209 research outputs found
On Reject and Refine Options in Multicategory Classification
In many real applications of statistical learning, a decision made from
misclassification can be too costly to afford; in this case, a reject option,
which defers the decision until further investigation is conducted, is often
preferred. In recent years, there has been much development for binary
classification with a reject option. Yet, little progress has been made for the
multicategory case. In this article, we propose margin-based multicategory
classification methods with a reject option. In addition, and more importantly,
we introduce a new and unique refine option for the multicategory problem,
where the class of an observation is predicted to be from a set of class
labels, whose cardinality is not necessarily one. The main advantage of both
options lies in their capacity of identifying error-prone observations.
Moreover, the refine option can provide more constructive information for
classification by effectively ruling out implausible classes. Efficient
implementations have been developed for the proposed methods. On the
theoretical side, we offer a novel statistical learning theory and show a fast
convergence rate of the excess -risk of our methods with emphasis on
diverging dimensionality and number of classes. The results can be further
improved under a low noise assumption. A set of comprehensive simulation and
real data studies has shown the usefulness of the new learning tools compared
to regular multicategory classifiers. Detailed proofs of theorems and extended
numerical results are included in the supplemental materials available online.Comment: A revised version of this paper was accepted for publication in the
Journal of the American Statistical Association Theory and Methods Section.
52 pages, 6 figure
Numerical Complete Solution for Random Genetic Drift by Energetic Variational Approach
In this paper, we focus on numerical solutions for random genetic drift
problem, which is governed by a degenerated convection-dominated parabolic
equation. Due to the fixation phenomenon of genes, Dirac delta singularities
will develop at boundary points as time evolves. Based on an energetic
variational approach (EnVarA), a balance between the maximal dissipation
principle (MDP) and least action principle (LAP), we obtain the trajectory
equation. In turn, a numerical scheme is proposed using a convex splitting
technique, with the unique solvability (on a convex set) and the energy decay
property (in time) justified at a theoretical level. Numerical examples are
presented for cases of pure drift and drift with semi-selection. The remarkable
advantage of this method is its ability to catch the Dirac delta singularity
close to machine precision over any equidistant grid.Comment: 22 pages, 11 figures, 2 table
A BP-MF-EP Based Iterative Receiver for Joint Phase Noise Estimation, Equalization and Decoding
In this work, with combined belief propagation (BP), mean field (MF) and
expectation propagation (EP), an iterative receiver is designed for joint phase
noise (PN) estimation, equalization and decoding in a coded communication
system. The presence of the PN results in a nonlinear observation model.
Conventionally, the nonlinear model is directly linearized by using the
first-order Taylor approximation, e.g., in the state-of-the-art soft-input
extended Kalman smoothing approach (soft-in EKS). In this work, MF is used to
handle the factor due to the nonlinear model, and a second-order Taylor
approximation is used to achieve Gaussian approximation to the MF messages,
which is crucial to the low-complexity implementation of the receiver with BP
and EP. It turns out that our approximation is more effective than the direct
linearization in the soft-in EKS with similar complexity, leading to
significant performance improvement as demonstrated by simulation results.Comment: 5 pages, 3 figures, Resubmitted to IEEE Signal Processing Letter
Two-dimensional Massless Dirac Fermions in Antiferromagnetic AFe2As2 (A = Ba, Sr)
We report infrared studies of AFeAs (A = Ba, Sr), two
representative parent compounds of iron-arsenide superconductors, at magnetic
fields (B) up to 17.5 T. Optical transitions between Landau levels (LLs) were
observed in the antiferromagnetic states of these two parent compounds. Our
observation of a dependence of the LL transition energies, the
zero-energy intercepts at B = 0 T under the linear extrapolations of the
transition energies and the energy ratio ( 2.4) between the observed LL
transitions, combined with the linear band dispersions in two-dimensional (2D)
momentum space obtained by theoretical calculations, demonstrates the existence
of massless Dirac fermions in antiferromagnetic BaFeAs. More
importantly, the observed dominance of the zeroth-LL-related absorption
features and the calculated bands with extremely weak dispersions along the
momentum direction indicate that massless Dirac fermions in
BaFeAs are 2D. Furthermore, we find that the total substitution of
the barium atoms in BaFeAs by strontium atoms not only maintains 2D
massless Dirac fermions in this system, but also enhances their Fermi velocity,
which supports that the Dirac points in iron-arsenide parent compounds are
topologically protected.Comment: Magneto-infrared study, Landau level spectroscopy, DFT+DMFT
calculation
Electron doping evolution of the magnetic excitations in BaFe2-xNixAs2
We use inelastic neutron scattering (INS) spectroscopy to study the magnetic
excitations spectra throughout the Brioullion zone in electron-doped iron
pnictide superconductors BaFeNiAs with .
While the sample is near optimal superconductivity with K
and has coexisting static incommensurate magnetic order, the
samples are electron-overdoped with reduced of 14 K and 8 K,
respectively, and have no static antiferromagnetic (AF) order. In previous INS
work on undoped () and electron optimally doped () samples, the
effect of electron-doping was found to modify spin waves in the parent compound
BaFeAs below 100 meV and induce a neutron spin resonance at the
commensurate AF ordering wave vector that couples with superconductivity. While
the new data collected on the sample confirms the overall features of
the earlier work, our careful temperature dependent study of the resonance
reveals that the resonance suddenly changes its -width below similar
to that of the optimally hole-doped iron pnictides
BaKFeAs. In addition, we establish the dispersion of
the resonance and find it to change from commensurate to transversely
incommensurate with increasing energy. Upon further electron-doping to
overdoped iron pnictides with and 0.18, the resonance becomes weaker
and transversely incommensurate at all energies, while spin excitations above
100 meV are still not much affected. Our absolute spin excitation
intensity measurements throughout the Brillouin zone for
confirm the notion that the low-energy spin excitation coupling with itinerant
electron is important for superconductivity in these materials, even though the
high-energy spin excitations are weakly doping dependent.Comment: 16 pages, 16 figure
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