful in understanding how that mechanism works.
This in turn may lead to better diagnoses and potentially can lead to a cure for that disease. This task becomes extremely challenging when the
data are characterised by only a small number of samples and a high number of dimensions, as it is often the case with gene expression data.
Motivated by this challenge, we present a general framework that focuses on simplicity and data perturbation. These are the keys for the robust
identification of the most predictive features in such data. Within this framework, we propose a simple selective na¨ıve Bayes classifier discovered using a global search technique, and combine it with data perturbation to
increase its robustness to small sample sizes.
An extensive validation of the method was carried out using two applied datasets from the field of microarrays and a simulated dataset, all
confounded by small sample sizes and high dimensionality. The method has been shown capable of identifying genes previously confirmed or associated with prostate cancer and viral infections
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ABC for Climate: Dealing with Expensive Simulators
A single molecule or molecule complex detection method is disclosed in certain aspects, comprising nano- or micro-fluidic channels.U
A new stepwise carbon cycle data assimilation system using multiple data streams to constrain the simulated land surface carbon cycle
Acknowledgements. This work was mainly funded by the EU FP7 CARBONES project (contracts FP7-SPACE-2009-1-242316), with also a small contribution from GEOCARBON project (ENV.2011.4.1.1-1-283080). This work used eddy covariance data acquired by the FLUXNET community and in particular by the following networks: AmeriFlux (U.S. Department of Energy, Biological and Environmental Research, Terrestrial Carbon Program; DE-FG02-04ER63917 and DE-FG02-04ER63911), AfriFlux, AsiaFlux, CarboAfrica, CarboEuropeIP, CarboItaly, CarboMont, ChinaFlux, Fluxnet-Canada (supported by CFCAS, NSERC, BIOCAP, Environment Canada, and NRCan), GreenGrass, KoFlux, LBA, NECC, OzFlux, TCOS-Siberia, USCCC. We acknowledge the financial support to the eddy covariance data harmonization provided by CarboEuropeIP, FAO-GTOS-TCO, iLEAPS, Max Planck Institute for Biogeochemistry, National Science Foundation, University of Tuscia, Université Laval and Environment Canada and US Department of Energy and the database development and technical support from Berkeley Water Center, Lawrence Berkeley National Laboratory, Microsoft Research eScience, Oak Ridge National Laboratory, University of California-Berkeley, University of Virginia. Philippe Ciais acknowledges support from the European Research Council through Synergy grant ERC-2013-SyG-610028 “IMBALANCE-P”. The authors wish to thank M. Jung for providing access to the GPP MTE data, which were downloaded from the GEOCARBON data portal (https://www.bgc-jena.mpg.de/geodb/projects/Data.php). The authors are also grateful to computing support and resources provided at LSCE and to the overall ORCHIDEE project that coordinate the development of the code (http://labex.ipsl.fr/orchidee/index.php/about-the-team).Peer reviewedPublisher PD
Hybrid One-Shot 3D Hand Pose Estimation by Exploiting Uncertainties
Model-based approaches to 3D hand tracking have been shown to perform well in
a wide range of scenarios. However, they require initialisation and cannot
recover easily from tracking failures that occur due to fast hand motions.
Data-driven approaches, on the other hand, can quickly deliver a solution, but
the results often suffer from lower accuracy or missing anatomical validity
compared to those obtained from model-based approaches. In this work we propose
a hybrid approach for hand pose estimation from a single depth image. First, a
learned regressor is employed to deliver multiple initial hypotheses for the 3D
position of each hand joint. Subsequently, the kinematic parameters of a 3D
hand model are found by deliberately exploiting the inherent uncertainty of the
inferred joint proposals. This way, the method provides anatomically valid and
accurate solutions without requiring manual initialisation or suffering from
track losses. Quantitative results on several standard datasets demonstrate
that the proposed method outperforms state-of-the-art representatives of the
model-based, data-driven and hybrid paradigms.Comment: BMVC 2015 (oral); see also
http://lrs.icg.tugraz.at/research/hybridhape
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