This section proposes additional regularization methods for learning stable deep Markov models. The most direct approach is to include the stability conditions as extra penalties in the DMM loss function.

In this paper, we provide sufficient conditions of DMM's stochastic stability as defined in the context of dynamical systems

However, due to the intractable partition function, they are typically trained via contrastive divergence for maximum likelihood estimation.

A popular approach for estimating the predictive uncertainty of neural networks is to define a prior distribution over the network parameters, infer an approximate posterior distribution, and use it to make stochastic predictions.

These techniques are often very effective in practice and benefit from favorable margin-based learning guarantees (Schapire et al.,