### Abstract

Classical learning theory is based on a tight linkage between hypothesis space (a class of function on a domain X), data space

(function-value examples (x, f(x))), and the space of queries for the learned model (predicting function values for new examples x). However, in many learning scenarios the 3-way association between hypotheses, data, and queries can really be much looser. Model classes can be overparameterized, i.e., different hypotheses may be equivalent with respect to the data observations. Queries may relate to model properties that do not directly correspond to the observations in the data. In this paper we make some initial steps to extend and adapt basic concepts of computational learnability and statistical identifiability to provide a foundation for investigating learnability in such broader contexts. We exemplify the use of the framework in three different applications: the identification of temporal logic properties of probabilistic automata learned from sequence data, the identification of causal dependencies in probabilistic graphical models, and the transfer of probabilistic relational models to new domains.

(function-value examples (x, f(x))), and the space of queries for the learned model (predicting function values for new examples x). However, in many learning scenarios the 3-way association between hypotheses, data, and queries can really be much looser. Model classes can be overparameterized, i.e., different hypotheses may be equivalent with respect to the data observations. Queries may relate to model properties that do not directly correspond to the observations in the data. In this paper we make some initial steps to extend and adapt basic concepts of computational learnability and statistical identifiability to provide a foundation for investigating learnability in such broader contexts. We exemplify the use of the framework in three different applications: the identification of temporal logic properties of probabilistic automata learned from sequence data, the identification of causal dependencies in probabilistic graphical models, and the transfer of probabilistic relational models to new domains.

Original language | English |
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Title of host publication | Machine Learning and Knowledge Discovery in Databases : European Conference, ECML PKDD 2013, Prague, Czech Republic, September 23-27, 2013, Proceedings, Part III |

Editors | Hendrik Blockeel, Kristian Kersting, Siegfried Nijssen, Filip Železný |

Number of pages | 16 |

Place of Publication | Berlin |

Publisher | Springer Publishing Company |

Publication date | 2013 |

Pages | 112-127 |

ISBN (Print) | 978-3-642-40993-6 |

ISBN (Electronic) | 978-3-642-40994-3 |

DOIs | |

Publication status | Published - 2013 |

Event | ECML PKDD 2013 - Prag, Czech Republic Duration: 23 Sep 2013 → 27 Sep 2013 |

### Conference

Conference | ECML PKDD 2013 |
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Country | Czech Republic |

City | Prag |

Period | 23/09/2013 → 27/09/2013 |

Series | Lecture Notes in Computer Science |
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Volume | 8190 |

ISSN | 0302-9743 |

### Fingerprint

### Cite this

Jaeger, M. (2013). Identifiability of Model Properties in Over-Parameterized Model Classes. In H. Blockeel, K. Kersting, S. Nijssen, & F. Železný (Eds.),

*Machine Learning and Knowledge Discovery in Databases: European Conference, ECML PKDD 2013, Prague, Czech Republic, September 23-27, 2013, Proceedings, Part III*(pp. 112-127). Springer Publishing Company. Lecture Notes in Computer Science, Vol.. 8190 https://doi.org/10.1007/978-3-642-40994-3_8