18,672 research outputs found
Finite size scaling in neural networks
We demonstrate that the fraction of pattern sets that can be stored in
single- and hidden-layer perceptrons exhibits finite size scaling. This feature
allows to estimate the critical storage capacity \alpha_c from simulations of
relatively small systems. We illustrate this approach by determining \alpha_c,
together with the finite size scaling exponent \nu, for storing Gaussian
patterns in committee and parity machines with binary couplings and up to K=5
hidden units.Comment: 4 pages, RevTex, 5 figures, uses multicol.sty and psfig.st
Monte Carlo tomographic reconstruction in SPECT impact of bootstrapping and number of generated events
In Single Photon Emission Computed Tomography (SPECT), 3D images usually
reconstructed by performing a set of bidimensional (2D) analytical or iterative
reconstructions can also be reconstructed using an iterative reconstruction
algorithm involving a 3D projector. Accurate Monte Carlo (MC) simulations
modeling all the physical effects that affect the imaging process can be used
to estimate this projector. However, the accuracy of the projector is affected
by the stochastic nature of MC simulations. In this paper, we study the
accuracy of the reconstructed images with respect to the number of simulated
histories used to estimate the MC projector. Furthermore, we study the impact
of applying the bootstrapping technique when estimating the projectorComment: 15 pages, 9 figures, 2 table
Quantifying statistical uncertainty in the attribution of human influence on severe weather
Event attribution in the context of climate change seeks to understand the
role of anthropogenic greenhouse gas emissions on extreme weather events,
either specific events or classes of events. A common approach to event
attribution uses climate model output under factual (real-world) and
counterfactual (world that might have been without anthropogenic greenhouse gas
emissions) scenarios to estimate the probabilities of the event of interest
under the two scenarios. Event attribution is then quantified by the ratio of
the two probabilities. While this approach has been applied many times in the
last 15 years, the statistical techniques used to estimate the risk ratio based
on climate model ensembles have not drawn on the full set of methods available
in the statistical literature and have in some cases used and interpreted the
bootstrap method in non-standard ways. We present a precise frequentist
statistical framework for quantifying the effect of sampling uncertainty on
estimation of the risk ratio, propose the use of statistical methods that are
new to event attribution, and evaluate a variety of methods using statistical
simulations. We conclude that existing statistical methods not yet in use for
event attribution have several advantages over the widely-used bootstrap,
including better statistical performance in repeated samples and robustness to
small estimated probabilities. Software for using the methods is available
through the climextRemes package available for R or Python. While we focus on
frequentist statistical methods, Bayesian methods are likely to be particularly
useful when considering sources of uncertainty beyond sampling uncertainty.Comment: 41 pages, 11 figures, 1 tabl
Discovering an active subspace in a single-diode solar cell model
Predictions from science and engineering models depend on the values of the
model's input parameters. As the number of parameters increases, algorithmic
parameter studies like optimization or uncertainty quantification require many
more model evaluations. One way to combat this curse of dimensionality is to
seek an alternative parameterization with fewer variables that produces
comparable predictions. The active subspace is a low-dimensional linear
subspace defined by important directions in the model's input space; input
perturbations along these directions change the model's prediction more, on
average, than perturbations orthogonal to the important directions. We describe
a method for checking if a model admits an exploitable active subspace, and we
apply this method to a single-diode solar cell model with five input
parameters. We find that the maximum power of the solar cell has a dominant
one-dimensional active subspace, which enables us to perform thorough parameter
studies in one dimension instead of five
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