17,150 research outputs found
Near-Optimal Target Learning With Stochastic Binary Signals
We study learning in a noisy bisection model: specifically, Bayesian
algorithms to learn a target value V given access only to noisy realizations of
whether V is less than or greater than a threshold theta. At step t = 0, 1, 2,
..., the learner sets threshold theta t and observes a noisy realization of
sign(V - theta t). After T steps, the goal is to output an estimate V^ which is
within an eta-tolerance of V . This problem has been studied, predominantly in
environments with a fixed error probability q < 1/2 for the noisy realization
of sign(V - theta t). In practice, it is often the case that q can approach
1/2, especially as theta -> V, and there is little known when this happens. We
give a pseudo-Bayesian algorithm which provably converges to V. When the true
prior matches our algorithm's Gaussian prior, we show near-optimal expected
performance. Our methods extend to the general multiple-threshold setting where
the observation noisily indicates which of k >= 2 regions V belongs to
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
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
A Nonparametric Conjugate Prior Distribution for the Maximizing Argument of a Noisy Function
We propose a novel Bayesian approach to solve stochastic optimization
problems that involve finding extrema of noisy, nonlinear functions. Previous
work has focused on representing possible functions explicitly, which leads to
a two-step procedure of first, doing inference over the function space and
second, finding the extrema of these functions. Here we skip the representation
step and directly model the distribution over extrema. To this end, we devise a
non-parametric conjugate prior based on a kernel regressor. The resulting
posterior distribution directly captures the uncertainty over the maximum of
the unknown function. We illustrate the effectiveness of our model by
optimizing a noisy, high-dimensional, non-convex objective function.Comment: 9 pages, 5 figure
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