Structured Inference Networks for Nonlinear State Space Models (1609.09869v2)

Abstract: 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.

• The paper presents a unified algorithm that integrates deep neural networks and RNNs into Gaussian state space models for both linear and nonlinear cases.
• It demonstrates that structured variational approximations outperform traditional mean-field methods, evidenced by improved held-out likelihood results on real-world and synthetic datasets.
• The introduction of Deep Markov Models enhances model capacity while maintaining a Markov structure, offering promising applications in robotics, healthcare, and sequential data analysis.

Structured Inference Networks for Nonlinear State Space Models

The paper "Structured Inference Networks for Nonlinear State Space Models" presents a sophisticated approach to learning in Gaussian state space models (GSSMs), particularly focusing on nonlinear systems. The authors introduce a unified algorithm capable of efficiently learning both linear and nonlinear state space models. Key to their approach is the integration of deep learning techniques, such as deep neural networks (DNNs) and recurrent neural networks (RNNs), into traditional state space models. This combination facilitates a structured variational approximation that mimics the model's posterior distribution.

Key Contributions

• Unified Learning Algorithm: The paper proposes a comprehensive algorithm that can handle a broad spectrum of GSSMs, including those with emission and transition distributions modeled by neural networks. This versatility enables applications in high-dimensional datasets, which are typical in fields like robotics and healthcare.
• Structured Variational Approximation: The authors leverage structured variational methods, employing RNNs to better approximate the posterior distribution of the model. This structured approach is posited to surpass the traditional mean-field approximations in quality, both theoretically and empirically.
• Deep Markov Models (DMMs): A novel module, DMMs, is introduced to extend the representational capacity of GSSMs. By incorporating multilayer perceptrons (MLPs) in the model's structure, DMMs maintain a Markovian structure while benefiting from the expressive power of deep networks.

Numerical Results

The paper reports substantive numerical results, highlighting the improved held-out likelihood performance of models utilizing structured approximations over those using simpler variational methods. Specifically, models equipped with the proposed inference networks demonstrated significantly enhanced performance on synthetic and real-world datasets, including polyphonic music and electronic health records (EHRs).

Implications and Future Directions

The implications of this research are multifaceted. Practically, it provides a methodological advancement for efficiently inferring and learning complex time-series models in high-dimensional spaces. This has potential applications in domains requiring sophisticated sequential data analysis, such as automated control systems and personalized healthcare analytics.

Theoretically, the paper contributes to the burgeoning field of deep generative modeling, suggesting that structured variational approximations can be a potent tool in overcoming the limitations of mean-field assumptions. Future research might explore further generalizations of the structured inference approach, potentially extending to multi-modal data or integrating additional forms of latent variable dependencies.

Additionally, the application in EHRs to infer treatment effects represents a move towards leveraging advanced AI models for causal inference—a currently evolving area within machine learning and data science.

Conclusion

The paper offers a robust framework for modeling and inference in nonlinear state space models, bridging traditional techniques with modern deep learning innovations. By introducing robust structured inference networks, it sets the stage for more effective analysis and application of GSSMs to real-world, complex datasets. The work not only advances the theoretical understanding of state space models but also proposes practical tools that could impact various sectors reliant on time-series data.