3,279 research outputs found
A tutorial on conformal prediction
Conformal prediction uses past experience to determine precise levels of
confidence in new predictions. Given an error probability , together
with a method that makes a prediction of a label , it produces a
set of labels, typically containing , that also contains with
probability . Conformal prediction can be applied to any method for
producing : a nearest-neighbor method, a support-vector machine, ridge
regression, etc.
Conformal prediction is designed for an on-line setting in which labels are
predicted successively, each one being revealed before the next is predicted.
The most novel and valuable feature of conformal prediction is that if the
successive examples are sampled independently from the same distribution, then
the successive predictions will be right of the time, even though
they are based on an accumulating dataset rather than on independent datasets.
In addition to the model under which successive examples are sampled
independently, other on-line compression models can also use conformal
prediction. The widely used Gaussian linear model is one of these.
This tutorial presents a self-contained account of the theory of conformal
prediction and works through several numerical examples. A more comprehensive
treatment of the topic is provided in "Algorithmic Learning in a Random World",
by Vladimir Vovk, Alex Gammerman, and Glenn Shafer (Springer, 2005).Comment: 58 pages, 9 figure
Testing conformal mapping with kitchen aluminum foil
We report an experimental verification of conformal mapping with kitchen
aluminum foil. This experiment can be reproduced in any laboratory by
undergraduate students and it is therefore an ideal experiment to introduce the
concept of conformal mapping. The original problem was the distribution of the
electric potential in a very long plate. The correct theoretical prediction was
recently derived by A. Czarnecki (Can. J. Phys. 92, 1297 (2014))
Transductive-Inductive Cluster Approximation Via Multivariate Chebyshev Inequality
Approximating adequate number of clusters in multidimensional data is an open
area of research, given a level of compromise made on the quality of acceptable
results. The manuscript addresses the issue by formulating a transductive
inductive learning algorithm which uses multivariate Chebyshev inequality.
Considering clustering problem in imaging, theoretical proofs for a particular
level of compromise are derived to show the convergence of the reconstruction
error to a finite value with increasing (a) number of unseen examples and (b)
the number of clusters, respectively. Upper bounds for these error rates are
also proved. Non-parametric estimates of these error from a random sample of
sequences empirically point to a stable number of clusters. Lastly, the
generalization of algorithm can be applied to multidimensional data sets from
different fields.Comment: 16 pages, 5 figure
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