k-NN Regression on Functional Data with Incomplete Observations

Sashank J. Reddi Carnegie Mellon University, Barnabas Poczos Carnegie Mellon Univeristy
Proceedings of the 30th Conference on Uncertainty in Artificial Intelligence, PMLR R12:176-185, 2014.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR12-university14d, title = {k-{NN} Regression on Functional Data with Incomplete Observations}, author = {University, Sashank J. Reddi Carnegie Mellon and Univeristy, Barnabas Poczos Carnegie Mellon}, booktitle = {Proceedings of the 30th Conference on Uncertainty in Artificial Intelligence}, pages = {176--185}, year = {2014}, editor = {Zhang, Nevin L. and Tian, Jin}, volume = {R12}, series = {Proceedings of Machine Learning Research}, month = {23--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r12/main/assets/university14d/university14d.pdf}, url = {https://proceedings.mlr.press/r12/university14d.html}, 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.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T k-NN Regression on Functional Data with Incomplete Observations %A Sashank J. Reddi Carnegie Mellon University %A Barnabas Poczos Carnegie Mellon Univeristy %B Proceedings of the 30th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2014 %E Nevin L. Zhang %E Jin Tian %F pmlr-vR12-university14d %I PMLR %P 176--185 %U https://proceedings.mlr.press/r12/university14d.html %V R12 %X 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. %Z Reissued by PMLR on 04 October 2026.
APA
University, S.J.R.C.M. & Univeristy, B.P.C.M.. (2014). k-NN Regression on Functional Data with Incomplete Observations. Proceedings of the 30th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R12:176-185 Available from https://proceedings.mlr.press/r12/university14d.html. Reissued by PMLR on 04 October 2026.

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