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A Poisson-Gamma Dynamic Factor Model with Time-Varying Transition Dynamics
Machine Learning · Submitted 26 Feb 2024
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Experiments show that, in comparison with related models, the proposed non-stationary PGDS achieves improved predictive performance due to its capacity to learn non-stationary dependency structure captured by the time-evolving transition matrices.
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The abstract, sentence by sentence
Probabilistic approaches for handling count-valued time sequences have attracted amounts of research attentions because their ability to infer explainable latent structures and to estimate uncertainties, and thus are especially suitable for dealing with \emph{noisy} and \emph{incomplete} count data. Among these models, Poisson-Gamma Dynamical Systems (PGDSs) are proven to be effective in capturing the evolving dynamics underlying observed count sequences. However, the state-of-the-art PGDS still fails to capture the \emph{time-varying} transition dynamics that are commonly observed in real-world count time sequences. To mitigate this gap, a non-stationary PGDS is proposed to allow the underlying transition matrices to evolve over time, and the evolving transition matrices are modeled by sophisticatedly-designed Dirichlet Markov chains. Leveraging Dirichlet-Multinomial-Beta data augmentation techniques, a fully-conjugate and efficient Gibbs sampler is developed to perform posterior simulation. Experiments show that, in comparison with related models, the proposed non-stationary PGDS achieves improved predictive performance due to its capacity to learn non-stationary dependency structure captured by the time-evolving transition matrices.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Probabilistic approaches for handling count-valued time sequences have attracted amounts of research attentions because their ability to infer explainable latent structures and to estimate uncertainties, and thus are especially suitable for dealing with \emph{noisy} and \emph{incomplete} count data. | background 1.00 | 0.05 | 0.02 | asserted 1.00 |
| s1 | Among these models, Poisson-Gamma Dynamical Systems (PGDSs) are proven to be effective in capturing the evolving dynamics underlying observed count sequences. | background 1.00 | 0.10 | 0.04 | asserted 1.00 |
| s2 | However, the state-of-the-art PGDS still fails to capture the \emph{time-varying} transition dynamics that are commonly observed in real-world count time sequences. | gap 1.00 | 0.11 | 0.06 | asserted 1.00 |
| s3 | To mitigate this gap, a non-stationary PGDS is proposed to allow the underlying transition matrices to evolve over time, and the evolving transition matrices are modeled by sophisticatedly-designed Dirichlet Markov chains. | contribution 0.79 | 0.93 | 0.10 | asserted 1.00 |
| s4 | Leveraging Dirichlet-Multinomial-Beta data augmentation techniques, a fully-conjugate and efficient Gibbs sampler is developed to perform posterior simulation. | method 0.97 | 0.94 | 0.04 | asserted 1.00 |
| s5 | Experiments show that, in comparison with related models, the proposed non-stationary PGDS achieves improved predictive performance due to its capacity to learn non-stationary dependency structure captured by the time-evolving transition matrices. | result 0.98 | 0.95 | 0.88 | asserted 1.00 |
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Original abstract
Probabilistic approaches for handling count-valued time sequences have attracted amounts of research attentions because their ability to infer explainable latent structures and to estimate uncertainties, and thus are especially suitable for dealing with \emph{noisy} and \emph{incomplete} count data. Among these models, Poisson-Gamma Dynamical Systems (PGDSs) are proven to be effective in capturing the evolving dynamics underlying observed count sequences. However, the state-of-the-art PGDS still fails to capture the \emph{time-varying} transition dynamics that are commonly observed in real-world count time sequences. To mitigate this gap, a non-stationary PGDS is proposed to allow the underlying transition matrices to evolve over time, and the evolving transition matrices are modeled by sophisticatedly-designed Dirichlet Markov chains. Leveraging Dirichlet-Multinomial-Beta data augmentation techniques, a fully-conjugate and efficient Gibbs sampler is developed to perform posterior simulation. Experiments show that, in comparison with related models, the proposed non-stationary PGDS achieves improved predictive performance due to its capacity to learn non-stationary dependency structure captured by the time-evolving transition matrices.
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States the same result 1 paper
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Experiments show that, in comparison with related models, the proposed PGDS achieves improved predictive performance due to its capacity to learn time-varying dependency structure captured by the time-evolving transition matrices.
Poisson-Gamma Dynamical Systems with Time-varying Transition Dynamics · 0.99
What it cites
Cites as background 1 paper
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To capture the latent dynamics underlying count sequences, some previous works [ref] model the observations as [equation] where $p( ·)$ is the observation likelihood function, and $f( ·)$ is a link function that maps the parameters of observation component to continuous-valued latent variables $x^(t) ∈ℝ^K$.
Graph Gamma Process Generalized Linear Dynamical Systems · Preliminaries · 0.94
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