14,386 research outputs found
Aggregation of Affine Estimators
We consider the problem of aggregating a general collection of affine
estimators for fixed design regression. Relevant examples include some commonly
used statistical estimators such as least squares, ridge and robust least
squares estimators. Dalalyan and Salmon (2012) have established that, for this
problem, exponentially weighted (EW) model selection aggregation leads to sharp
oracle inequalities in expectation, but similar bounds in deviation were not
previously known. While results indicate that the same aggregation scheme may
not satisfy sharp oracle inequalities with high probability, we prove that a
weaker notion of oracle inequality for EW that holds with high probability.
Moreover, using a generalization of the newly introduced -aggregation scheme
we also prove sharp oracle inequalities that hold with high probability.
Finally, we apply our results to universal aggregation and show that our
proposed estimator leads simultaneously to all the best known bounds for
aggregation, including -aggregation, , with high
probability
U-Statistic Reduction: Higher-Order Accurate Risk Control and Statistical-Computational Trade-Off, with Application to Network Method-of-Moments
U-statistics play central roles in many statistical learning tools but face
the haunting issue of scalability. Significant efforts have been devoted into
accelerating computation by U-statistic reduction. However, existing results
almost exclusively focus on power analysis, while little work addresses risk
control accuracy -- comparatively, the latter requires distinct and much more
challenging techniques. In this paper, we establish the first statistical
inference procedure with provably higher-order accurate risk control for
incomplete U-statistics. The sharpness of our new result enables us to reveal
how risk control accuracy also trades off with speed for the first time in
literature, which complements the well-known variance-speed trade-off. Our
proposed general framework converts the long-standing challenge of formulating
accurate statistical inference procedures for many different designs into a
surprisingly routine task. This paper covers non-degenerate and degenerate
U-statistics, and network moments. We conducted comprehensive numerical studies
and observed results that validate our theory's sharpness. Our method also
demonstrates effectiveness on real-world data applications
Energy-Efficient Full Diversity Collaborative Unitary Space-Time Block Code Design via Unique Factorization of Signals
In this paper, a novel concept called a \textit{uniquely factorable
constellation pair} (UFCP) is proposed for the systematic design of a
noncoherent full diversity collaborative unitary space-time block code by
normalizing two Alamouti codes for a wireless communication system having two
transmitter antennas and a single receiver antenna. It is proved that such a
unitary UFCP code assures the unique identification of both channel
coefficients and transmitted signals in a noise-free case as well as full
diversity for the noncoherent maximum likelihood (ML) receiver in a noise case.
To further improve error performance, an optimal unitary UFCP code is designed
by appropriately and uniquely factorizing a pair of energy-efficient cross
quadrature amplitude modulation (QAM) constellations to maximize the coding
gain subject to a transmission bit rate constraint. After a deep investigation
of the fractional coding gain function, a technical approach developed in this
paper to maximizing the coding gain is to carefully design an energy scale to
compress the first three largest energy points in the corner of the QAM
constellations in the denominator of the objective as well as carefully design
a constellation triple forming two UFCPs, with one collaborating with the other
two so as to make the accumulated minimum Euclidean distance along the two
transmitter antennas in the numerator of the objective as large as possible and
at the same time, to avoid as many corner points of the QAM constellations with
the largest energy as possible to achieve the minimum of the numerator. In
other words, the optimal coding gain is attained by intelligent constellations
collaboration and efficient energy compression
Secure Direct Communication Based on Secret Transmitting Order of Particles
We propose the schemes of quantum secure direct communication (QSDC) based on
secret transmitting order of particles. In these protocols, the secret
transmitting order of particles ensures the security of communication, and no
secret messages are leaked even if the communication is interrupted for
security. This strategy of security for communication is also generalized to
quantum dialogue. It not only ensures the unconditional security but also
improves the efficiency of communication.Comment: To appear in Phys. Rev.
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