12,580 research outputs found
Private Incremental Regression
Data is continuously generated by modern data sources, and a recent challenge
in machine learning has been to develop techniques that perform well in an
incremental (streaming) setting. In this paper, we investigate the problem of
private machine learning, where as common in practice, the data is not given at
once, but rather arrives incrementally over time.
We introduce the problems of private incremental ERM and private incremental
regression where the general goal is to always maintain a good empirical risk
minimizer for the history observed under differential privacy. Our first
contribution is a generic transformation of private batch ERM mechanisms into
private incremental ERM mechanisms, based on a simple idea of invoking the
private batch ERM procedure at some regular time intervals. We take this
construction as a baseline for comparison. We then provide two mechanisms for
the private incremental regression problem. Our first mechanism is based on
privately constructing a noisy incremental gradient function, which is then
used in a modified projected gradient procedure at every timestep. This
mechanism has an excess empirical risk of , where is the
dimensionality of the data. While from the results of [Bassily et al. 2014]
this bound is tight in the worst-case, we show that certain geometric
properties of the input and constraint set can be used to derive significantly
better results for certain interesting regression problems.Comment: To appear in PODS 201
Braidings of Tensor Spaces
Let be a braided vector space, that is, a vector space together with a
solution of the Yang--Baxter equation.
Denote . We associate to a solution
of the Yang--Baxter equation on
the tensor space . The correspondence is functorial with respect to .Comment: 10 pages, no figure
Integer quantum Hall effect for hard-core bosons and a failure of bosonic Chern-Simons mean-field theories for electrons at half-filled Landau level
Field-theoretical methods have been shown to be useful in constructing simple
effective theories for two-dimensional (2D) systems. These effective theories
are usually studied by perturbing around a mean-field approximation, so the
question whether such an approximation is meaningful arises immediately. We
here study 2D interacting electrons in a half-filled Landau level mapped onto
interacting hard-core bosons in a magnetic field. We argue that an interacting
hard-core boson system in a uniform external field such that there is one flux
quantum per particle (unit filling) exhibits an integer quantum Hall effect. As
a consequence, the mean-field approximation for mapping electrons at
half-filling to a boson system at integer filling fails.Comment: 13 pages latex with revtex. To be published in Phys. Rev.
Cosmological Model Predictions for Weak Lensing: Linear and Nonlinear Regimes
Weak lensing by large scale structure induces correlated ellipticities in the
images of distant galaxies. The two-point correlation is determined by the
matter power spectrum along the line of sight. We use the fully nonlinear
evolution of the power spectrum to compute the predicted ellipticity
correlation. We present results for different measures of the second moment for
angular scales \theta \simeq 1'-3 degrees and for alternative normalizations of
the power spectrum, in order to explore the best strategy for constraining the
cosmological parameters. Normalizing to observed cluster abundance the rms
amplitude of ellipticity within a 15' radius is \simeq 0.01 z_s^{0.6}, almost
independent of the cosmological model, with z_s being the median redshift of
background galaxies.
Nonlinear effects in the evolution of the power spectrum significantly
enhance the ellipticity for \theta < 10' -- on 1' the rms ellipticity is \simeq
0.05, which is nearly twice the linear prediction. This enhancement means that
the signal to noise for the ellipticity is only weakly increasing with angle
for 2'< \theta < 2 degrees, unlike the expectation from linear theory that it
is strongly peaked on degree scales. The scaling with cosmological parameters
also changes due to nonlinear effects. By measuring the correlations on small
(nonlinear) and large (linear) angular scales, different cosmological
parameters can be independently constrained to obtain a model independent
estimate of both power spectrum amplitude and matter density \Omega_m.
Nonlinear effects also modify the probability distribution of the ellipticity.
Using second order perturbation theory we find that over most of the range of
interest there are significant deviations from a normal distribution.Comment: 38 pages, 11 figures included. Extended discussion of observational
prospects, matches accepted version to appear in Ap
The Proton Electromagnetic Form Factor and Quark Orbital Angular Momentum
We analyze the proton electromagnetic form factor ratio
as a function of momentum transfer
within perturbative QCD. We find that the prediction for at large
momentum transfer depends on the exclusive quark wave functions, which are
unknown. For a wide range of wave functions we find that $ QF_2/F_1 \sim\
const$ at large momentum transfer, in agreement with recent JLAB data.Comment: 8 pages, 2 figures. To appear in Proceedings of the Workshop QCD
2002, IIT Kanpur, 18-22 November (2002
Association of CAG repeat loci on chromosome 22 with schizophrenia and bipolar disorder
Chromosome 22 has been implicated in schizophrenia and bipolar disorder in a number of linkage, association and cytogenetic studies. Recent evidence has also implicated CAG repeat tract expansion in these diseases. In order to explore the involvement of CAG repeats on chromosome 22 in these diseases, we have created an integrated map of all CAG repeats 5 on this chromosome together with microsatellite markers associated with these diseases using the recently completed nucleotide sequence of chromosome 22. Of the 52 CAG repeat loci identified in this manner, four of the longest repeat stretches in regions previously implicated by linkage analyses were chosen for further study. Three of the four repeat containing loci, were found in the coding region with the CAG repeats coding for glutamine and were expressed in the brain. All the loci studied showed varying degrees of polymorphism with one of the loci exhibiting two alleles of 7 and 8 CAG repeats. The 8-repeat allele at this locus was significantly overrepresented in both schizophrenia and bipolar patient groups when compared to ethnically matched controls, while alleles at the other three loci did not show any such difference. The repeat lies within a gene which shows homology to an androgen receptor related apoptosis protein in rat. We have also identified other candidate genes in the vicinity of this locus. Our results suggest that the repeats within this gene or other genes in the vicinity of this locus are likely to be implicated in bipolar disorder and schizophrenia
Ultra-Slow Light and Enhanced Nonlinear Optical Effects in a Coherently Driven Hot Atomic Gas
We report the observation of small group velocities of order 90 meters per
second, and large group delays of greater than 0.26 ms, in an optically dense
hot rubidium gas (~360 K). Media of this kind yield strong nonlinear
interactions between very weak optical fields, and very sharp spectral
features. The result is in agreement with previous studies on nonlinear
spectroscopy of dense coherent media
The approach to thermal equilibrium in quantized chaotic systems
We consider many-body quantum systems that exhibit quantum chaos, in the
sense that the observables of interest act on energy eigenstates like banded
random matrices. We study the time-dependent expectation values of these
observables, assuming that the system is in a definite (but arbitrary) pure
quantum state. We induce a probability distribution for the expectation values
by treating the zero of time as a uniformly distributed random variable. We
show explicitly that if an observable has a nonequilibrium expectation value at
some particular moment, then it is overwhelmingly likely to move towards
equilibrium, both forwards and backwards in time. For deviations from
equilibrium that are not much larger than a typical quantum or thermal
fluctuation, we find that the time dependence of the move towards equilibrium
is given by the Kubo correlation function, in agreement with Onsager's
postulate. These results are independent of the details of the system's quantum
state.Comment: 15 pages, no figures; some arguments are clarified in the revised
versio
Second Generation of Composite Fermions in the Hamiltonian Theory
In the framework of a recently developed model of interacting composite
fermions restricted to a single level, we calculate the activation gaps of a
second generation of spin-polarized composite fermions. These composite
particles consist each of a composite fermion of the first generation and a
vortex-like excitation and may be responsible for the recently observed
fractional quantum Hall states at unusual filling factors such as
nu=4/11,5/13,5/17, and 6/17. Because the gaps of composite fermions of the
second generation are found to be more than one order of magnitude smaller than
those of the first generation, these states are less visible than the usual
states observed at filling factors nu=p/(2ps+1). Their stability is discussed
in the context of a pseudopotential expansion of the composite-fermion
interaction potential.Comment: 5 pages, 3 figures; after publication in PRB, we have realized that a
factor was missing in one of the expressions; the erroneous results are now
corrected; an erratum has been sent to PR
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