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Models of Models: Multivariate Metamodels
Harald Martens
Norwegian University of Life Sciences / IMT; Nofima, Aas,
Norway
ABSTRACT
This lecture outlines how multivariate metamodelling, based on
PLS-modelling, can be used to simplify
complicated mathematical models in different fields of science.
At various institutes at the Norwegian University
of Life Science and the Norwegian Food Research Institute at
Campus Aas, my colleagues and I have developed
new methodology for studying hard, knowledge-driven mechanistic
models, not only for sensitivity analysis
(classical metamodelling), but also for a number of other
purposes. In our first application areas - systems biology
and biospectroscopy - the mechanistic models are usually
constituted by sets of coupled nonlinear dynamic ODE
and PDE equations. But other kinds of complex computational
systems may be treated likewise. Complicated
mechanistic models can represent current knowledge very well,
but are often difficult to overview and assess, and
slow to compute.
By multivariate metamodelling i.e. by developing a model of the
model, we can overview, assess and
speed up a complicated mechanistic model. And we have shown how
this simplifies the fit of non-linear models to
massive amounts of empirical data, since it replaces non-linear
optimization by simple linear projections, without
the conventional curve-fitting problems (local minima, long
search processes etc). Various metamodelling tools
will be outlined, including a new experimental design method for
more efficient computer experiments, various
non-linear regression methods, and bilinear representations of
mechanistic model behavior.
Literature
Martens, H. (2009). Non-Linear Multivariate Dynamics Modelled by
PLSR. Proceedings of the 6th
International Conference on Partial Least Squares and Related
Methods, Beijing 4-7 2009 (V. E. Vinzi, M.
Tenenhaus and R. Guan, eds), Publishing House of Electronics
Industry,http://www.phei.com.cn,pp. 139-144.
Martens, H., Veflingstad, S. R., Plahte, E., Martens, M.,
Bertrand, D. and Omholt S. W. (2009). The Genotype-Phenotype
Relationship in Multicellular Pattern-Generating models - the
Neglected Role of Pattern Descriptors.
BMC Systems Biology, 3:87, doi:10.1186/1752-0509-3-87
Martens, H., Mge I, Tndel, K., Isaeva, J., Hy, M. and Sb, S.
(2010). Multi-Level Binary Replacement
(MBR) Design for Computer Experiments in High-Dimensional
Nonlinear Systems.J. Chemometrics, 24(11-12)
pp. 748-756.
Tndel, K., Gjuvsland, A. B., Mge, I. and Martens, H. (2010).
Screening Design for Computer Experiments:
Metamodelling of a Deterministic Mathematical Model of the
Mammalian Circadian Clock, J. Chemometrics,24
(11-12) pp. 738-747.
Isaeva, J., Sb, S., Wyller, J. A.,Wolkenhauer, O. and Martens,
H. (2011). Nonlinear Modelling of Curvature
by Bi-linear Metamodelling. In press, Chemometrics and
Intelligent Laboratory Systems.
Isaeva, J., Sb, S., Wyller, J. A., Nhek, S., and Martens, H
(2011). Fast and Comprehensive Estimation and
Fitting of Complex Mathematical Models to Massive Amounts of
Empirical Data. In Press, Chemometrics and
Intelligent Laboratory Systems.
Martens, H. (2011). The Informative Converse Paradox: Windows
into the Unknown. Chemometrics and
Intelligent Laboratory Systems, 107, pp. 124-138.
Keynote Presentation: 7th International Conference on Partial
Least Squares and Related MethodsMay 19-May 22, 2012 Houston,
Texas, USA
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SPEAKERS BIO
Harald Martens was originally trained as biochemist, and has
worked as a chemometrician
in applied multivariate analysis since 1972, in a number of
different disciplines ranging
from multivariate calibration of instruments for chemical
analysis of "dirty" samples, viamultivariate image, compression of
video signals, assessment of human sensory perception
and description of quality, language analysis, genetic analysis
and functional genomics, to
statistical metamodelling of nonlinear nonlinear dynamic models
in systems biology and
medicine. He is presently working as professor of chemometrics
at the Norwegian
University of Life Sciences and as senior research scientist at
the Norwegian Food
Research Institute (Nofima), both at Campus Aas, south of Oslo,
Norway. His primary
research activity at present concerns the bridging between
"soft", data-driven statistical
modelling (usually static and linear) on one hand, and "hard",
theory-driven mathematical
modelling (usually dynamic and nonlinear) on the other, based on
extensive computer
experiments and multivariate metamodelling, using methods like
PLS regression and
extensions thereof. Harald Martens was originally trained as
biochemist, and has worked
as a chemometrician in applied multivariate analysis since 1972,
in a number of different
disciplines ranging from multivariate calibration of instruments
for chemical analysis of"dirty" samples, via multivariate image,
compression of video signals, assessment of
human sensory perception and description of quality, language
analysis, genetic analysis
and functional genomics, to statistical metamodelling of
nonlinear nonlinear dynamic
models in systems biology and medicine. He is presently working
as professor of
chemometrics at the Norwegian University of Life Sciences and as
senior research
scientist at the Norwegian Food Research Institute (Nofima),
both at Campus Aas, south of
Oslo, Norway. His primary research activity at present concerns
the bridging between
"soft", data-driven statistical modelling (usually static and
linear) on one hand, and "hard",
theory-driven mathematical modelling (usually dynamic and
nonlinear) on the other, based
on extensive computer experiments and multivariate
metamodelling, using methods like
PLS regression and extensions thereof.
Keynote Presentation: 7th International Conference on Partial
Least Squares and Related MethodsMay 19-May 22, 2012 Houston,
Texas, USA
