25,458 research outputs found
Active Sensing as Bayes-Optimal Sequential Decision Making
Sensory inference under conditions of uncertainty is a major problem in both
machine learning and computational neuroscience. An important but poorly
understood aspect of sensory processing is the role of active sensing. Here, we
present a Bayes-optimal inference and control framework for active sensing,
C-DAC (Context-Dependent Active Controller). Unlike previously proposed
algorithms that optimize abstract statistical objectives such as information
maximization (Infomax) [Butko & Movellan, 2010] or one-step look-ahead accuracy
[Najemnik & Geisler, 2005], our active sensing model directly minimizes a
combination of behavioral costs, such as temporal delay, response error, and
effort. We simulate these algorithms on a simple visual search task to
illustrate scenarios in which context-sensitivity is particularly beneficial
and optimization with respect to generic statistical objectives particularly
inadequate. Motivated by the geometric properties of the C-DAC policy, we
present both parametric and non-parametric approximations, which retain
context-sensitivity while significantly reducing computational complexity.
These approximations enable us to investigate the more complex problem
involving peripheral vision, and we notice that the difference between C-DAC
and statistical policies becomes even more evident in this scenario.Comment: Scheduled to appear in UAI 201
Data-Driven Shape Analysis and Processing
Data-driven methods play an increasingly important role in discovering
geometric, structural, and semantic relationships between 3D shapes in
collections, and applying this analysis to support intelligent modeling,
editing, and visualization of geometric data. In contrast to traditional
approaches, a key feature of data-driven approaches is that they aggregate
information from a collection of shapes to improve the analysis and processing
of individual shapes. In addition, they are able to learn models that reason
about properties and relationships of shapes without relying on hard-coded
rules or explicitly programmed instructions. We provide an overview of the main
concepts and components of these techniques, and discuss their application to
shape classification, segmentation, matching, reconstruction, modeling and
exploration, as well as scene analysis and synthesis, through reviewing the
literature and relating the existing works with both qualitative and numerical
comparisons. We conclude our report with ideas that can inspire future research
in data-driven shape analysis and processing.Comment: 10 pages, 19 figure
Curriculum Guidelines for Undergraduate Programs in Data Science
The Park City Math Institute (PCMI) 2016 Summer Undergraduate Faculty Program
met for the purpose of composing guidelines for undergraduate programs in Data
Science. The group consisted of 25 undergraduate faculty from a variety of
institutions in the U.S., primarily from the disciplines of mathematics,
statistics and computer science. These guidelines are meant to provide some
structure for institutions planning for or revising a major in Data Science
A Geometric Variational Approach to Bayesian Inference
We propose a novel Riemannian geometric framework for variational inference
in Bayesian models based on the nonparametric Fisher-Rao metric on the manifold
of probability density functions. Under the square-root density representation,
the manifold can be identified with the positive orthant of the unit
hypersphere in L2, and the Fisher-Rao metric reduces to the standard L2 metric.
Exploiting such a Riemannian structure, we formulate the task of approximating
the posterior distribution as a variational problem on the hypersphere based on
the alpha-divergence. This provides a tighter lower bound on the marginal
distribution when compared to, and a corresponding upper bound unavailable
with, approaches based on the Kullback-Leibler divergence. We propose a novel
gradient-based algorithm for the variational problem based on Frechet
derivative operators motivated by the geometry of the Hilbert sphere, and
examine its properties. Through simulations and real-data applications, we
demonstrate the utility of the proposed geometric framework and algorithm on
several Bayesian models
Geometry-Aware Learning of Maps for Camera Localization
Maps are a key component in image-based camera localization and visual SLAM
systems: they are used to establish geometric constraints between images,
correct drift in relative pose estimation, and relocalize cameras after lost
tracking. The exact definitions of maps, however, are often
application-specific and hand-crafted for different scenarios (e.g. 3D
landmarks, lines, planes, bags of visual words). We propose to represent maps
as a deep neural net called MapNet, which enables learning a data-driven map
representation. Unlike prior work on learning maps, MapNet exploits cheap and
ubiquitous sensory inputs like visual odometry and GPS in addition to images
and fuses them together for camera localization. Geometric constraints
expressed by these inputs, which have traditionally been used in bundle
adjustment or pose-graph optimization, are formulated as loss terms in MapNet
training and also used during inference. In addition to directly improving
localization accuracy, this allows us to update the MapNet (i.e., maps) in a
self-supervised manner using additional unlabeled video sequences from the
scene. We also propose a novel parameterization for camera rotation which is
better suited for deep-learning based camera pose regression. Experimental
results on both the indoor 7-Scenes dataset and the outdoor Oxford RobotCar
dataset show significant performance improvement over prior work. The MapNet
project webpage is https://goo.gl/mRB3Au.Comment: CVPR 2018 camera ready paper + supplementary materia
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