18,328 research outputs found
EigenGP: Gaussian Process Models with Adaptive Eigenfunctions
Gaussian processes (GPs) provide a nonparametric representation of functions.
However, classical GP inference suffers from high computational cost for big
data. In this paper, we propose a new Bayesian approach, EigenGP, that learns
both basis dictionary elements--eigenfunctions of a GP prior--and prior
precisions in a sparse finite model. It is well known that, among all
orthogonal basis functions, eigenfunctions can provide the most compact
representation. Unlike other sparse Bayesian finite models where the basis
function has a fixed form, our eigenfunctions live in a reproducing kernel
Hilbert space as a finite linear combination of kernel functions. We learn the
dictionary elements--eigenfunctions--and the prior precisions over these
elements as well as all the other hyperparameters from data by maximizing the
model marginal likelihood. We explore computational linear algebra to simplify
the gradient computation significantly. Our experimental results demonstrate
improved predictive performance of EigenGP over alternative sparse GP methods
as well as relevance vector machine.Comment: Accepted by IJCAI 201
Progenitor delay-time distribution of short gamma-ray bursts: Constraints from observations
Context. The progenitors of short gamma-ray bursts (SGRBs) have not yet been
well identified. The most popular model is the merger of compact object
binaries (NS-NS/NS-BH). However, other progenitor models cannot be ruled out.
The delay-time distribution of SGRB progenitors, which is an important property
to constrain progenitor models, is still poorly understood. Aims. We aim to
better constrain the luminosity function of SGRBs and the delay-time
distribution of their progenitors with newly discovered SGRBs. Methods. We
present a low-contamination sample of 16 Swift SGRBs that is better defined by
a duration shorter than 0.8 s. By using this robust sample and by combining a
self-consistent star formation model with various models for the distribution
of time delays, the redshift distribution of SGRBs is calculated and then
compared to the observational data. Results. We find that the power-law delay
distribution model is disfavored and that only the lognormal delay distribution
model with the typical delay tau >= 3 Gyr is consistent with the data.
Comparing Swift SGRBs with T90 > 0.8 s to our robust sample (T90 < 0.8 s), we
find a significant difference in the time delays between these two samples.
Conclusions. Our results show that the progenitors of SGRBs are dominated by
relatively long-lived systems (tau >= 3 Gyr), which contrasts the results found
for Type Ia supernovae. We therefore conclude that primordial NS-NS systems are
not favored as the dominant SGRB progenitors. Alternatively, dynamically formed
NS-NS/BH and primordial NS-BH systems with average delays longer than 5 Gyr may
contribute a significant fraction to the overall SGRB progenitors.Comment: 8 pages, 6 figures, Astron. Astrophys. in pres
Spatial Variational Auto-Encoding via Matrix-Variate Normal Distributions
The key idea of variational auto-encoders (VAEs) resembles that of
traditional auto-encoder models in which spatial information is supposed to be
explicitly encoded in the latent space. However, the latent variables in VAEs
are vectors, which can be interpreted as multiple feature maps of size 1x1.
Such representations can only convey spatial information implicitly when
coupled with powerful decoders. In this work, we propose spatial VAEs that use
feature maps of larger size as latent variables to explicitly capture spatial
information. This is achieved by allowing the latent variables to be sampled
from matrix-variate normal (MVN) distributions whose parameters are computed
from the encoder network. To increase dependencies among locations on latent
feature maps and reduce the number of parameters, we further propose spatial
VAEs via low-rank MVN distributions. Experimental results show that the
proposed spatial VAEs outperform original VAEs in capturing rich structural and
spatial information.Comment: Accepted by SDM2019. Code is publicly available at
https://github.com/divelab/sva
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