13,993 research outputs found
Effective Warm Start for the Online Actor-Critic Reinforcement Learning based mHealth Intervention
Online reinforcement learning (RL) is increasingly popular for the
personalized mobile health (mHealth) intervention. It is able to personalize
the type and dose of interventions according to user's ongoing statuses and
changing needs. However, at the beginning of online learning, there are usually
too few samples to support the RL updating, which leads to poor performances. A
delay in good performance of the online learning algorithms can be especially
detrimental in the mHealth, where users tend to quickly disengage with the
mHealth app. To address this problem, we propose a new online RL methodology
that focuses on an effective warm start. The main idea is to make full use of
the data accumulated and the decision rule achieved in a former study. As a
result, we can greatly enrich the data size at the beginning of online learning
in our method. Such case accelerates the online learning process for new users
to achieve good performances not only at the beginning of online learning but
also through the whole online learning process. Besides, we use the decision
rules achieved in a previous study to initialize the parameter in our online RL
model for new users. It provides a good initialization for the proposed online
RL algorithm. Experiment results show that promising improvements have been
achieved by our method compared with the state-of-the-art method
Second-order asymptotics for convolution of distributions with light tails
In this paper, asymptotic behavior of convolution of distributions belonging
to two subclasses of distributions with exponential tails are considered,
respectively. The precise second-order tail asymptotics of the convolutions are
derived under the condition of second-order regular variation.Comment: 22 page
Asymptotics and statistical inferences on independent and non-identically distributed bivariate Gaussian triangular arrays
In this paper, we establish the first and the second-order asymptotics of
distributions of normalized maxima of independent and non-identically
distributed bivariate Gaussian triangular arrays, where each vector of the
th row follows from a bivariate Gaussian distribution with correlation
coefficient being a monotone continuous function of . Furthermore,
parametric inference for this unknown function is studied. Some simulation
study and real data sets analysis are also presented.Comment: 19 pages, 8 figure
Dynamic Bivariate Normal Copula
Normal copula with a correlation coefficient between and is tail
independent and so it severely underestimates extreme probabilities. By letting
the correlation coefficient in a normal copula depend on the sample size,
H\"usler and Reiss (1989) showed that the tail can become asymptotically
dependent. In this paper, we extend this result by deriving the limit of the
normalized maximum of independent observations, where the -th
observation follows from a normal copula with its correlation coefficient being
either a parametric or a nonparametric function of . Furthermore, both
parametric and nonparametric inference for this unknown function are studied,
which can be employed to test the condition in H\"usler and Reiss (1989). A
simulation study and real data analysis are presented too.Comment: 22pages, 4 figure
Effective field theory approach to light propagation in an external magnetic field
The recent PVLAS experiment observed the rotation of polarization and the
ellipticity when a linearly polarized laser beam passes through a transverse
magnetic field. The phenomenon cannot be explained in the conventional QED. We
attempt to accommodate the result by employing an effective theory for the
electromagnetic field alone. No new particles with a mass of order the laser
frequency or below are assumed. To quartic terms in the field strength, a
parity-violating term appears besides the two ordinary terms. The rotation of
polarization and ellipticity are computed for parity asymmetric and symmetric
experimental set-ups. While rotation occurs in an ideal asymmetric case and has
the same magnitude as the ellipticity, it disappears in a symmetric set-up like
PVLAS. This would mean that we have to appeal to some low-mass new particles
with nontrivial interactions with photons to understand the PVLAS result.Comment: 10 pages, no figure
Higher-order expansions of extremes from mixed skew-t distribution
In this paper, we study the asymptotic behaviors of the extreme of mixed
skew-t distribution. We considered limits on distribution and density of
maximum of mixed skew-t distribution under linear and power normalization, and
further derived their higher-order expansions, respectively. Examples are given
to support our findings.Comment: 24 pages,8 figure
Rates of convergence of extremes from skew normal samples
For a skew normal random sequence, convergence rates of the distribution of
its partial maximum to the Gumbel extreme value distribution are derived. The
asymptotic expansion of the distribution of the normalized maximum is given
under an optimal choice of norming constants. We find that the optimal
convergence rate of the normalized maximum to the Gumbel extreme value
distribution is proportional to
The stratified micro-randomized trial design: sample size considerations for testing nested causal effects of time-varying treatments
Technological advancements in the field of mobile devices and wearable
sensors have helped overcome obstacles in the delivery of care, making it
possible to deliver behavioral treatments anytime and anywhere. Increasingly
the delivery of these treatments is triggered by predictions of risk or
engagement which may have been impacted by prior treatments. Furthermore the
treatments are often designed to have an impact on individuals over a span of
time during which subsequent treatments may be provided.
Here we discuss our work on the design of a mobile health smoking cessation
experimental study in which two challenges arose. First the randomizations to
treatment should occur at times of stress and second the outcome of interest
accrues over a period that may include subsequent treatment. To address these
challenges we develop the "stratified micro-randomized trial," in which each
individual is randomized among treatments at times determined by predictions
constructed from outcomes to prior treatment and with randomization
probabilities depending on these outcomes. We define both conditional and
marginal proximal treatment effects. Depending on the scientific goal these
effects may be defined over a period of time during which subsequent treatments
may be provided. We develop a primary analysis method and associated sample
size formulae for testing these effects
Sample Size Calculations for Micro-randomized Trials in mHealth
The use and development of mobile interventions are experiencing rapid
growth. In "just-in-time" mobile interventions, treatments are provided via a
mobile device and they are intended to help an individual make healthy
decisions "in the moment," and thus have a proximal, near future impact.
Currently the development of mobile interventions is proceeding at a much
faster pace than that of associated data science methods. A first step toward
developing data-based methods is to provide an experimental design for testing
the proximal effects of these just-in-time treatments. In this paper, we
propose a "micro-randomized" trial design for this purpose. In a
micro-randomized trial, treatments are sequentially randomized throughout the
conduct of the study, with the result that each participant may be randomized
at the 100s or 1000s of occasions at which a treatment might be provided.
Further, we develop a test statistic for assessing the proximal effect of a
treatment as well as an associated sample size calculator. We conduct
simulation evaluations of the sample size calculator in various settings. Rules
of thumb that might be used in designing a micro-randomized trial are
discussed. This work is motivated by our collaboration on the HeartSteps mobile
application designed to increase physical activity.Comment: 29 pages, 5 figures, 18 table
Long-distance continuous-variable quantum key distribution using non-Gaussian state-discrimination detection
We propose a long-distance continuous-variable quantum key distribution
(CVQKD) with four-state protocol using non-Gaussian state-discrimination
detection. A photon subtraction operation, which is deployed at the
transmitter, is used for splitting the signal required for generating the
non-Gaussian operation to lengthen the maximum transmission distance of CVQKD.
Whereby an improved state-discrimination detector, which can be deemed as an
optimized quantum measurement that allows the discrimination of nonorthogonal
coherent states beating the standard quantum limit, is applied at the receiver
to codetermine the measurement result with conventional coherent detector. By
tactfully exploiting multiplexing technique, the resulting signals can be
simultaneously transmitted through an untrusted quantum channel, and
subsequently sent to the state-discrimination detector and coherent detector
respectively. Security analysis shows that the proposed scheme can lengthen the
maximum transmission distance up to hundreds of kilometers. Furthermore, by
taking finite-size effect and composable security into account we obtain the
tightest bound of the secure distance, which is more practical than that
obtained in the asymptotic limit.Comment: 13 pages, 9 figure
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