1,107 research outputs found
HyperBO+: Pre-training a universal prior for Bayesian optimization with hierarchical Gaussian processes
Bayesian optimization (BO), while proved highly effective for many black-box
function optimization tasks, requires practitioners to carefully select priors
that well model their functions of interest. Rather than specifying by hand,
researchers have investigated transfer learning based methods to automatically
learn the priors, e.g. multi-task BO (Swersky et al., 2013), few-shot BO
(Wistuba and Grabocka, 2021) and HyperBO (Wang et al., 2022). However, those
prior learning methods typically assume that the input domains are the same for
all tasks, weakening their ability to use observations on functions with
different domains or generalize the learned priors to BO on different search
spaces. In this work, we present HyperBO+: a pre-training approach for
hierarchical Gaussian processes that enables the same prior to work universally
for Bayesian optimization on functions with different domains. We propose a
two-step pre-training method and analyze its appealing asymptotic properties
and benefits to BO both theoretically and empirically. On real-world
hyperparameter tuning tasks that involve multiple search spaces, we demonstrate
that HyperBO+ is able to generalize to unseen search spaces and achieves lower
regrets than competitive baselines.Comment: Full version of the workshop paper at 2022 NeurIPS Workshop on
Gaussian Processes, Spatiotemporal Modeling, and Decision-making System
Transfer Learning for Bayesian Optimization on Heterogeneous Search Spaces
Bayesian optimization (BO) is a popular black-box function optimization
method, which makes sequential decisions based on a Bayesian model, typically a
Gaussian process (GP), of the function. To ensure the quality of the model,
transfer learning approaches have been developed to automatically design GP
priors by learning from observations on "training" functions. These training
functions are typically required to have the same domain as the "test" function
(black-box function to be optimized). In this paper, we introduce MPHD, a model
pre-training method on heterogeneous domains, which uses a neural net mapping
from domain-specific contexts to specifications of hierarchical GPs. MPHD can
be seamlessly integrated with BO to transfer knowledge across heterogeneous
search spaces. Our theoretical and empirical results demonstrate the validity
of MPHD and its superior performance on challenging black-box function
optimization tasks
Emergence, Evolution and Scaling of Online Social Networks
This work was partially supported by AFOSR under Grant No. FA9550-10-1-0083, NSF under Grant No. CDI-1026710, NSF of China under Grants Nos. 61473060 and 11275003, and NBRPC under Grant No. 2010CB731403. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.Peer reviewedPublisher PD
Algebraic quantification of an active region's contribution to the solar cycle
The solar dipole moment at cycle minimum is considered to be the most
successful precursor for the amplitude of the subsequent cycle. Numerical
simulations of the surface flux transport (SFT) model are widely used to
effectively predict the dipole moment at cycle minimum. Recently an algebraic
method has been proposed to quickly predict the contribution of an active
region (AR) to the axial dipole moment at cycle minimum instead of SFT
simulations. However, the method assumes a bipolar magnetic region (BMR)
configuration of ARs. Actually most ARs are asymmetric in configuration of
opposite polarities, or have more complex configurations. Such ARs evolve
significantly differently from that of BMR approximations. We propose a
generalized algebraic method to describe the axial dipole contribution of an AR
with an arbitrary configuration, and evaluate its effectiveness compared to the
BMR-based method. We employ mathematical deductions to obtain the generalized
method. We compare the results of the generalized method with SFT simulations
of observed ARs, artificially created BMRs, and ARs with more complex
configurations. We also compare the results with that from the BMR-based
method. The generalized method is equivalent to the SFT model, and precisely
predicts the ARs' contributions to the dipole moment. The method has a much
higher computational efficiency than SFT simulations. Although the BMR-based
method has similar computational efficiency as the generalized method, it is
only accurate for symmetric bipolar ARs. The BMR-based method systematically
overestimates the dipole contributions of asymmetric bipolar ARs, and randomly
miscalculate the contributions of more complex ARs. The generalized method
provides a quick and precise quantification of an AR's contribution to the
solar cycle evolution, which paves the way for the application into the
physics-based solar cycle prediction.Comment: 9 pages, 5 figures. Accepted for publication in A&
Sunspot tilt angles revisited: Dependence on the solar cycle strength
The tilt angle of sunspot groups is crucial in the BL type dynamo. Some
studies have shown that the tilt coefficient is anti-correlated with the cycle
strength. If the anti-correlation exists, it will be shown to act as an
effective nonlinearity of the BL-type dynamo to modulate the solar cycle.
However, some studies have shown that the anti-correlation has no statistical
significance. We aim to investigate the causes behind the controversial results
of tilt angle studies and to establish whether the tilt coefficient is indeed
anti-correlated with the cycle strength. We first analyzed the tilt angles from
DPD. Based on the methods applied in previous studies, we took two criteria to
select the data, along with the linear and square-root functions to describe
Joy's law, and three methods to derive the tilt coefficients for cycles 21-24.
This allowed us to evaluate different methods based on comparisons of the
differences among the tilt coefficients and the tilt coefficient uncertainties.
Then we utilized Monte Carlo experiments to verify the results. Finally, we
extended these methods to analyze the separate hemispheric DPD data and the
tilt angle data from Kodaikanal and Mount Wilson. The tilt angles exhibit an
extremely wide scatter due to both the intrinsic mechanism for its generation
and measurement errors, for instance, the unipolar regions included in data
sets. Different methods to deal with the uncertainties are mainly responsible
for the controversial character of the previous results. The linear fit to the
tilt-latitude relation of sunspot groups with of a cycle carried
out without binning the data can minimize the effect of the tilt scatter on the
uncertainty of the tilt coefficient. Based on this method the tilt angle
coefficient is anti-correlated with the cycle strength with strong statistical
significance.Comment: 14 pages, 7 figures, 8 Tables, Accepted for publication in A&
Nuclear spectrum from projected shell model (I): allowed one-to-one transition
Nuclear spectrum and the corresponding (anti-)neutrino spectrum play
important roles in many aspects of nuclear astrophysics, particle physics,
nuclear industry and nuclear data. In this work we propose a projected shell
model (PSM) to calculate the level energies as well as the reduced one-body
transition density (ROBTD) by the Pfaffian algorithm for nuclear
decays. The calculated level energies and ROBTD are inputed to the Beta
Spectrum Generator (BSG) code to study the high precision spectrum of
allowed one-to-one transitions. When experimental level energies are adopted,
the calculated spectrum by ROBTD of the PSM deviates from the one by
the extreme simple particle evaluation of the BSG by up to , reflecting
the importance of nuclear many-body correlations. When calculated level
energies are adopted, the calculated spectrum shows sensitive
dependence on the reliability of calculated level energies. The developed
method for ROBTD by the PSM will also be useful for study of the
first-forbidden transitions, the isovector spin monopole resonance etc. in a
straightforward way
Quantum mechanical photon-count formula derived by entangled state representation
By introducing the thermo entangled state representation, we derived four new
photocount distribution formulas for a given density operator of light field.
It is shown that these new formulas, which is convenient to calculate the
photocount, can be expressed as such integrations over Laguree-Gaussian
function with characteristic function, Wigner function, Q-function, and
P-function, respectively.Comment: 5 pages, no figur
A broken "-intensity" relation caused by the evolving photosphere emission and the nature of the extraordinarily bright GRB~230307A
GRB~230307A is one of the brightest gamma-ray bursts detected so far. With
the excellent observation of GRB~230307A by Fermi-GBM, we can reveal the
details of the prompt emission evolution. As found in high-time-resolution
spectral analysis, the early low-energy spectral indices () of this
burst exceed the limit of synchrotron radiation (), and gradually
decreases with the energy flux (). A tight
correlation anyhow holds within the whole duration of the burst, where is the spectral peak energy. Such evolution pattern of and with intensity is called ``double tracking". For the relation,
we find a log Bayes factor 210 in favor of a smoothly broken power-law
function over a linear function in log-linear space. We call this particular
relation as broken ``-intensity", and interpret it as the
evolution of the ratio of thermal and non-thermal components, which is also the
evolution of the photosphere. We also show that GRB 230307A with a duration of
, if indeed at a redshift of , is likely a neutron star
merger event (i.e., it is intrinsically ``short"). Intriguingly, different from
GRB 060614 and GRB 211211A, this long event is not composed of a hard spike
followed by a soft tail, suggesting that the properties of the prompt emission
light curves are not a good tracer of the astrophysical origins of the bursts.
The other possibility of would point toward very peculiar nature of
both GRB 230307A and its late time thermal-like emission.Comment: 14 pages, 6 figures, 1 table. We have excluded the GBM instrument
pile-up time interval in the data analysis and also discussed the nature of
this even
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