Learning Hidden Markov Models When the Locations of Missing Observations are Unknown

Binyamin Perets, Mark Kozdoba, Shie Mannor

Research output: Contribution to journalConference articlepeer-review


The Hidden Markov Model (HMM) is one of the most widely used statistical models for sequential data analysis. One of the key reasons for this versatility is the ability of HMM to deal with missing data. However, standard HMM learning algorithms rely crucially on the assumption that the positions of the missing observations within the observation sequence are known. In the natural sciences, where this assumption is often violated, special variants of HMM, commonly known as Silent-state HMMs (SHMMs), are used. Despite their widespread use, these algorithms strongly rely on specific structural assumptions of the underlying chain, such as acyclicity, thus limiting the applicability of these methods. Moreover, even in the acyclic case, it has been shown that these methods can lead to poor reconstruction. In this paper we consider the general problem of learning an HMM from data with unknown missing observation locations. We provide reconstruction algorithms that do not require any assumptions about the structure of the underlying chain, and can also be used with limited prior knowledge, unlike SHMM. We evaluate and compare the algorithms in a variety of scenarios, measuring their reconstruction precision, and robustness under model miss-specification. Notably, we show that under proper specifications one can reconstruct the process dynamics as well as if the missing observations positions were known.

Original languageEnglish
Pages (from-to)27642-27667
Number of pages26
JournalProceedings of Machine Learning Research
StatePublished - 2023
Event40th International Conference on Machine Learning, ICML 2023 - Honolulu, United States
Duration: 23 Jul 202329 Jul 2023

ASJC Scopus subject areas

  • Artificial Intelligence
  • Software
  • Control and Systems Engineering
  • Statistics and Probability


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