4,933 research outputs found
A Reproducing Kernel Perspective of Smoothing Spline Estimators
Spline functions have a long history as smoothers of noisy time series data, and several equivalent kernel representations have been proposed in terms of the Green's function solving the related boundary value problem. In this study we make use of the reproducing kernel property of the Green's function to obtain an hierarchy of time-invariant spline kernels of different order. The reproducing kernels give a good representation of smoothing splines for medium and long length filters, with a better performance of the asymmetric weights in terms of signal passing, noise suppression and revisions. Empirical comparisons of time-invariant filters are made with the classical non linear ones. The former are shown to loose part of their optimal properties when we fixed the length of the filter according to the noise to signal ratio as done in nonparametric seasonal adjustment procedures.equivalent kernels, nonparametric regression, Hilbert spaces, time series filtering, spectral properties
A volume-averaged nodal projection method for the Reissner-Mindlin plate model
We introduce a novel meshfree Galerkin method for the solution of
Reissner-Mindlin plate problems that is written in terms of the primitive
variables only (i.e., rotations and transverse displacement) and is devoid of
shear-locking. The proposed approach uses linear maximum-entropy approximations
and is built variationally on a two-field potential energy functional wherein
the shear strain, written in terms of the primitive variables, is computed via
a volume-averaged nodal projection operator that is constructed from the
Kirchhoff constraint of the three-field mixed weak form. The stability of the
method is rendered by adding bubble-like enrichment to the rotation degrees of
freedom. Some benchmark problems are presented to demonstrate the accuracy and
performance of the proposed method for a wide range of plate thicknesses
Quantum machine learning: a classical perspective
Recently, increased computational power and data availability, as well as
algorithmic advances, have led machine learning techniques to impressive
results in regression, classification, data-generation and reinforcement
learning tasks. Despite these successes, the proximity to the physical limits
of chip fabrication alongside the increasing size of datasets are motivating a
growing number of researchers to explore the possibility of harnessing the
power of quantum computation to speed-up classical machine learning algorithms.
Here we review the literature in quantum machine learning and discuss
perspectives for a mixed readership of classical machine learning and quantum
computation experts. Particular emphasis will be placed on clarifying the
limitations of quantum algorithms, how they compare with their best classical
counterparts and why quantum resources are expected to provide advantages for
learning problems. Learning in the presence of noise and certain
computationally hard problems in machine learning are identified as promising
directions for the field. Practical questions, like how to upload classical
data into quantum form, will also be addressed.Comment: v3 33 pages; typos corrected and references adde
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