537,568 research outputs found
Transportation cost-information inequalities and applications to random dynamical systems and diffusions
We first give a characterization of the L^1-transportation cost-information
inequality on a metric space and next find some appropriate sufficient
condition to transportation cost-information inequalities for dependent
sequences. Applications to random dynamical systems and diffusions are studied.Comment: Published by the Institute of Mathematical Statistics
(http://www.imstat.org) in the Annals of Probability
(http://www.imstat.org/aop/) at http://dx.doi.org/10.1214/00911790400000053
Consistency of maximum likelihood estimation for some dynamical systems
We consider the asymptotic consistency of maximum likelihood parameter
estimation for dynamical systems observed with noise. Under suitable conditions
on the dynamical systems and the observations, we show that maximum likelihood
parameter estimation is consistent. Our proof involves ideas from both
information theory and dynamical systems. Furthermore, we show how some
well-studied properties of dynamical systems imply the general statistical
properties related to maximum likelihood estimation. Finally, we exhibit
classical families of dynamical systems for which maximum likelihood estimation
is consistent. Examples include shifts of finite type with Gibbs measures and
Axiom A attractors with SRB measures.Comment: Published in at http://dx.doi.org/10.1214/14-AOS1259 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Maximum Fisher information in mixed state quantum systems
We deal with the maximization of classical Fisher information in a quantum
system depending on an unknown parameter. This problem has been raised by
physicists, who defined [Helstrom (1967) Phys. Lett. A 25 101-102] a quantum
counterpart of classical Fisher information, which has been found to constitute
an upper bound for classical information itself [Braunstein and Caves (1994)
Phys. Rev. Lett. 72 3439-3443]. It has then become of relevant interest among
statisticians, who investigated the relations between classical and quantum
information and derived a condition for equality in the particular case of
two-dimensional pure state systems [Barndorff-Nielsen and Gill (2000) J. Phys.
A 33 4481-4490]. In this paper we show that this condition holds even in the
more general setting of two-dimensional mixed state systems. We also derive the
expression of the maximum Fisher information achievable and its relation with
that attainable in pure states.Comment: Published by the Institute of Mathematical Statistics
(http://www.imstat.org) in the Annals of Statistics
(http://www.imstat.org/aos/) at http://dx.doi.org/10.1214/00905360400000043
Accuracy of state space collapse for earliest-deadline-first Queues
This paper presents a second-order heavy traffic analysis of a single server
queue that processes customers having deadlines using the
earliest-deadline-first scheduling policy. For such systems, referred to as
real-time queueing systems, performance is measured by the fraction of
customers who meet their deadline, rather than more traditional performance
measures, such as customer delay, queue length or server utilization. To model
such systems, one must keep track of customer lead times (the time remaining
until a customer deadline elapses) or equivalent information. This paper
reviews the earlier heavy traffic analysis of such systems that provided
approximations to the system's behavior. The main result of this paper is the
development of a second-order analysis that gives the accuracy of the
approximations and the rate of convergence of the sequence of real-time
queueing systems to its heavy traffic limit.Comment: Published at http://dx.doi.org/10.1214/105051605000000809 in the
Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute
of Mathematical Statistics (http://www.imstat.org
Statistical analysis of -nearest neighbor collaborative recommendation
Collaborative recommendation is an information-filtering technique that
attempts to present information items that are likely of interest to an
Internet user. Traditionally, collaborative systems deal with situations with
two types of variables, users and items. In its most common form, the problem
is framed as trying to estimate ratings for items that have not yet been
consumed by a user. Despite wide-ranging literature, little is known about the
statistical properties of recommendation systems. In fact, no clear
probabilistic model even exists which would allow us to precisely describe the
mathematical forces driving collaborative filtering. To provide an initial
contribution to this, we propose to set out a general sequential stochastic
model for collaborative recommendation. We offer an in-depth analysis of the
so-called cosine-type nearest neighbor collaborative method, which is one of
the most widely used algorithms in collaborative filtering, and analyze its
asymptotic performance as the number of users grows. We establish consistency
of the procedure under mild assumptions on the model. Rates of convergence and
examples are also provided.Comment: Published in at http://dx.doi.org/10.1214/09-AOS759 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Quantum discord is Bohr's notion of non-mechanical disturbance introduced in his answer to EPR
By rigorously formalizing the Einstein-Podolsky-Rosen (EPR) argument, and
Bohr's reply, one can appreciate that both arguments were technically correct.
Their opposed conclusions about the completeness of quantum mechanics hinged
upon an explicit difference in their criteria for when a measurement on Alice's
system can be regarded as not disturbing Bob's system. The EPR criteria allow
their conclusion (incompletness) to be reached by establishing the physical
reality of just a single observable (not a conjugate pair and ), but
I show that Bohr's definition of disturbance prevents the EPR chain of
reasoning from establishing even this. Moreover, I show that Bohr's definition
is intimately related to the asymmetric concept of quantum discord from quantum
information theory: if and only if the joint state has no Alice-discord, she
can measure any observable without disturbing (in Bohr's sense) Bob's system.
Discord can be present even when systems are unentangled, and this has
implications for our understanding of the historical development of notions of
quantum nonlocality.Comment: 17 pages. Accepted for publication in Annals of Physics on 4th May
201
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