11,240 research outputs found
Joint Estimation of Multiple Graphical Models from High Dimensional Time Series
In this manuscript we consider the problem of jointly estimating multiple
graphical models in high dimensions. We assume that the data are collected from
n subjects, each of which consists of T possibly dependent observations. The
graphical models of subjects vary, but are assumed to change smoothly
corresponding to a measure of closeness between subjects. We propose a kernel
based method for jointly estimating all graphical models. Theoretically, under
a double asymptotic framework, where both (T,n) and the dimension d can
increase, we provide the explicit rate of convergence in parameter estimation.
It characterizes the strength one can borrow across different individuals and
impact of data dependence on parameter estimation. Empirically, experiments on
both synthetic and real resting state functional magnetic resonance imaging
(rs-fMRI) data illustrate the effectiveness of the proposed method.Comment: 40 page
Emulating dynamic non-linear simulators using Gaussian processes
The dynamic emulation of non-linear deterministic computer codes where the
output is a time series, possibly multivariate, is examined. Such computer
models simulate the evolution of some real-world phenomenon over time, for
example models of the climate or the functioning of the human brain. The models
we are interested in are highly non-linear and exhibit tipping points,
bifurcations and chaotic behaviour. However, each simulation run could be too
time-consuming to perform analyses that require many runs, including
quantifying the variation in model output with respect to changes in the
inputs. Therefore, Gaussian process emulators are used to approximate the
output of the code. To do this, the flow map of the system under study is
emulated over a short time period. Then, it is used in an iterative way to
predict the whole time series. A number of ways are proposed to take into
account the uncertainty of inputs to the emulators, after fixed initial
conditions, and the correlation between them through the time series. The
methodology is illustrated with two examples: the highly non-linear dynamical
systems described by the Lorenz and Van der Pol equations. In both cases, the
predictive performance is relatively high and the measure of uncertainty
provided by the method reflects the extent of predictability in each system
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