Research map / Probabilistic and scientific modeling / Variational and generative sampling
On the Stochastic Stability of Deep Markov Models
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use parametric stability constraints with an inner expanding, middle marginal, and outer contractive region | Deep Markov Models · Two-dimensional phase-space experiments | trajectory behavior | Helped |
| Add biases to the mean and variance networks (ablation) | Deep Markov Models · Two-dimensional phase-space experiments | stability behavior | No clear effect |
| Add biases to the mean and variance networks (ablation) | Deep Markov Models · Two-dimensional phase-space experiments | equilibrium location | Mixed |
| Increase mean-network depth using mildly contractive layers (ablation) | Deep Markov Models · Two-dimensional phase-space experiments | trajectory convergence | Helped |
| Use deeper networks with contractive layers (ablation) | Deep Markov Models · Training stability | gradient behavior | Hurt |
| Use ReLU or tanh activations rather than non-contractive activations (ablation) | Deep Markov Models · Two-dimensional phase-space experiments | stochastic trajectory stability | Helped |
| Use SELU or Softplus activations rather than contractive activations (ablation) | Deep Markov Models · Two-dimensional phase-space experiments | stochastic trajectory stability | Hurt |
| Use Softplus instead of ReLU with marginally stable SVD-regularized weights (ablation) | Deep Markov Models · Two-dimensional phase-space experiments | trajectory uncertainty | Hurt |
| Use SELU instead of ReLU with marginally stable SVD-regularized weights (ablation) | Deep Markov Models · Two-dimensional phase-space experiments | trajectory stability | Mixed |
| Use tanh instead of ReLU or Softplus with Gershgorin-disc factorization (ablation) | Deep Markov Models · Two-dimensional phase-space experiments | trajectory stability | Helped |
| Use marginally stable mean dynamics with converging variance dynamics (ablation) | Deep Markov Models · Two-dimensional phase-space experiments | trajectory convergence | Helped |
| Use marginally stable variance dynamics with marginally stable mean dynamics (ablation) | Deep Markov Models · Two-dimensional phase-space experiments | trajectory stability | Hurt |
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