### Abstract

This note is a short version of that in [1]. It is intended as a survey for the 2015 Algorithmic Learning Theory (ALT) conference. This work considers a computationally and statistically efficient parameter estimation method for a wide class of latent variable models— including Gaussian mixture models, hidden Markov models, and latent Dirichlet allocation—which exploits a certain tensor structure in their low-order observable moments (typically, of second- and third-order). Specifically, parameter estimation is reduced to the problem of extracting a certain (orthogonal) decomposition of a symmetric tensor derived from the moments; this decomposition can be viewed as a natural generalization of the singular value decomposition for matrices. Although tensor decompositions are generally intractable to compute, the decomposition of these specially structured tensors can be efficiently obtained by a variety of approaches, including power iterations and maximization approaches (similar to the case of matrices). A detailed analysis of a robust tensor power method is provided, establishing an analogue of Wedin’s perturbation theorem for the singular vectors of matrices. This implies a robust and computationally tractable estimation approach for several popular latent variable models.

Original language | English (US) |
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Title of host publication | Algorithmic Learning Theory - 26th International Conference, ALT 2015 |

Editors | Claudio Gentile, Sandra Zilles, Kamalika Chaudhuri |

Publisher | Springer-Verlag |

Pages | 19-38 |

Number of pages | 20 |

ISBN (Print) | 9783319244853 |

DOIs | |

State | Published - Jan 1 2015 |

Externally published | Yes |

Event | 26th International Conference on Algorithmic Learning Theory, ALT 2015 - Banff, Canada Duration: Oct 4 2015 → Oct 6 2015 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 9355 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 26th International Conference on Algorithmic Learning Theory, ALT 2015 |
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Country | Canada |

City | Banff |

Period | 10/4/15 → 10/6/15 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Algorithmic Learning Theory - 26th International Conference, ALT 2015*(pp. 19-38). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9355). Springer-Verlag. https://doi.org/10.1007/978-3-319-24486-0_2