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Activity Number:
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521
- Statistical Methods for Functional Data
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Type:
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Contributed
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Date/Time:
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Thursday, August 11, 2022 : 8:30 AM to 10:20 AM
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Sponsor:
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Section on Nonparametric Statistics
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Abstract #322736
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Title:
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Topological Hidden Markov Models
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Author(s):
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Adam B Kashlak* and Giseon Heo and Prachi Loliencar
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Companies:
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University of Alberta and University of Alberta and University of Alberta
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Keywords:
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HMM;
Functional Data;
Signals Data;
Topological Vector Space;
Biological Data
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Abstract:
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Hidden Markov Models (HMMs) have been applied to many areas of data analysis since their inception almost 60 years ago. However, their reliance on probability density functions fit parameter re-estimation makes them ill-suited for handling data in infinite dimensional spaces. In this talk, we introduce a new approach to modelling data using HMMs where the observed data are realizations of a Gaussian measure on a locally convex topological vector space. This allows for modelling of sequential functional observations or stochastic processes. Our topological HMM is shown to successfully model biological signals data such as electrical responses within muscles via electromyography (EMG) and brain waves via electroencephalogram (EEG).
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Authors who are presenting talks have a * after their name.
