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 regression where each covariate itself is a functional 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 covariate 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 paper we present a general framework and a $k$-NN based estimator for this regression problem. 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 regression where each covariate itself is a functional 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 covariate 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 paper we present a general framework and a $k$-NN based estimator for this regression problem. 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 regression where each covariate itself is a functional 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 covariate 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 paper we present a general framework and a $k$-NN based estimator for this regression problem. 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.

Related Material