826 research outputs found
The worst-case data-generating probability measure in statistical learning
The worst-case data-generating (WCDG) probability measure is introduced as a tool for characterizing the generalization capabilities of machine learning algorithms. Such a WCDG probability measure is shown to be the unique solution to two different optimization problems: (a) The maximization of the expected loss over the set of probability measures on the datasets whose relative entropy with respect to a reference measure is not larger than a given threshold; and (b) The maximization of the expected loss with regularization by relative entropy with respect to the reference measure. Such a reference measure can be interpreted as a prior on the datasets. The WCDG cumulants are finite and bounded in terms of the cumulants of the reference measure. To analyze the concentration of the expected empirical induced by the WCDG probability measure, the notion of (,δ)-robustness of models is introduced. Closed-form expressions are presented for the sensitivity of the expected loss for a fixed model. These tools result in the characterization of a novel expression for the generalization error of arbitrary machine learning algorithms. This exact expression is provided in terms of the WCDG probability measure and leads to an upper bound that is equal to the sum of the mutual information and the lautum information between the models and the datasets, up to a constant factor. This upper bound is achieved by a Gibbs algorithm. This finding reveals that an exploration into the generalization error of the Gibbs algorithm facilitates the derivation of overarching insights applicable to any machine learning algorithm
Inhomogeneous magnetism in La-doped CaMnO3. (I) Nanometric-scale spin clusters and long-range spin canting
Neutron measurements on Ca{1-x}La{x}MnO3 (0.00 <= x <= 0.20) reveal the
development of a liquid-like spatial distribution of magnetic droplets of
average size ~10 Angstroms, the concentration of which is proportional to x
(one cluster per ~60 doped electrons). In addition, a long-range ordered
ferromagnetic component is observed for ~0.05 < x < ~0.14. This component is
perpendicularly coupled to the simple G-type antiferromagnetic (G-AFM)
structure of the undoped compound, which is a signature of a G-AFM + FM
spin-canted state. The possible relationship between cluster formation and the
stabilization of a long-range spin-canting for intermediate doping is
discussed.Comment: Submitted to Physical Review
Spin-Charge Separation in the Model: Magnetic and Transport Anomalies
A real spin-charge separation scheme is found based on a saddle-point state
of the model. In the one-dimensional (1D) case, such a saddle-point
reproduces the correct asymptotic correlations at the strong-coupling
fixed-point of the model. In the two-dimensional (2D) case, the transverse
gauge field confining spinon and holon is shown to be gapped at {\em finite
doping} so that a spin-charge deconfinement is obtained for its first time in
2D. The gap in the gauge fluctuation disappears at half-filling limit, where a
long-range antiferromagnetic order is recovered at zero temperature and spinons
become confined. The most interesting features of spin dynamics and transport
are exhibited at finite doping where exotic {\em residual} couplings between
spin and charge degrees of freedom lead to systematic anomalies with regard to
a Fermi-liquid system. In spin dynamics, a commensurate antiferromagnetic
fluctuation with a small, doping-dependent energy scale is found, which is
characterized in momentum space by a Gaussian peak at (, ) with
a doping-dependent width (, is the doping
concentration). This commensurate magnetic fluctuation contributes a
non-Korringa behavior for the NMR spin-lattice relaxation rate. There also
exits a characteristic temperature scale below which a pseudogap behavior
appears in the spin dynamics. Furthermore, an incommensurate magnetic
fluctuation is also obtained at a {\em finite} energy regime. In transport, a
strong short-range phase interference leads to an effective holon Lagrangian
which can give rise to a series of interesting phenomena including linear-
resistivity and Hall-angle. We discuss the striking similarities of these
theoretical features with those found in the high- cuprates and give aComment: 70 pages, RevTex, hard copies of 7 figures available upon request;
minor revisions in the text and references have been made; To be published in
July 1 issue of Phys. Rev. B52, (1995
The pole in
Using a sample of 58 million events recorded in the BESII detector,
the decay is studied. There are conspicuous
and signals. At low mass, a large
broad peak due to the is observed, and its pole position is determined
to be - MeV from the mean of six analyses.
The errors are dominated by the systematic errors.Comment: 15 pages, 6 figures, submitted to PL
Partial Wave Analysis of
BES data on are presented. The
contribution peaks strongly near threshold. It is fitted with a
broad resonance with mass MeV, width MeV. A broad resonance peaking at 2020 MeV is also required
with width MeV. There is further evidence for a component
peaking at 2.55 GeV. The non- contribution is close to phase
space; it peaks at 2.6 GeV and is very different from .Comment: 15 pages, 6 figures, 1 table, Submitted to PL
Study of
New data are presented on from a sample of 58M
events in the upgraded BES II detector at the BEPC. There is a
conspicuous signal for and a peak at higher mass which
may be fitted with . From a combined analysis with
data, the branching ratio
is at the 95%
confidence level.Comment: 11 pages, 5 figures. Submitted to Phys. Lett.
Measurements of the observed cross sections for exclusive light hadron production in e^+e^- annihilation at \sqrt{s}= 3.773 and 3.650 GeV
By analyzing the data sets of 17.3 pb taken at GeV
and 6.5 pb taken at GeV with the BESII detector at the
BEPC collider, we have measured the observed cross sections for 12 exclusive
light hadron final states produced in annihilation at the two energy
points. We have also set the upper limits on the observed cross sections and
the branching fractions for decay to these final states at 90%
C.L.Comment: 8 pages, 5 figur
Search for the Rare Decays J/Psi --> Ds- e+ nu_e, J/Psi --> D- e+ nu_e, and J/Psi --> D0bar e+ e-
We report on a search for the decays J/Psi --> Ds- e+ nu_e + c.c., J/Psi -->
D- e+ nu_e + c.c., and J/Psi --> D0bar e+ e- + c.c. in a sample of 5.8 * 10^7
J/Psi events collected with the BESII detector at the BEPC. No excess of signal
above background is observed, and 90% confidence level upper limits on the
branching fractions are set: B(J/Psi --> Ds- e+ nu_e + c.c.)<4.8*10^-5, B(J/Psi
--> D- e+ nu_e + c.c.) D0bar e+ e- + c.c.)<1.1*10^-5Comment: 10 pages, 4 figure
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