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Composing graphical models with neural networks for structured representations and fast inference (1603.06277v5)

Published 20 Mar 2016 in stat.ML

Abstract: We propose a general modeling and inference framework that composes probabilistic graphical models with deep learning methods and combines their respective strengths. Our model family augments graphical structure in latent variables with neural network observation models. For inference, we extend variational autoencoders to use graphical model approximating distributions with recognition networks that output conjugate potentials. All components of these models are learned simultaneously with a single objective, giving a scalable algorithm that leverages stochastic variational inference, natural gradients, graphical model message passing, and the reparameterization trick. We illustrate this framework with several example models and an application to mouse behavioral phenotyping.

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Authors (5)
  1. Matthew J. Johnson (13 papers)
  2. David Duvenaud (65 papers)
  3. Alexander B. Wiltschko (5 papers)
  4. Sandeep R. Datta (1 paper)
  5. Ryan P. Adams (74 papers)
Citations (474)

Summary

  • The paper presents a novel integrated framework that combines structured graphical models with neural network observation likelihoods to enhance representation learning and inference speed.
  • The methodology employs recognition networks and efficient message-passing algorithms to automatically generate local evidence potentials within a stochastic variational inference framework.
  • Experimental results, including mouse behavior segmentation, demonstrate the framework's practical effectiveness in capturing complex patterns and driving accurate long-term predictions.

Composing Graphical Models with Neural Networks for Structured Representations and Fast Inference

The paper under discussion proposes a novel framework that synergizes the structured probabilistic representation of graphical models with the flexible data representation capabilities of deep learning methodologies. This integration facilitates the automatic learning of representations, addressing the limitations posed by each approach when used in isolation.

Framework Overview

The essence of this framework lies in a model family that harmonizes latent graphical models with neural network observation likelihoods. Inference within this framework is driven by recognition networks that generate local evidence potentials, which are then integrated with model distributions using efficient message-passing algorithms typical of graphical models. The system is optimized through a unified stochastic variational inference objective.

Model Applications

The practical applicability of this framework is illustrated through a diverse range of models. The authors have demonstrated the capability of this framework to handle tasks such as the segmentation and categorization of mouse behavior from raw depth video. Other proposed example models include:

  • Warped Mixtures for Arbitrary Cluster Shapes: Enhancing discrete mixture models by incorporating neural network density models to capture non-traditional cluster shapes effectively. This model demonstrates a capability to reveal intricate patterns in data that conventional Gaussian Mixture Models (GMMs) might fail to capture.
  • Latent Linear Dynamical Systems (LDS) for Video Modeling: Extending a density network model of images to handle video data by incorporating continuous latent dynamical systems. This allows the model to capture higher-level temporal dynamics present in video data.
  • Latent Switching Linear Dynamical Systems (SLDS) for Behavioral Analysis: This model identifies behavioral units from video, representing them with continuous states governed by a library of discrete linear dynamics.

Inference Strategy

The paper emphasizes that the combination of conjugate exponential family graphical models and non-conjugate neural network likelihoods poses inference challenges. The challenge is elegantly addressed by employing recognition networks, following the variational autoencoder paradigm, to output conjugate graphical model potentials. These are further processed using efficient probabilistic graphical model inference algorithms, enabling a balance between expressiveness and tractability.

Evaluation and Experimental Detail

Through rigorous experimentation, the paper substantiates the applicability of the proposed framework in real-world tasks. The LDS and SLDS models, for instance, have been evaluated for their efficacy in capturing complex patterns in synthetic data and video recordings of mouse behavior, respectively. These models exhibit significant competency in generating interpretable representations and making accurate long-term predictions, as depicted in the experiments on mouse depth video.

Implications and Future Directions

The proposed structured variational autoencoder (SVAE) framework holds substantial potential for diverse applications in computational science domains where capturing the interplay between high-dimensional data features and their underlying structure is crucial. It presents a robust foundation for advancements in behavioral phenotyping, an area critical to neuroscience and pharmacological research. Furthermore, this framework invites future explorations into richer model architectures and deeper integration with progressively sophisticated neural architectures.

The advancement showcased in the paper provides a comprehensive approach to merging the structured inference strengths of graphical models with the representational power of neural networks. In the foreseeable trajectory of AI research, this framework may serve as a foundational aspect for complex data interpretation tasks, driving further innovations in automatic feature learning and inference efficiency.

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