Differentially-private learning of low dimensional manifolds

Anna Choromanska, Krzysztof Choromanski, Geetha Jagannathan, Claire Monteleoni

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In this paper, we study the problem of differentially-private learning of low dimensional manifolds embedded in high dimensional spaces. The problems one faces in learning in high dimensional spaces are compounded in differentially-private learning. We achieve the dual goals of learning the manifold while maintaining the privacy of the dataset by constructing a differentially-private data structure that adapts to the doubling dimension of the dataset. Our differentially-private manifold learning algorithm extends random projection trees of Dasgupta and Freund. A naive construction of differentially-private random projection trees could involve queries with high global sensitivity that would affect the usefulness of the trees. Instead, we present an alternate way of constructing differentially-private random projection trees that uses low sensitivity queries that are precise enough for learning the low dimensional manifolds. We prove that the size of the tree depends only on the doubling dimension of the dataset and not its extrinsic dimension.

Original languageEnglish (US)
Title of host publicationAlgorithmic Learning Theory - 24th International Conference, ALT 2013, Proceedings
Pages249-263
Number of pages15
Volume8139 LNAI
DOIs
StatePublished - 2013
Event24th International Conference on Algorithmic Learning Theory, ALT 2013 - Singapore, Singapore
Duration: Oct 6 2013Oct 9 2013

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8139 LNAI
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other24th International Conference on Algorithmic Learning Theory, ALT 2013
CountrySingapore
CitySingapore
Period10/6/1310/9/13

Fingerprint

Learning algorithms
Data structures
Random Projection
Doubling
High-dimensional
Query
Manifold Learning
Alternate
Privacy
Learning Algorithm
Data Structures
Learning
Face

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Choromanska, A., Choromanski, K., Jagannathan, G., & Monteleoni, C. (2013). Differentially-private learning of low dimensional manifolds. In Algorithmic Learning Theory - 24th International Conference, ALT 2013, Proceedings (Vol. 8139 LNAI, pp. 249-263). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8139 LNAI). https://doi.org/10.1007/978-3-642-40935-6_18

Differentially-private learning of low dimensional manifolds. / Choromanska, Anna; Choromanski, Krzysztof; Jagannathan, Geetha; Monteleoni, Claire.

Algorithmic Learning Theory - 24th International Conference, ALT 2013, Proceedings. Vol. 8139 LNAI 2013. p. 249-263 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8139 LNAI).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Choromanska, A, Choromanski, K, Jagannathan, G & Monteleoni, C 2013, Differentially-private learning of low dimensional manifolds. in Algorithmic Learning Theory - 24th International Conference, ALT 2013, Proceedings. vol. 8139 LNAI, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 8139 LNAI, pp. 249-263, 24th International Conference on Algorithmic Learning Theory, ALT 2013, Singapore, Singapore, 10/6/13. https://doi.org/10.1007/978-3-642-40935-6_18
Choromanska A, Choromanski K, Jagannathan G, Monteleoni C. Differentially-private learning of low dimensional manifolds. In Algorithmic Learning Theory - 24th International Conference, ALT 2013, Proceedings. Vol. 8139 LNAI. 2013. p. 249-263. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-40935-6_18
Choromanska, Anna ; Choromanski, Krzysztof ; Jagannathan, Geetha ; Monteleoni, Claire. / Differentially-private learning of low dimensional manifolds. Algorithmic Learning Theory - 24th International Conference, ALT 2013, Proceedings. Vol. 8139 LNAI 2013. pp. 249-263 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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