Metadata only
Date
2023Type
- Conference Paper
ETH Bibliography
yes
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Abstract
Many dynamical systems in the real world are naturally described by latent states with intrinsic ordering, such as “ally”, “neutral”, and “enemy” relationships in international relations. These latent states manifest through countries’ cooperative versus conflictual interactions over time. State-space models (SSMs) explicitly relate the dynamics of observed measurements to transitions in latent states. For discrete data, SSMs commonly do so through a state-to-action emission matrix and a state-to-state transition matrix. This paper introduces the Ordered Matrix Dirichlet (OMD) as a prior distribution over ordered stochastic matrices wherein the discrete distribution in the kth row is stochastically dominated by the (k+1)th, such that probability mass is shifted to the right when moving down rows. We illustrate the OMD prior within two SSMs: a hidden Markov model, and a novel dynamic Poisson Tucker decomposition model tailored to international relations data. We find that models built on the OMD recover interpretable ordered latent structure without forfeiting predictive performance. We suggest future applications to other domains where models with stochastic matrices are popular (e.g., topic modeling), and publish user-friendly code. Show more
Publication status
publishedExternal links
Book title
Proceedings of The 26th International Conference on Artificial Intelligence and StatisticsJournal / series
Proceedings of Machine Learning ResearchVolume
Pages / Article No.
Publisher
PMLREvent
Organisational unit
09682 - Cotterell, Ryan / Cotterell, Ryan
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ETH Bibliography
yes
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