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

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

Deep Markov models (DMM) are generative models which are scalable and expressive generalization of Markov models for representation, learning, and inference problems. However, the fundamental stochastic stability guarantees of such models have not been thoroughly investigated. In this paper, we present a novel stability analysis method and provide sufficient conditions of DMM's stochastic stability. The proposed stability analysis is based on the contraction of probabilistic maps modeled by deep neural networks. We make connections between the spectral properties of neural network's weights and different types of used activation function on the stability and overall dynamic behavior of DMMs with Gaussian distributions.

In this paper, we propose a novel reinforcement learning (RL) based path generation (RL-PG) approach for mobile robot navigation without a prior exploration of an unknown environment. Multiple predictive path points are dynamically generated by a deep Markov model optimized using RL approach for robot to track. To ensure the safety when tracking the predictive points, the robot's motion is fine-tuned by a motion fine-tuning module. Such an approach, using the deep Markov model with RL algorithm for planning, focuses on the relationship between adjacent path points. We analyze the benefits that our proposed approach are more effective and are with higher success rate than RL-Based approach DWA-RL and a traditional navigation approach APF. We deploy our model on both simulation and physical platforms and demonstrate our model performs robot navigation effectively and safely.

Clinical practice in intensive care units (ICUs) requires early warnings when a patient's condition is about to deteriorate so that preventive measures can be undertaken. To this end, prediction algorithms have been developed that estimate the risk of mortality in ICUs. In this work, we propose a novel generative deep probabilistic model for real-time risk scoring in ICUs. Specifically, we develop an attentive deep Markov model called AttDMM. To the best of our knowledge, AttDMM is the first ICU prediction model that jointly learns both long-term disease dynamics (via attention) and different disease states in health trajectory (via a latent variable model). Our evaluations were based on an established baseline dataset (MIMIC-III) with 53,423 ICU stays. The results confirm that compared to state-of-the-art baselines, our AttDMM was superior: AttDMM achieved an area under the receiver operating characteristic curve (AUROC) of 0.876, which yielded an improvement over the state-of-the-art method by 2.2%. In addition, the risk score from the AttDMM provided warnings several hours earlier. Thereby, our model shows a path towards identifying patients at risk so that health practitioners can intervene early and save patient lives.

Integrating deep learning with latent state space models has the potential to yield temporal models that are powerful, yet tractable and interpretable. Unfortunately, current models are not designed to handle missing data or multiple data modalities, which are both prevalent in real-world data. In this work, we introduce a factorized inference method for Multimodal Deep Markov Models (MDMMs), allowing us to filter and smooth in the presence of missing data, while also performing uncertainty-aware multimodal fusion. We derive this method by factorizing the posterior p(z|x) for non-linear state space models, and develop a variational backward-forward algorithm for inference. Because our method handles incompleteness over both time and modalities, it is capable of interpolation, extrapolation, conditional generation, and label prediction in multimodal time series. We demonstrate these capabilities on both synthetic and real-world multimodal data under high levels of data deletion. Our method performs well even with more than 50% missing data, and outperforms existing deep approaches to inference in latent time series.