Uncertainty in Artificial Intelligence
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k-NN Regression on Functional Data with Incomplete Observations
Sashank Reddi, Barnabas Poczos
Abstract:
In this paper we study a general version of re- gression where each covariate itself is a func- tional data such as distributions or functions. In real applications, however, typically we do not have direct access to such data; instead only some noisy estimates of the true co- variate functions/distributions are available to us. For example, when each covariate is a distribution, then we might not be able to directly observe these distributions, but it can be assumed that i.i.d. sample sets from these distributions are available. In this pa- per we present a general framework and a k- NN based estimator for this regression prob- lem. We prove consistency of the estimator and derive its convergence rates. We further show that the proposed estimator can adapt to the local intrinsic dimension in our case and provide a simple approach for choosing k. Finally, we illustrate the applicability of our framework with numerical experiments.
Keywords:
Pages: 692-701
PS Link:
PDF Link: /papers/14/p692-reddi.pdf
BibTex:
@INPROCEEDINGS{Reddi14,
AUTHOR = "Sashank Reddi and Barnabas Poczos",
TITLE = "k-NN Regression on Functional Data with Incomplete Observations",
BOOKTITLE = "Proceedings of the Thirtieth Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-14)",
PUBLISHER = "AUAI Press",
ADDRESS = "Corvallis, Oregon",
YEAR = "2014",
PAGES = "692--701"
}


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