Disease progression models are instrumental in predicting individual-level health trajectories and understanding disease dynamics. Existing models are capable of providing either accurate predictions of patients prognoses or clinically interpretable representations of disease pathophysiology, but not both. In this paper, we develop the phased attentive state space (PASS) model of disease progression, a deep probabilistic model that captures complex representations for disease progression while maintaining clinical interpretability. Unlike Markovian state space models which assume memoryless dynamics, PASS uses an attention mechanism to induce "memoryful" state transitions, whereby repeatedly updated attention weights are used to focus on past state realizations that best predict future states. This gives rise to complex, non-stationary state dynamics that remain interpretable through the generated attention weights, which designate the relationships between the realized state variables for individual patients. PASS uses phased LSTM units (with time gates controlled by parametrized oscillations) to generate the attention weights in continuous time, which enables handling irregularly-sampled and potentially missing medical observations. Experiments on data from a realworld cohort of patients show that PASS successfully balances the tradeoff between accuracy and interpretability: it demonstrates superior predictive accuracy and learns insightful individual-level representations of disease progression.
Deep probabilistic models , , Most existing works on deep probabilistic models have focused on developed structured inference algorithms for deep Markov models and their variants @cite_17 @cite_18 @cite_6 @cite_25 . All such models use neural networks to model the transition and emission distributions, but are limited to Markovian dynamics. Other works develop stochastic versions of RNNs for the sake of generative modeling; examples include variational RNNs @cite_12 , SRNN @cite_5 , and STORN @cite_11 . All such models augment stochastic layers to an RNN in order to enrich its output distribution. However, the transition and emission distributions in all these models cannot be decoupled, and hence their latent state representations would not lead to clinically meaningful identification of disease states. To the best of our knowledge, PASS is the first deep probabilistic model that provides both a clinically interpretable latent representation, and interpretable non-Markovian state dynamics.
@cite_18 @cite_11 @cite_6 @cite_5 @cite_25 @cite_12 @cite_17
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Leveraging advances in variational inference, we propose to enhance recurrent neural networks with latent variables, resulting in Stochastic Recurrent Networks (STORNs). The model i) can be trained with stochastic gradient methods, ii) allows structured and multi-modal conditionals at each time step, iii) features a reliable estimator of the marginal likelihood and iv) is a generalisation of deterministic recurrent neural networks. We evaluate the method on four polyphonic musical data sets and motion capture data. We introduce Deep Variational Bayes Filters (DVBF), a new method for unsupervised learning of latent Markovian state space models. Leveraging recent advances in Stochastic Gradient Variational Bayes, DVBF can overcome intractable inference distributions by means of variational inference. Thus, it can handle highly nonlinear input data with temporal and spatial dependencies such as image sequences without domain knowledge. Our experiments show that enabling backpropagation through transitions enforces state space assumptions and significantly improves information content of the latent embedding. This also enables realistic long-term prediction. How can we efficiently propagate uncertainty in a latent state representation with recurrent neural networks? This paper introduces stochastic recurrent neural networks which glue a deterministic recurrent neural network and a state space model together to form a stochastic and sequential neural generative model. The clear separation of deterministic and stochastic layers allows a structured variational inference network to track the factorization of the model's posterior distribution. By retaining both the nonlinear recursive structure of a recurrent neural network and averaging over the uncertainty in a latent path, like a state space model, we improve the state of the art results on the Blizzard and TIMIT speech modeling data sets by a large margin, while achieving comparable performances to competing methods on polyphonic music modeling. The goal of personalized history-based recommendation is to automatically output a distribution over all the items given a sequence of previous purchases of a user. In this work, we present a novel approach that uses a recurrent network for summarizing the history of purchases, continuous vectors representing items for scalability, and a novel attention-based recurrent mixture density network, which outputs each component in a mixture sequentially, for modelling a multi-modal conditional distribution. We evaluate the proposed approach on two publicly available datasets, MovieLens-20M and RecSys15. The experiments show that the proposed approach, which explicitly models the multi-modal nature of the predictive distribution, is able to improve the performance over various baselines in terms of precision, recall and nDCG. Gaussian state space models have been used for decades as generative models of sequential data. They admit an intuitive probabilistic interpretation, have a simple functional form, and enjoy widespread adoption. We introduce a unified algorithm to efficiently learn a broad class of linear and non-linear state space models, including variants where the emission and transition distributions are modeled by deep neural networks. Our learning algorithm simultaneously learns a compiled inference network and the generative model, leveraging a structured variational approximation parameterized by recurrent neural networks to mimic the posterior distribution. We apply the learning algorithm to both synthetic and real-world datasets, demonstrating its scalability and versatility. We find that using the structured approximation to the posterior results in models with significantly higher held-out likelihood.