2,593 research outputs found
On non-asymptotic bounds for estimation in generalized linear models with highly correlated design
We study a high-dimensional generalized linear model and penalized empirical
risk minimization with penalty. Our aim is to provide a non-trivial
illustration that non-asymptotic bounds for the estimator can be obtained
without relying on the chaining technique and/or the peeling device.Comment: Published at http://dx.doi.org/10.1214/074921707000000319 in the IMS
Lecture Notes Monograph Series
(http://www.imstat.org/publications/lecnotes.htm) by the Institute of
Mathematical Statistics (http://www.imstat.org
The Smooth-Lasso and other -penalized methods
We consider a linear regression problem in a high dimensional setting where
the number of covariates can be much larger than the sample size . In
such a situation, one often assumes sparsity of the regression vector, \textit
i.e., the regression vector contains many zero components. We propose a
Lasso-type estimator (where '' stands for quadratic)
which is based on two penalty terms. The first one is the norm of the
regression coefficients used to exploit the sparsity of the regression as done
by the Lasso estimator, whereas the second is a quadratic penalty term
introduced to capture some additional information on the setting of the
problem. We detail two special cases: the Elastic-Net , which
deals with sparse problems where correlations between variables may exist; and
the Smooth-Lasso , which responds to sparse problems where
successive regression coefficients are known to vary slowly (in some
situations, this can also be interpreted in terms of correlations between
successive variables). From a theoretical point of view, we establish variable
selection consistency results and show that achieves a
Sparsity Inequality, \textit i.e., a bound in terms of the number of non-zero
components of the 'true' regression vector. These results are provided under a
weaker assumption on the Gram matrix than the one used by the Lasso. In some
situations this guarantees a significant improvement over the Lasso.
Furthermore, a simulation study is conducted and shows that the S-Lasso
performs better than known methods as the Lasso, the
Elastic-Net , and the Fused-Lasso with respect to the
estimation accuracy. This is especially the case when the regression vector is
'smooth', \textit i.e., when the variations between successive coefficients of
the unknown parameter of the regression are small. The study also reveals that
the theoretical calibration of the tuning parameters and the one based on 10
fold cross validation imply two S-Lasso solutions with close performance
On the conditions used to prove oracle results for the Lasso
Oracle inequalities and variable selection properties for the Lasso in linear
models have been established under a variety of different assumptions on the
design matrix. We show in this paper how the different conditions and concepts
relate to each other. The restricted eigenvalue condition (Bickel et al., 2009)
or the slightly weaker compatibility condition (van de Geer, 2007) are
sufficient for oracle results. We argue that both these conditions allow for a
fairly general class of design matrices. Hence, optimality of the Lasso for
prediction and estimation holds for more general situations than what it
appears from coherence (Bunea et al, 2007b,c) or restricted isometry (Candes
and Tao, 2005) assumptions.Comment: 33 pages, 1 figur
Performance of the MIND detector at a Neutrino Factory using realistic muon reconstruction
A Neutrino Factory producing an intense beam composed of nu_e(nubar_e) and
nubar_mu(nu_mu) from muon decays has been shown to have the greatest
sensitivity to the two currently unmeasured neutrino mixing parameters,
theta_13 and delta_CP . Using the `wrong-sign muon' signal to measure nu_e to
nu_mu(nubar_e to nubar_mu) oscillations in a 50 ktonne Magnetised Iron Neutrino
Detector (MIND) sensitivity to delta_CP could be maintained down to small
values of theta_13. However, the detector efficiencies used in previous studies
were calculated assuming perfect pattern recognition. In this paper, MIND is
re-assessed taking into account, for the first time, a realistic pattern
recognition for the muon candidate. Reoptimisation of the analysis utilises a
combination of methods, including a multivariate analysis similar to the one
used in MINOS, to maintain high efficiency while suppressing backgrounds,
ensuring that the signal selection efficiency and the background levels are
comparable or better than the ones in previous analyses
Matter profile effect in neutrino factory
We point out that the matter profile effect --- the effect of matter density
fluctuation on the baseline --- is very important to estimate the parameters in
a neutrino factory with a very long baseline. To make it clear, we propose the
method of the Fourier series expansion of the matter profile. By using this
method, we can take account of both the matter profile effect and its
ambiguity. For very long baseline experiment, such as L=7332km, in the analysis
of the oscillation phenomena we need to introduce a new parameter ---
the Fourier coefficient of the matter profile --- as a theoretical parameter to
deal with the matter profile effects.Comment: 21 pages, 15 figure
Including Limited Partners in the Diversity Jurisdiction Analysis
This paper presents the results of the Dynamic Pricing Challenge, held on the occasion of the 17th INFORMS Revenue Management and Pricing Section Conference on June 29–30, 2017 in Amsterdam, The Netherlands. For this challenge, participants submitted algorithms for pricing and demand learning of which the numerical performance was analyzed in simulated market environments. This allows consideration of market dynamics that are not analytically tractable or can not be empirically analyzed due to practical complications. Our findings implicate that the relative performance of algorithms varies substantially across different market dynamics, which confirms the intrinsic complexity of pricing and learning in the presence of competition
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