Reconstructing Trees from Traces

Sami Davies, Miklos Z. Racz, Cyrus Rashtchian
; Proceedings of the Thirty-Second Conference on Learning Theory, PMLR 99:961-978, 2019.

Abstract

We study the problem of learning a node-labeled tree given independent traces from an appropriately defined deletion channel. This problem, tree trace reconstruction, generalizes string trace reconstruction, which corresponds to the tree being a path. For many classes of trees, including complete trees and spiders, we provide algorithms that reconstruct the labels using only a polynomial number of traces. This exhibits a stark contrast to known results on string trace reconstruction, which require exponentially many traces, and where a central open problem is to determine whether a polynomial number of traces suffice. Our techniques combine novel combinatorial and complex analytic methods.

Cite this Paper


BibTeX
@InProceedings{pmlr-v99-davies19a, title = {Reconstructing Trees from Traces}, author = {Davies, Sami and Racz, Miklos Z. and Rashtchian, Cyrus}, booktitle = {Proceedings of the Thirty-Second Conference on Learning Theory}, pages = {961--978}, year = {2019}, editor = {Alina Beygelzimer and Daniel Hsu}, volume = {99}, series = {Proceedings of Machine Learning Research}, address = {Phoenix, USA}, month = {25--28 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v99/davies19a/davies19a.pdf}, url = {http://proceedings.mlr.press/v99/davies19a.html}, abstract = { We study the problem of learning a node-labeled tree given independent traces from an appropriately defined deletion channel. This problem, tree trace reconstruction, generalizes string trace reconstruction, which corresponds to the tree being a path. For many classes of trees, including complete trees and spiders, we provide algorithms that reconstruct the labels using only a polynomial number of traces. This exhibits a stark contrast to known results on string trace reconstruction, which require exponentially many traces, and where a central open problem is to determine whether a polynomial number of traces suffice. Our techniques combine novel combinatorial and complex analytic methods.} }
Endnote
%0 Conference Paper %T Reconstructing Trees from Traces %A Sami Davies %A Miklos Z. Racz %A Cyrus Rashtchian %B Proceedings of the Thirty-Second Conference on Learning Theory %C Proceedings of Machine Learning Research %D 2019 %E Alina Beygelzimer %E Daniel Hsu %F pmlr-v99-davies19a %I PMLR %J Proceedings of Machine Learning Research %P 961--978 %U http://proceedings.mlr.press %V 99 %W PMLR %X We study the problem of learning a node-labeled tree given independent traces from an appropriately defined deletion channel. This problem, tree trace reconstruction, generalizes string trace reconstruction, which corresponds to the tree being a path. For many classes of trees, including complete trees and spiders, we provide algorithms that reconstruct the labels using only a polynomial number of traces. This exhibits a stark contrast to known results on string trace reconstruction, which require exponentially many traces, and where a central open problem is to determine whether a polynomial number of traces suffice. Our techniques combine novel combinatorial and complex analytic methods.
APA
Davies, S., Racz, M.Z. & Rashtchian, C.. (2019). Reconstructing Trees from Traces. Proceedings of the Thirty-Second Conference on Learning Theory, in PMLR 99:961-978

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