3,008 research outputs found
The Degrees of Freedom of Partial Least Squares Regression
The derivation of statistical properties for Partial Least Squares regression
can be a challenging task. The reason is that the construction of latent
components from the predictor variables also depends on the response variable.
While this typically leads to good performance and interpretable models in
practice, it makes the statistical analysis more involved. In this work, we
study the intrinsic complexity of Partial Least Squares Regression. Our
contribution is an unbiased estimate of its Degrees of Freedom. It is defined
as the trace of the first derivative of the fitted values, seen as a function
of the response. We establish two equivalent representations that rely on the
close connection of Partial Least Squares to matrix decompositions and Krylov
subspace techniques. We show that the Degrees of Freedom depend on the
collinearity of the predictor variables: The lower the collinearity is, the
higher the Degrees of Freedom are. In particular, they are typically higher
than the naive approach that defines the Degrees of Freedom as the number of
components. Further, we illustrate how the Degrees of Freedom approach can be
used for the comparison of different regression methods. In the experimental
section, we show that our Degrees of Freedom estimate in combination with
information criteria is useful for model selection.Comment: to appear in the Journal of the American Statistical Associatio
Partial orderings of default predictions
We compare and generalize various partial orderings of probability
forecasters according to the quality of their predictions. It appears that
the calibration requirement is quite at odds with the possibility of some
such ordering. However, if the requirements of calibration and identical
sets of debtors are relaxed, comparability obtains more easily. Taking
default predictions in the credit rating industry as an example, we show
for a data base of 5333 (Moodyâs) and 6505 ten-year default predictions
(S&P), that Moodyâs and S&P cannot be ordered neither according to
their grade distributions given default or non-default or to their Ginicurves,
but Moodyâs dominate S&P with respect to the ROC-criterion
Spatially Resolved Magnetization in the Bose-Einstein Condensed State of BaCuSi2O6: Evidence for Imperfect Frustration
In order to understand the nature of the two-dimensional Bose-Einstein
condensed (BEC) phase in BaCuSi2O6, we performed detailed 63Cu and 29Si NMR
above the critical magnetic field, Hc1= 23.4 T. The two different alternating
layers present in the system have very different local magnetizations close to
Hc1; one is very weak, and its size and field dependence are highly sensitive
to the nature of inter-layer coupling. Its precise value could only be
determined by "on-site" 63Cu NMR, and the data are fully reproduced by a model
of interacting hard-core bosons in which the perfect frustration associated to
tetragonal symmetry is slightly lifted, leading to the conclusion that the
population of the less populated layers is not fully incoherent but must be
partially condensed
Free-electron Model for Mesoscopic Force Fluctuations in Nanowires
When two metal electrodes are separated, a nanometer sized wire (nanowire) is
formed just before the contact breaks. The electrical conduction measured
during this retraction process shows signs of quantized conductance in units of
G_0=2e^2/h. Recent experiments show that the force acting on the wire during
separation fluctuates, which has been interpreted as being due to atomic
rearrangements. In this report we use a simple free electron model, for two
simple geometries, and show that the electronic contribution to the force
fluctuations is comparable to the experimentally found values, about 2 nN.Comment: 4 pages, 3 figures, reference correcte
Rotation of an atomic Bose-Einstein condensate with and without a quantized vortex
We theoretically examine the rotation of an atomic Bose-Einstein condensate
in an elliptical trap, both in the absence and presence of a quantized vortex.
Two methods of introducing the rotating potential are considered -
adiabatically increasing the rotation frequency at fixed ellipticity, and
adiabatically increasing the trap ellipticity at fixed rotation frequency.
Extensive simulations of the Gross-Pitaevskii equation are employed to map out
the points where the condensate becomes unstable and ultimately forms a vortex
lattice. We highlight the key features of having a quantized vortex in the
initial condensate. In particular, we find that the presence of the vortex
causes the instabilities to shift to lower or higher rotation frequencies,
depending on the direction of the vortex relative to the trap rotation.Comment: 15 pages, 8 figure
Highly parallel multi-physics simulation of muscular activation and EMG
Simulation of skeletal muscle activation can help to interpret electromyographic measurements and infer the behavior of the muscle ïŹbers. Existing models consider simpliïŹed geometries or a low number of muscle ïŹbers to reduce the computation time. We demonstrate how to simulate a ïŹnely-resolved model of biceps brachii with a typical number of 270.000 ïŹbers. We have used domain decomposition to run simulations on 27.000 cores of the supercomputer HazelHen at HLRS in Stuttgart, Germany. We present details on opendihu, our software framework. Its conïŹgurability, eïŹcient data structures and modular software architecture target usability, performance and extensibility for future models. We present good parallel weak scaling of the simulations
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