Automatic Differentiation Variational Inference (1603.00788v1)

Abstract: Probabilistic modeling is iterative. A scientist posits a simple model, fits it to her data, refines it according to her analysis, and repeats. However, fitting complex models to large data is a bottleneck in this process. Deriving algorithms for new models can be both mathematically and computationally challenging, which makes it difficult to efficiently cycle through the steps. To this end, we develop automatic differentiation variational inference (ADVI). Using our method, the scientist only provides a probabilistic model and a dataset, nothing else. ADVI automatically derives an efficient variational inference algorithm, freeing the scientist to refine and explore many models. ADVI supports a broad class of models-no conjugacy assumptions are required. We study ADVI across ten different models and apply it to a dataset with millions of observations. ADVI is integrated into Stan, a probabilistic programming system; it is available for immediate use.

• The paper presents ADVI, an automated method that converts variational inference into an optimization task without requiring conjugacy assumptions.
• It employs automatic differentiation and stochastic gradient descent to efficiently approximate posterior distributions across diverse probabilistic models.
• Integration with Stan enables rapid model compilation and significant computational speed-ups compared to traditional MCMC techniques.

Overview of "Automatic Differentiation Variational Inference"

The paper "Automatic Differentiation Variational Inference" introduces ADVI, a method designed to automate the process of variational inference for complex probabilistic models. It discusses the challenges of fitting these models to large datasets and addresses the bottleneck of deriving tailored inference algorithms by integrating ADVI into the probabilistic programming system, Stan.

Key Contributions

ADVI enhances the efficiency of variational inference by automating the derivation of the inference algorithm. This is achieved without requiring the user to input anything beyond a probabilistic model and dataset. The method eliminates the need for conjugacy assumptions and supports a diverse class of models. The integration with Stan means models can be quickly compiled into executable inference programs.

Technical Methodology

ADVI transforms inference into an optimization problem through variational inference. Key steps of ADVI include:

1. Transformation of Latent Variables: ADVI automatically maps constrained latent variables into an unconstrained real-coordinate space, allowing a uniform variational family across different models.
2. Optimization with Stochastic Gradient Descent: By employing stochastic optimization and Monte Carlo integration, ADVI efficiently approximates the necessary gradients for posterior inference.
3. Adaptation to Model Classes: The use of automatic differentiation in Stan enables ADVI to handle a wide array of models, supported by Stan's extensive library of transformations and differentiation capabilities.

This workflow circumvents traditional challenges involved in specifying variational families and deriving corresponding optimization procedures.

Empirical Evaluation

ADVI was evaluated across ten different models, including linear regression with automatic relevance determination, hierarchical logistic regression, mixture models, and non-negative matrix factorization, among others. ADVI displayed significant computational efficiency compared to Markov chain Monte Carlo (MCMC) techniques, particularly in high-dimensional and large-scale data settings.

Numerical Results

The experiments demonstrated that ADVI, both in its mean-field and full-rank configurations, provides close approximations to posterior distributions, often achieving accuracy on par with more computationally intensive sampling methods while offering considerable speed advantages.

Implications and Future Directions

ADVI facilitates rapid model development and iterative model refinement by removing computational constraints traditionally associated with complex probabilistic models. Its implementation in probabilistic programming offers immediate applicability across various scientific disciplines, such as population genetics and computational neuroscience.

Moving forward, research could optimize ADVI’s sensitivity to variable transformations, explore higher-order gradient methods, and enhance convergence robustness through refined step-size adaptation. Expanding ADVI’s capabilities to handle discrete latent variables might also extend its applicability to a broader range of probabilistic programming environments.

In conclusion, ADVI represents a significant advance in automating variational inference processes, enabling researchers to explore and refine probabilistic models more effectively and efficiently within the rich framework of Stan.