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Markov Observation Models and Deepfakes

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  • Michael A. Kouritzin

    (Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB T6G 2G1, Canada)

Abstract

Herein, expanded Hidden Markov Models (HMMs) are considered as potential deepfake generation and detection tools. The most specific model is the HMM, while the most general is the pairwise Markov chain (PMC). In between, the Markov observation model (MOM) is proposed, where the observations form a Markov chain conditionally on the hidden state. An expectation-maximization (EM) analog to the Baum–Welch algorithm is developed to estimate the transition probabilities as well as the initial hidden-state-observation joint distribution for all the models considered. This new EM algorithm also includes a recursive log-likelihood equation so that model selection can be performed (after parameter convergence). Once models have been learnt through the EM algorithm, deepfakes are generated through simulation, while they are detected using the log-likelihood. Our three models were compared empirically in terms of their generative and detective ability. PMC and MOM consistently produced the best deepfake generator and detector, respectively.

Suggested Citation

  • Michael A. Kouritzin, 2025. "Markov Observation Models and Deepfakes," Mathematics, MDPI, vol. 13(13), pages 1-25, June.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:13:p:2128-:d:1690359
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    1. Kloek, Tuen & van Dijk, Herman K, 1978. "Bayesian Estimates of Equation System Parameters: An Application of Integration by Monte Carlo," Econometrica, Econometric Society, vol. 46(1), pages 1-19, January.
    2. Date, Paresh & Mamon, Rogemar & Tenyakov, Anton, 2013. "Filtering and forecasting commodity futures prices under an HMM framework," Energy Economics, Elsevier, vol. 40(C), pages 1001-1013.
    3. Derrode, Stéphane & Pieczynski, Wojciech, 2013. "Unsupervised data classification using pairwise Markov chains with automatic copulas selection," Computational Statistics & Data Analysis, Elsevier, vol. 63(C), pages 81-98.
    4. Kristi Kuljus & Jüri Lember, 2023. "Pairwise Markov Models and Hybrid Segmentation Approach," Methodology and Computing in Applied Probability, Springer, vol. 25(2), pages 1-32, June.
    5. Kouritzin, Michael A. & Long, Hongwei, 2008. "On extending classical filtering equations," Statistics & Probability Letters, Elsevier, vol. 78(18), pages 3195-3202, December.
    6. Drew Creal, 2012. "A Survey of Sequential Monte Carlo Methods for Economics and Finance," Econometric Reviews, Taylor & Francis Journals, vol. 31(3), pages 245-296.
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