7,176 research outputs found
Bayesian exponential family projections for coupled data sources
Exponential family extensions of principal component analysis (EPCA) have received a considerable amount of attention in recent years, demonstrating the growing need for basic modeling tools that do not assume the squared loss or Gaussian distribution. We extend the EPCA model toolbox by presenting the first exponential family multi-view learning methods of the partial least squares and canonical correlation analysis, based on a unified representation of EPCA as matrix factorization of the natural parameters of exponential family. The models are based on a new family of priors that are generally usable for all such factorizations. We also introduce new inference strategies, and demonstrate how the methods outperform earlier ones when the Gaussianity assumption does not hold
Bayesian Inference on Matrix Manifolds for Linear Dimensionality Reduction
We reframe linear dimensionality reduction as a problem of Bayesian inference
on matrix manifolds. This natural paradigm extends the Bayesian framework to
dimensionality reduction tasks in higher dimensions with simpler models at
greater speeds. Here an orthogonal basis is treated as a single point on a
manifold and is associated with a linear subspace on which observations vary
maximally. Throughout this paper, we employ the Grassmann and Stiefel manifolds
for various dimensionality reduction problems, explore the connection between
the two manifolds, and use Hybrid Monte Carlo for posterior sampling on the
Grassmannian for the first time. We delineate in which situations either
manifold should be considered. Further, matrix manifold models are used to
yield scientific insight in the context of cognitive neuroscience, and we
conclude that our methods are suitable for basic inference as well as accurate
prediction.Comment: All datasets and computer programs are publicly available at
http://www.ics.uci.edu/~babaks/Site/Codes.htm
Calibrating an ice sheet model using high-dimensional binary spatial data
Rapid retreat of ice in the Amundsen Sea sector of West Antarctica may cause
drastic sea level rise, posing significant risks to populations in low-lying
coastal regions. Calibration of computer models representing the behavior of
the West Antarctic Ice Sheet is key for informative projections of future sea
level rise. However, both the relevant observations and the model output are
high-dimensional binary spatial data; existing computer model calibration
methods are unable to handle such data. Here we present a novel calibration
method for computer models whose output is in the form of binary spatial data.
To mitigate the computational and inferential challenges posed by our approach,
we apply a generalized principal component based dimension reduction method. To
demonstrate the utility of our method, we calibrate the PSU3D-ICE model by
comparing the output from a 499-member perturbed-parameter ensemble with
observations from the Amundsen Sea sector of the ice sheet. Our methods help
rigorously characterize the parameter uncertainty even in the presence of
systematic data-model discrepancies and dependence in the errors. Our method
also helps inform environmental risk analyses by contributing to improved
projections of sea level rise from the ice sheets
How are emergent constraints quantifying uncertainty and what do they leave behind?
The use of emergent constraints to quantify uncertainty for key policy
relevant quantities such as Equilibrium Climate Sensitivity (ECS) has become
increasingly widespread in recent years. Many researchers, however, claim that
emergent constraints are inappropriate or even under-report uncertainty. In
this paper we contribute to this discussion by examining the emergent
constraints methodology in terms of its underpinning statistical assumptions.
We argue that the existing frameworks are based on indefensible assumptions,
then show how weakening them leads to a more transparent Bayesian framework
wherein hitherto ignored sources of uncertainty, such as how reality might
differ from models, can be quantified. We present a guided framework for the
quantification of additional uncertainties that is linked to the confidence we
can have in the underpinning physical arguments for using linear constraints.
We provide a software tool for implementing our general framework for emergent
constraints and use it to illustrate the framework on a number of recent
emergent constraints for ECS. We find that the robustness of any constraint to
additional uncertainties depends strongly on the confidence we can have in the
underpinning physics, allowing a future framing of the debate over the validity
of a particular constraint around the underlying physical arguments, rather
than statistical assumptions
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