3,787 research outputs found
Modelling Spatial Compositional Data: Reconstructions of past land cover and uncertainties
In this paper, we construct a hierarchical model for spatial compositional
data, which is used to reconstruct past land-cover compositions (in terms of
coniferous forest, broadleaved forest, and unforested/open land) for five time
periods during the past years over Europe. The model consists of a
Gaussian Markov Random Field (GMRF) with Dirichlet observations. A block
updated Markov chain Monte Carlo (MCMC), including an adaptive Metropolis
adjusted Langevin step, is used to estimate model parameters. The sparse
precision matrix in the GMRF provides computational advantages leading to a
fast MCMC algorithm. Reconstructions are obtained by combining pollen-based
estimates of vegetation cover at a limited number of locations with scenarios
of past deforestation and output from a dynamic vegetation model. To evaluate
uncertainties in the predictions a novel way of constructing joint confidence
regions for the entire composition at each prediction location is proposed. The
hierarchical model's ability to reconstruct past land cover is evaluated
through cross validation for all time periods, and by comparing reconstructions
for the recent past to a present day European forest map. The evaluation
results are promising and the model is able to capture known structures in past
land-cover compositions
Robust Linear Spectral Unmixing using Anomaly Detection
This paper presents a Bayesian algorithm for linear spectral unmixing of
hyperspectral images that accounts for anomalies present in the data. The model
proposed assumes that the pixel reflectances are linear mixtures of unknown
endmembers, corrupted by an additional nonlinear term modelling anomalies and
additive Gaussian noise. A Markov random field is used for anomaly detection
based on the spatial and spectral structures of the anomalies. This allows
outliers to be identified in particular regions and wavelengths of the data
cube. A Bayesian algorithm is proposed to estimate the parameters involved in
the model yielding a joint linear unmixing and anomaly detection algorithm.
Simulations conducted with synthetic and real hyperspectral images demonstrate
the accuracy of the proposed unmixing and outlier detection strategy for the
analysis of hyperspectral images
Deep Exponential Families
We describe \textit{deep exponential families} (DEFs), a class of latent
variable models that are inspired by the hidden structures used in deep neural
networks. DEFs capture a hierarchy of dependencies between latent variables,
and are easily generalized to many settings through exponential families. We
perform inference using recent "black box" variational inference techniques. We
then evaluate various DEFs on text and combine multiple DEFs into a model for
pairwise recommendation data. In an extensive study, we show that going beyond
one layer improves predictions for DEFs. We demonstrate that DEFs find
interesting exploratory structure in large data sets, and give better
predictive performance than state-of-the-art models
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