134 research outputs found
Identifying Sources and Sinks in the Presence of Multiple Agents with Gaussian Process Vector Calculus
In systems of multiple agents, identifying the cause of observed agent
dynamics is challenging. Often, these agents operate in diverse, non-stationary
environments, where models rely on hand-crafted environment-specific features
to infer influential regions in the system's surroundings. To overcome the
limitations of these inflexible models, we present GP-LAPLACE, a technique for
locating sources and sinks from trajectories in time-varying fields. Using
Gaussian processes, we jointly infer a spatio-temporal vector field, as well as
canonical vector calculus operations on that field. Notably, we do this from
only agent trajectories without requiring knowledge of the environment, and
also obtain a metric for denoting the significance of inferred causal features
in the environment by exploiting our probabilistic method. To evaluate our
approach, we apply it to both synthetic and real-world GPS data, demonstrating
the applicability of our technique in the presence of multiple agents, as well
as its superiority over existing methods.Comment: KDD '18 Proceedings of the 24th ACM SIGKDD International Conference
on Knowledge Discovery & Data Mining, Pages 1254-1262, 9 pages, 5 figures,
conference submission, University of Oxford. arXiv admin note: text overlap
with arXiv:1709.0235
Marginal likelihoods in phylogenetics: a review of methods and applications
By providing a framework of accounting for the shared ancestry inherent to
all life, phylogenetics is becoming the statistical foundation of biology. The
importance of model choice continues to grow as phylogenetic models continue to
increase in complexity to better capture micro and macroevolutionary processes.
In a Bayesian framework, the marginal likelihood is how data update our prior
beliefs about models, which gives us an intuitive measure of comparing model
fit that is grounded in probability theory. Given the rapid increase in the
number and complexity of phylogenetic models, methods for approximating
marginal likelihoods are increasingly important. Here we try to provide an
intuitive description of marginal likelihoods and why they are important in
Bayesian model testing. We also categorize and review methods for estimating
marginal likelihoods of phylogenetic models, highlighting several recent
methods that provide well-behaved estimates. Furthermore, we review some
empirical studies that demonstrate how marginal likelihoods can be used to
learn about models of evolution from biological data. We discuss promising
alternatives that can complement marginal likelihoods for Bayesian model
choice, including posterior-predictive methods. Using simulations, we find one
alternative method based on approximate-Bayesian computation (ABC) to be
biased. We conclude by discussing the challenges of Bayesian model choice and
future directions that promise to improve the approximation of marginal
likelihoods and Bayesian phylogenetics as a whole.Comment: 33 pages, 3 figure
An Ensemble of Bayesian Neural Networks for Exoplanetary Atmospheric Retrieval
Machine learning is now used in many areas of astrophysics, from detecting
exoplanets in Kepler transit signals to removing telescope systematics. Recent
work demonstrated the potential of using machine learning algorithms for
atmospheric retrieval by implementing a random forest to perform retrievals in
seconds that are consistent with the traditional, computationally-expensive
nested-sampling retrieval method. We expand upon their approach by presenting a
new machine learning model, \texttt{plan-net}, based on an ensemble of Bayesian
neural networks that yields more accurate inferences than the random forest for
the same data set of synthetic transmission spectra. We demonstrate that an
ensemble provides greater accuracy and more robust uncertainties than a single
model. In addition to being the first to use Bayesian neural networks for
atmospheric retrieval, we also introduce a new loss function for Bayesian
neural networks that learns correlations between the model outputs.
Importantly, we show that designing machine learning models to explicitly
incorporate domain-specific knowledge both improves performance and provides
additional insight by inferring the covariance of the retrieved atmospheric
parameters. We apply \texttt{plan-net} to the Hubble Space Telescope Wide Field
Camera 3 transmission spectrum for WASP-12b and retrieve an isothermal
temperature and water abundance consistent with the literature. We highlight
that our method is flexible and can be expanded to higher-resolution spectra
and a larger number of atmospheric parameters
Direct Amortized Likelihood Ratio Estimation
We introduce a new amortized likelihood ratio estimator for likelihood-free
simulation-based inference (SBI). Our estimator is simple to train and
estimates the likelihood ratio using a single forward pass of the neural
estimator. Our approach directly computes the likelihood ratio between two
competing parameter sets which is different from the previous approach of
comparing two neural network output values. We refer to our model as the direct
neural ratio estimator (DNRE). As part of introducing the DNRE, we derive a
corresponding Monte Carlo estimate of the posterior. We benchmark our new ratio
estimator and compare to previous ratio estimators in the literature. We show
that our new ratio estimator often outperforms these previous approaches. As a
further contribution, we introduce a new derivative estimator for likelihood
ratio estimators that enables us to compare likelihood-free Hamiltonian Monte
Carlo (HMC) with random-walk Metropolis-Hastings (MH). We show that HMC is
equally competitive, which has not been previously shown. Finally, we include a
novel real-world application of SBI by using our neural ratio estimator to
design a quadcopter. Code is available at https://github.com/SRI-CSL/dnre.Comment: 12 Pages, 10 Figures, GitHub: https://github.com/SRI-CSL/dnr
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