11,026 research outputs found
How priors of initial hyperparameters affect Gaussian process regression models
The hyperparameters in Gaussian process regression (GPR) model with a
specified kernel are often estimated from the data via the maximum marginal
likelihood. Due to the non-convexity of marginal likelihood with respect to the
hyperparameters, the optimization may not converge to the global maxima. A
common approach to tackle this issue is to use multiple starting points
randomly selected from a specific prior distribution. As a result the choice of
prior distribution may play a vital role in the predictability of this
approach. However, there exists little research in the literature to study the
impact of the prior distributions on the hyperparameter estimation and the
performance of GPR. In this paper, we provide the first empirical study on this
problem using simulated and real data experiments. We consider different types
of priors for the initial values of hyperparameters for some commonly used
kernels and investigate the influence of the priors on the predictability of
GPR models. The results reveal that, once a kernel is chosen, different priors
for the initial hyperparameters have no significant impact on the performance
of GPR prediction, despite that the estimates of the hyperparameters are very
different to the true values in some cases
Constructing A Flexible Likelihood Function For Spectroscopic Inference
We present a modular, extensible likelihood framework for spectroscopic
inference based on synthetic model spectra. The subtraction of an imperfect
model from a continuously sampled spectrum introduces covariance between
adjacent datapoints (pixels) into the residual spectrum. For the high
signal-to-noise data with large spectral range that is commonly employed in
stellar astrophysics, that covariant structure can lead to dramatically
underestimated parameter uncertainties (and, in some cases, biases). We
construct a likelihood function that accounts for the structure of the
covariance matrix, utilizing the machinery of Gaussian process kernels. This
framework specifically address the common problem of mismatches in model
spectral line strengths (with respect to data) due to intrinsic model
imperfections (e.g., in the atomic/molecular databases or opacity
prescriptions) by developing a novel local covariance kernel formalism that
identifies and self-consistently downweights pathological spectral line
"outliers." By fitting many spectra in a hierarchical manner, these local
kernels provide a mechanism to learn about and build data-driven corrections to
synthetic spectral libraries. An open-source software implementation of this
approach is available at http://iancze.github.io/Starfish, including a
sophisticated probabilistic scheme for spectral interpolation when using model
libraries that are sparsely sampled in the stellar parameters. We demonstrate
some salient features of the framework by fitting the high resolution -band
spectrum of WASP-14, an F5 dwarf with a transiting exoplanet, and the moderate
resolution -band spectrum of Gliese 51, an M5 field dwarf.Comment: Accepted to ApJ. Incorporated referees' comments. New figures 1, 8,
10, 12, and 14. Supplemental website: http://iancze.github.io/Starfish
Brain MRI Super Resolution Using 3D Deep Densely Connected Neural Networks
Magnetic resonance image (MRI) in high spatial resolution provides detailed
anatomical information and is often necessary for accurate quantitative
analysis. However, high spatial resolution typically comes at the expense of
longer scan time, less spatial coverage, and lower signal to noise ratio (SNR).
Single Image Super-Resolution (SISR), a technique aimed to restore
high-resolution (HR) details from one single low-resolution (LR) input image,
has been improved dramatically by recent breakthroughs in deep learning. In
this paper, we introduce a new neural network architecture, 3D Densely
Connected Super-Resolution Networks (DCSRN) to restore HR features of
structural brain MR images. Through experiments on a dataset with 1,113
subjects, we demonstrate that our network outperforms bicubic interpolation as
well as other deep learning methods in restoring 4x resolution-reduced images.Comment: Accepted by ISBI'1
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