2,228 research outputs found
Communication Lower Bounds for Statistical Estimation Problems via a Distributed Data Processing Inequality
We study the tradeoff between the statistical error and communication cost of
distributed statistical estimation problems in high dimensions. In the
distributed sparse Gaussian mean estimation problem, each of the machines
receives data points from a -dimensional Gaussian distribution with
unknown mean which is promised to be -sparse. The machines
communicate by message passing and aim to estimate the mean . We
provide a tight (up to logarithmic factors) tradeoff between the estimation
error and the number of bits communicated between the machines. This directly
leads to a lower bound for the distributed \textit{sparse linear regression}
problem: to achieve the statistical minimax error, the total communication is
at least , where is the number of observations that
each machine receives and is the ambient dimension. These lower results
improve upon [Sha14,SD'14] by allowing multi-round iterative communication
model. We also give the first optimal simultaneous protocol in the dense case
for mean estimation.
As our main technique, we prove a \textit{distributed data processing
inequality}, as a generalization of usual data processing inequalities, which
might be of independent interest and useful for other problems.Comment: To appear at STOC 2016. Fixed typos in theorem 4.5 and incorporated
reviewers' suggestion
Delay differential equations with Hill's type growth rate and linear harvesting
AbstractFor the equation, N˙(t)=r(t)N(t)1+[N(t)]γ−b(t)N(t)−a(t)N(g(t)),we obtain the following results: boundedness of all positive solutions, extinction, and persistence conditions. The proofs employ recent results in the theory of linear delay equations with positive and negative coefficients
Bohl-Perron type stability theorems for linear difference equations with infinite delay
Relation between two properties of linear difference equations with infinite
delay is investigated: (i) exponential stability, (ii) \l^p-input
\l^q-state stability (sometimes is called Perron's property). The latter
means that solutions of the non-homogeneous equation with zero initial data
belong to \l^q when non-homogeneous terms are in \l^p. It is assumed that
at each moment the prehistory (the sequence of preceding states) belongs to
some weighted \l^r-space with an exponentially fading weight (the phase
space). Our main result states that (i) (ii) whenever and a certain boundedness condition on coefficients is
fulfilled. This condition is sharp and ensures that, to some extent,
exponential and \l^p-input \l^q-state stabilities does not depend on the
choice of a phase space and parameters and , respectively. \l^1-input
\l^\infty-state stability corresponds to uniform stability. We provide some
evidence that similar criteria should not be expected for non-fading memory
spaces.Comment: To be published in Journal of Difference Equations and Application
ASTRO Journals' Data Sharing Policy and Recommended Best Practices.
Transparency, openness, and reproducibility are important characteristics in scientific publishing. Although many researchers embrace these characteristics, data sharing has yet to become common practice. Nevertheless, data sharing is becoming an increasingly important topic among societies, publishers, researchers, patient advocates, and funders, especially as it pertains to data from clinical trials. In response, ASTRO developed a data policy and guide to best practices for authors submitting to its journals. ASTRO's data sharing policy is that authors should indicate, in data availability statements, if the data are being shared and if so, how the data may be accessed
Fixed Points of Hopfield Type Neural Networks
The set of the fixed points of the Hopfield type network is under
investigation. The connection matrix of the network is constructed according to
the Hebb rule from the set of memorized patterns which are treated as distorted
copies of the standard-vector. It is found that the dependence of the set of
the fixed points on the value of the distortion parameter can be described
analytically. The obtained results are interpreted in the terms of neural
networks and the Ising model.Comment: RevTEX, 19 pages, 2 Postscript figures, the full version of the
earler brief report (cond-mat/9901251
On algebraic integrability of the deformed elliptic Calogero--Moser problem
Algebraic integrability of the elliptic Calogero--Moser quantum problem
related to the deformed root systems \pbf{A_{2}(2)} is proved. Explicit
formulae for integrals are found
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