Pattern Recognition and Density Estimation Under the General I.i.d. Assumption
Abstract
Statistical learning theory considers three main problems, pattern recognition, regression and density estimation. This paper studies solvability of these problems (mainly concentrating on pattern recognition and density estimation) in the “high-dimensional” case, where the patterns in the training and test sets are never repeated. We show that, assuming an i.i.d. data source but without any further assumptions, the problems of pattern recognition and regression can often be solved (and there are practically useful algorithms to solve them). On the other hand, the problem of density estimation, as we formalize it, cannot be solved under the general i.i.d. assumption, and additional assumptions are required.
Cite
Text
Nouretdinov et al. "Pattern Recognition and Density Estimation Under the General I.i.d. Assumption." Annual Conference on Computational Learning Theory, 2001. doi:10.1007/3-540-44581-1_22Markdown
[Nouretdinov et al. "Pattern Recognition and Density Estimation Under the General I.i.d. Assumption." Annual Conference on Computational Learning Theory, 2001.](https://mlanthology.org/colt/2001/nouretdinov2001colt-pattern/) doi:10.1007/3-540-44581-1_22BibTeX
@inproceedings{nouretdinov2001colt-pattern,
title = {{Pattern Recognition and Density Estimation Under the General I.i.d. Assumption}},
author = {Nouretdinov, Ilia and Vovk, Volodya and Vyugin, Michael V. and Gammerman, Alex},
booktitle = {Annual Conference on Computational Learning Theory},
year = {2001},
pages = {337-353},
doi = {10.1007/3-540-44581-1_22},
url = {https://mlanthology.org/colt/2001/nouretdinov2001colt-pattern/}
}