2,941 research outputs found
On surrogate loss functions and -divergences
The goal of binary classification is to estimate a discriminant function
from observations of covariate vectors and corresponding binary
labels. We consider an elaboration of this problem in which the covariates are
not available directly but are transformed by a dimensionality-reducing
quantizer . We present conditions on loss functions such that empirical risk
minimization yields Bayes consistency when both the discriminant function and
the quantizer are estimated. These conditions are stated in terms of a general
correspondence between loss functions and a class of functionals known as
Ali-Silvey or -divergence functionals. Whereas this correspondence was
established by Blackwell [Proc. 2nd Berkeley Symp. Probab. Statist. 1 (1951)
93--102. Univ. California Press, Berkeley] for the 0--1 loss, we extend the
correspondence to the broader class of surrogate loss functions that play a key
role in the general theory of Bayes consistency for binary classification. Our
result makes it possible to pick out the (strict) subset of surrogate loss
functions that yield Bayes consistency for joint estimation of the discriminant
function and the quantizer.Comment: Published in at http://dx.doi.org/10.1214/08-AOS595 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
A structured prediction approach for robot imitation learning
We propose a structured prediction approach for robot imitation learning from demonstrations. Among various tools for robot imitation learning, supervised learning has been observed to have a prominent role. Structured prediction is a form of supervised learning that enables learning models to operate on output spaces with complex structures. Through the lens of structured prediction, we show how robots can learn to imitate trajectories belonging to not only Euclidean spaces but also Riemannian manifolds. Exploiting ideas from information theory, we propose a class of loss functions based on the f-divergence to measure the information loss between the demonstrated and reproduced probabilistic trajectories. Different types of f-divergence will result in different policies, which we call imitation modes. Furthermore, our approach enables the incorporation of spatial and temporal trajectory modulation, which is necessary for robots to be adaptive to the change in working conditions. We benchmark our algorithm against state-of-the-art methods in terms of trajectory reproduction and adaptation. The quantitative evaluation shows that our approach outperforms other algorithms regarding both accuracy and efficiency. We also report real-world experimental results on learning manifold trajectories in a polishing task with a KUKA LWR robot arm, illustrating the effectiveness of our algorithmic framework
A Structured Prediction Approach for Robot Imitation Learning
We propose a structured prediction approach for robot imitation learning from
demonstrations. Among various tools for robot imitation learning, supervised
learning has been observed to have a prominent role. Structured prediction is a
form of supervised learning that enables learning models to operate on output
spaces with complex structures. Through the lens of structured prediction, we
show how robots can learn to imitate trajectories belonging to not only
Euclidean spaces but also Riemannian manifolds. Exploiting ideas from
information theory, we propose a class of loss functions based on the
f-divergence to measure the information loss between the demonstrated and
reproduced probabilistic trajectories. Different types of f-divergence will
result in different policies, which we call imitation modes. Furthermore, our
approach enables the incorporation of spatial and temporal trajectory
modulation, which is necessary for robots to be adaptive to the change in
working conditions. We benchmark our algorithm against state-of-the-art methods
in terms of trajectory reproduction and adaptation. The quantitative evaluation
shows that our approach outperforms other algorithms regarding both accuracy
and efficiency. We also report real-world experimental results on learning
manifold trajectories in a polishing task with a KUKA LWR robot arm,
illustrating the effectiveness of our algorithmic framework
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