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Fast and Consistent Learning of Hidden Markov Models by Incorporating Non-Consecutive Correlations
Robert Mattila · Cristian R. Rojas · Eric Moulines · Vikram Krishnamurthy · Bo Wahlberg

Wed Jul 15 09:00 AM -- 09:45 AM & Wed Jul 15 10:00 PM -- 10:45 PM (PDT) @

Can the parameters of a hidden Markov model (HMM) be estimated from a single sweep through the observations -- and additionally, without being trapped at a local optimum in the likelihood surface? That is the premise of recent method of moments algorithms devised for HMMs. In these, correlations between consecutive pair- or triplet-wise observations are empirically estimated and used to compute estimates of the HMM parameters. Albeit computationally very attractive, the main drawback is that by restricting to only low-order correlations in the data, information is being neglected which results in a loss of accuracy (compared to standard maximum likelihood schemes). In this paper, we propose extending these methods (both pair- and triplet-based) by also including non-consecutive correlations in a way which does not significantly increase the computational cost (which scales linearly with the number of additional lags included). We prove strong consistency of the new methods, and demonstrate an improved performance in numerical experiments on both synthetic and real-world financial time-series datasets.

Author Information

Robert Mattila (KTH Royal Institute of Technology)
Cristian R. Rojas (KTH Royal Institute of Technology)
Eric Moulines (Ecole Polytechnique)
Vikram Krishnamurthy (Cornell University)
Bo Wahlberg (KTH Royal Institute of Technology)

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