1,734 research outputs found
Better subset regression
To find efficient screening methods for high dimensional linear regression
models, this paper studies the relationship between model fitting and screening
performance. Under a sparsity assumption, we show that a subset that includes
the true submodel always yields smaller residual sum of squares (i.e., has
better model fitting) than all that do not in a general asymptotic setting.
This indicates that, for screening important variables, we could follow a
"better fitting, better screening" rule, i.e., pick a "better" subset that has
better model fitting. To seek such a better subset, we consider the
optimization problem associated with best subset regression. An EM algorithm,
called orthogonalizing subset screening, and its accelerating version are
proposed for searching for the best subset. Although the two algorithms cannot
guarantee that a subset they yield is the best, their monotonicity property
makes the subset have better model fitting than initial subsets generated by
popular screening methods, and thus the subset can have better screening
performance asymptotically. Simulation results show that our methods are very
competitive in high dimensional variable screening even for finite sample
sizes.Comment: 24 pages, 1 figur
A time/frequency quantum analysis of the light generated by synchronously pumped optical parametric oscillators
We present in this paper a general model for determining the quantum
properties of the light generated by a synchronously pumped optical parametric
oscillator (SPOPO) operating below threshold. This model considers time and
frequency on an equal footing, which allows us to find new quantum properties,
related for example to the carrier envelope offset (CEO) phase, and to consider
situations that are close to real experiments. We show that, in addition to
multimode squeezing in the so-called 'supermodes', the system exhibits
quadrature entanglement between frequency combs of opposite CEO phases. We have
also determined the quantum properties of the individual pulses and their
quantum correlations with the neighboring pulses. Finally, we determine the
quantum Cramer-Rao limit for an ultra-short time delay measurement using a
given number of pulses generated by the SPOPO.Comment: This is an author-created, un-copyedited version of an article
accepted for publication in New Journal of Physics. IOP Publishing Ltd is not
responsible for any errors or omissions in this version of the manuscript or
any version derived from it. The definitive publisher-authenticated version
is available online at http://stacks.iop.org/1367-2630/14/04300
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