10,371 research outputs found
Decomposing feature-level variation with Covariate Gaussian Process Latent Variable Models
The interpretation of complex high-dimensional data typically requires the
use of dimensionality reduction techniques to extract explanatory
low-dimensional representations. However, in many real-world problems these
representations may not be sufficient to aid interpretation on their own, and
it would be desirable to interpret the model in terms of the original features
themselves. Our goal is to characterise how feature-level variation depends on
latent low-dimensional representations, external covariates, and non-linear
interactions between the two. In this paper, we propose to achieve this through
a structured kernel decomposition in a hybrid Gaussian Process model which we
call the Covariate Gaussian Process Latent Variable Model (c-GPLVM). We
demonstrate the utility of our model on simulated examples and applications in
disease progression modelling from high-dimensional gene expression data in the
presence of additional phenotypes. In each setting we show how the c-GPLVM can
extract low-dimensional structures from high-dimensional data sets whilst
allowing a breakdown of feature-level variability that is not present in other
commonly used dimensionality reduction approaches
Root traits predict decomposition across a landscape-scale grazing experiment
Acknowledgements We are grateful to the Woodland Trust for maintenance of and access to the Glen Finglas experiment. We thank Debbie Fielding, William Smith, Sarah McCormack, Allan Sim, Marcel Junker and Elaine Runge for help in the field and the laboratory. This research was part of the Glen Finglas project (formerly Grazing and Upland Birds (GRUB)) funded by the Scottish Government (RERAS). S.W.S. was funded by a BBSRC studentship.Peer reviewedPublisher PD
Generalized Hoeffding-Sobol Decomposition for Dependent Variables -Application to Sensitivity Analysis
In this paper, we consider a regression model built on dependent variables.
This regression modelizes an input output relationship. Under boundedness
assumptions on the joint distribution function of the input variables, we show
that a generalized Hoeffding-Sobol decomposition is available. This leads to
new indices measuring the sensitivity of the output with respect to the input
variables. We also study and discuss the estimation of these new indices
A New Combined Framework for the Cellular Manufacturing Systems Design
Cellular Manufacturing (CM) system has been recognized as an efficient and effective way to improve productivity in a factory. In recent years, there have been continuous research efforts to study different facet of CM system. The literature does not contain much published research on CM design which includes all design aspects. In this paper we provide a framework for the complete CM system design. It combines Axiomatic Design (AD) and Experimental Design (ED) to generate several feasible and potentially profitable designs. The AD approach is used as the basis for establishing a systematic CM systems design structure. ED has been a very useful tool to design and analyze complicated industrial design problems. AD helps secure valid input-factors to the ED. An element of the proposed framework is desmontrate through a numerical example for cell formation with alternative process.Cellular manufacturing; Design methodology Axiomatic Design; Experimental Design.
Super- and Anti-Principal Modes in Multi-Mode Waveguides
We introduce a new type of states for light in multimode waveguides featuring
strongly enhanced or reduced spectral correlations. Based on the experimentally
measured multi-spectral transmission matrix of a multimode fiber, we generate a
set of states that outperform the established "principal modes" in terms of the
spectral stability of their output spatial field profiles. Inverting this
concept also allows us to create states with a minimal spectral correlation
width, whose output profiles are considerably more sensitive to a frequency
change than typical input wavefronts. The resulting "super-" and
"anti-principal" modes are made orthogonal to each other even in the presence
of mode-dependent loss. By decomposing them in the principal mode basis, we
show that the super-principal modes are formed via interference of principal
modes with closeby delay times, whereas the anti-principal modes are a
superposition of principal modes with the most different delay times available
in the fiber. Such novel states are expected to have broad applications in
fiber communication, imaging, and spectroscopy.Comment: 8 pages, 5 figures, plus supplementary materia
On ANOVA decompositions of kernels and Gaussian random field paths
The FANOVA (or "Sobol'-Hoeffding") decomposition of multivariate functions
has been used for high-dimensional model representation and global sensitivity
analysis. When the objective function f has no simple analytic form and is
costly to evaluate, a practical limitation is that computing FANOVA terms may
be unaffordable due to numerical integration costs. Several approximate
approaches relying on random field models have been proposed to alleviate these
costs, where f is substituted by a (kriging) predictor or by conditional
simulations. In the present work, we focus on FANOVA decompositions of Gaussian
random field sample paths, and we notably introduce an associated kernel
decomposition (into 2^{2d} terms) called KANOVA. An interpretation in terms of
tensor product projections is obtained, and it is shown that projected kernels
control both the sparsity of Gaussian random field sample paths and the
dependence structure between FANOVA effects. Applications on simulated data
show the relevance of the approach for designing new classes of covariance
kernels dedicated to high-dimensional kriging
Managing structural uncertainty in health economic decision models: a discrepancy approach
Healthcare resource allocation decisions are commonly informed by computer model predictions of population mean costs and health effects. It is common to quantify the uncertainty in the prediction due to uncertain model inputs, but methods for quantifying uncertainty due to inadequacies in model structure are less well developed. We introduce an example of a model that aims to predict the costs and health effects of a physical activity promoting intervention. Our goal is to develop a framework in which we can manage our uncertainty about the costs and health effects due to deficiencies in the model structure. We describe the concept of `model discrepancy': the difference between the model evaluated at its true inputs, and the true costs and health effects. We then propose a method for quantifying discrepancy based on decomposing the cost-effectiveness model into a series of sub-functions, and considering potential error at each sub-function. We use a variance based sensitivity analysis to locate important sources of discrepancy within the model in order to guide model refinement. The resulting improved model is judged to contain less structural error, and the distribution on the model output better reflects our true uncertainty about the costs and effects of the intervention
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