29,974 research outputs found
Sequential Design for Ranking Response Surfaces
We propose and analyze sequential design methods for the problem of ranking
several response surfaces. Namely, given response surfaces over a
continuous input space , the aim is to efficiently find the index of
the minimal response across the entire . The response surfaces are not
known and have to be noisily sampled one-at-a-time. This setting is motivated
by stochastic control applications and requires joint experimental design both
in space and response-index dimensions. To generate sequential design
heuristics we investigate stepwise uncertainty reduction approaches, as well as
sampling based on posterior classification complexity. We also make connections
between our continuous-input formulation and the discrete framework of pure
regret in multi-armed bandits. To model the response surfaces we utilize
kriging surrogates. Several numerical examples using both synthetic data and an
epidemics control problem are provided to illustrate our approach and the
efficacy of respective adaptive designs.Comment: 26 pages, 7 figures (updated several sections and figures
Active Classification: Theory and Application to Underwater Inspection
We discuss the problem in which an autonomous vehicle must classify an object
based on multiple views. We focus on the active classification setting, where
the vehicle controls which views to select to best perform the classification.
The problem is formulated as an extension to Bayesian active learning, and we
show connections to recent theoretical guarantees in this area. We formally
analyze the benefit of acting adaptively as new information becomes available.
The analysis leads to a probabilistic algorithm for determining the best views
to observe based on information theoretic costs. We validate our approach in
two ways, both related to underwater inspection: 3D polyhedra recognition in
synthetic depth maps and ship hull inspection with imaging sonar. These tasks
encompass both the planning and recognition aspects of the active
classification problem. The results demonstrate that actively planning for
informative views can reduce the number of necessary views by up to 80% when
compared to passive methods.Comment: 16 page
On computational tools for Bayesian data analysis
While Robert and Rousseau (2010) addressed the foundational aspects of
Bayesian analysis, the current chapter details its practical aspects through a
review of the computational methods available for approximating Bayesian
procedures. Recent innovations like Monte Carlo Markov chain, sequential Monte
Carlo methods and more recently Approximate Bayesian Computation techniques
have considerably increased the potential for Bayesian applications and they
have also opened new avenues for Bayesian inference, first and foremost
Bayesian model choice.Comment: This is a chapter for the book "Bayesian Methods and Expert
Elicitation" edited by Klaus Bocker, 23 pages, 9 figure
- …