13,868 research outputs found
High-Dimensional Bayesian Geostatistics
With the growing capabilities of Geographic Information Systems (GIS) and
user-friendly software, statisticians today routinely encounter geographically
referenced data containing observations from a large number of spatial
locations and time points. Over the last decade, hierarchical spatiotemporal
process models have become widely deployed statistical tools for researchers to
better understand the complex nature of spatial and temporal variability.
However, fitting hierarchical spatiotemporal models often involves expensive
matrix computations with complexity increasing in cubic order for the number of
spatial locations and temporal points. This renders such models unfeasible for
large data sets. This article offers a focused review of two methods for
constructing well-defined highly scalable spatiotemporal stochastic processes.
Both these processes can be used as "priors" for spatiotemporal random fields.
The first approach constructs a low-rank process operating on a
lower-dimensional subspace. The second approach constructs a Nearest-Neighbor
Gaussian Process (NNGP) that ensures sparse precision matrices for its finite
realizations. Both processes can be exploited as a scalable prior embedded
within a rich hierarchical modeling framework to deliver full Bayesian
inference. These approaches can be described as model-based solutions for big
spatiotemporal datasets. The models ensure that the algorithmic complexity has
floating point operations (flops), where the number of spatial
locations (per iteration). We compare these methods and provide some insight
into their methodological underpinnings
Learning and Acting in Peripersonal Space: Moving, Reaching, and Grasping
The young infant explores its body, its sensorimotor system, and the
immediately accessible parts of its environment, over the course of a few
months creating a model of peripersonal space useful for reaching and grasping
objects around it. Drawing on constraints from the empirical literature on
infant behavior, we present a preliminary computational model of this learning
process, implemented and evaluated on a physical robot. The learning agent
explores the relationship between the configuration space of the arm, sensing
joint angles through proprioception, and its visual perceptions of the hand and
grippers. The resulting knowledge is represented as the peripersonal space
(PPS) graph, where nodes represent states of the arm, edges represent safe
movements, and paths represent safe trajectories from one pose to another. In
our model, the learning process is driven by intrinsic motivation. When
repeatedly performing an action, the agent learns the typical result, but also
detects unusual outcomes, and is motivated to learn how to make those unusual
results reliable. Arm motions typically leave the static background unchanged,
but occasionally bump an object, changing its static position. The reach action
is learned as a reliable way to bump and move an object in the environment.
Similarly, once a reliable reach action is learned, it typically makes a
quasi-static change in the environment, moving an object from one static
position to another. The unusual outcome is that the object is accidentally
grasped (thanks to the innate Palmar reflex), and thereafter moves dynamically
with the hand. Learning to make grasps reliable is more complex than for
reaches, but we demonstrate significant progress. Our current results are steps
toward autonomous sensorimotor learning of motion, reaching, and grasping in
peripersonal space, based on unguided exploration and intrinsic motivation.Comment: 35 pages, 13 figure
Graph Dynamical Networks for Unsupervised Learning of Atomic Scale Dynamics in Materials
Understanding the dynamical processes that govern the performance of
functional materials is essential for the design of next generation materials
to tackle global energy and environmental challenges. Many of these processes
involve the dynamics of individual atoms or small molecules in condensed
phases, e.g. lithium ions in electrolytes, water molecules in membranes, molten
atoms at interfaces, etc., which are difficult to understand due to the
complexity of local environments. In this work, we develop graph dynamical
networks, an unsupervised learning approach for understanding atomic scale
dynamics in arbitrary phases and environments from molecular dynamics
simulations. We show that important dynamical information can be learned for
various multi-component amorphous material systems, which is difficult to
obtain otherwise. With the large amounts of molecular dynamics data generated
everyday in nearly every aspect of materials design, this approach provides a
broadly useful, automated tool to understand atomic scale dynamics in material
systems.Comment: 25 + 7 pages, 5 + 3 figure
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