7,042 research outputs found
Multi-resolution Tensor Learning for Large-Scale Spatial Data
High-dimensional tensor models are notoriously computationally expensive to
train. We present a meta-learning algorithm, MMT, that can significantly speed
up the process for spatial tensor models. MMT leverages the property that
spatial data can be viewed at multiple resolutions, which are related by
coarsening and finegraining from one resolution to another. Using this
property, MMT learns a tensor model by starting from a coarse resolution and
iteratively increasing the model complexity. In order to not "over-train" on
coarse resolution models, we investigate an information-theoretic fine-graining
criterion to decide when to transition into higher-resolution models. We
provide both theoretical and empirical evidence for the advantages of this
approach. When applied to two real-world large-scale spatial datasets for
basketball player and animal behavior modeling, our approach demonstrate 3 key
benefits: 1) it efficiently captures higher-order interactions (i.e., tensor
latent factors), 2) it is orders of magnitude faster than fixed resolution
learning and scales to very fine-grained spatial resolutions, and 3) it
reliably yields accurate and interpretable models
SurReal: enhancing Surgical simulation Realism using style transfer
Surgical simulation is an increasingly important element of surgical
education. Using simulation can be a means to address some of the significant
challenges in developing surgical skills with limited time and resources. The
photo-realistic fidelity of simulations is a key feature that can improve the
experience and transfer ratio of trainees. In this paper, we demonstrate how we
can enhance the visual fidelity of existing surgical simulation by performing
style transfer of multi-class labels from real surgical video onto synthetic
content. We demonstrate our approach on simulations of cataract surgery using
real data labels from an existing public dataset. Our results highlight the
feasibility of the approach and also the powerful possibility to extend this
technique to incorporate additional temporal constraints and to different
applications
Geometrically Intrinsic Nonlinear Recursive Filters I: Algorithms
The Geometrically Intrinsic Nonlinear Recursive Filter, or GI Filter, is
designed to estimate an arbitrary continuous-time Markov diffusion process X
subject to nonlinear discrete-time observations. The GI Filter is fundamentally
different from the much-used Extended Kalman Filter (EKF), and its second-order
variants, even in the simplest nonlinear case, in that: (i) It uses a quadratic
function of a vector observation to update the state, instead of the linear
function used by the EKF. (ii) It is based on deeper geometric principles,
which make the GI Filter coordinate-invariant. This implies, for example, that
if a linear system were subjected to a nonlinear transformation f of the
state-space and analyzed using the GI Filter, the resulting state estimates and
conditional variances would be the push-forward under f of the Kalman Filter
estimates for the untransformed system - a property which is not shared by the
EKF or its second-order variants.
The noise covariance of X and the observation covariance themselves induce
geometries on state space and observation space, respectively, and associated
canonical connections. A sequel to this paper develops stochastic differential
geometry results - based on "intrinsic location parameters", a notion derived
from the heat flow of harmonic mappings - from which we derive the
coordinate-free filter update formula. The present article presents the
algorithm with reference to a specific example - the problem of tracking and
intercepting a target, using sensors based on a moving missile. Computational
experiments show that, when the observation function is highly nonlinear, there
exist choices of the noise parameters at which the GI Filter significantly
outperforms the EKF.Comment: 22 pages, 4 figure
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