Automatic Reparameterisation of Probabilistic Programs (1906.03028v1)

Abstract: Probabilistic programming has emerged as a powerful paradigm in statistics, applied science, and machine learning: by decoupling modelling from inference, it promises to allow modellers to directly reason about the processes generating data. However, the performance of inference algorithms can be dramatically affected by the parameterisation used to express a model, requiring users to transform their programs in non-intuitive ways. We argue for automating these transformations, and demonstrate that mechanisms available in recent modeling frameworks can implement non-centring and related reparameterisations. This enables new inference algorithms, and we propose two: a simple approach using interleaved sampling and a novel variational formulation that searches over a continuous space of parameterisations. We show that these approaches enable robust inference across a range of models, and can yield more efficient samplers than the best fixed parameterisation.

• The paper introduces automated reparameterisation to improve inference efficiency in probabilistic programs by transforming hierarchical Bayesian models.
• It presents the iHMC method, which interleaves centred and non-centred parameterisations to manage shifts in posterior geometry effectively.
• The VIP algorithm optimizes parameterisations to produce near-independent Gaussian posteriors, significantly boosting effective sample sizes.

Automatic Reparameterisation of Probabilistic Programs: A Methodological Exploration

This essay examines the methodological contributions of the paper titled "Automatic Reparameterisation of Probabilistic Programs." The paper primarily tackles the challenges associated with parameterisation in probabilistic programming and proposes automated mechanisms to enhance inference efficiency across diverse models. The paper makes significant contributions by offering methods to automate model transformations.

Technical Contributions

The central notion in this work is the reparameterisation of probabilistic models using automated techniques. Reparameterisation involves transforming models by expressing them in terms of new variables derived through bijective transformations of the original variables. The paper focuses on non-centring, a well-recognized technique in Bayesian hierarchical models. This transformation can significantly alter the posterior geometry, thereby impacting the performance of inference algorithms.

Novel Algorithms

The authors introduce two innovative inference algorithms that leverage automatic reparameterisation:

1. Interleaved Hamiltonian Monte Carlo (iHMC): This method involves alternating HMC steps between centred and non-centred parameterisations. This approach is particularly beneficial as it is robust against different parameterisations, ensuring performance comparable to or better than using a single fixed parameterisation.
2. Variationally Inferred Parameterisation (VIP): This novel algorithm traverses a continuous space of parameterisations, seeking those that optimize inference. The objective is to identify parameterisations under which the posterior is effectively independent and Gaussian, thus improving the efficiency of various inference techniques.

These algorithms illustrate the potential of automatic reparameterisation to alleviate the burdens on practitioners who traditionally transform models through manual interventions—a process both error-prone and time-consuming.

Results and Implications

The experiments showcased in the paper demonstrate considerable advancements in inference efficiency. The application of iHMC and VIP to various hierarchical Bayesian models, including the "Eight Schools" problem and logistic regression models, showed robust performance. Notably, there were instances where the new methodologies outperformed traditional approaches, particularly when neither centred nor non-centred methods alone sufficed. For instance, in some models, VIP achieved an effective sample size (ESS) several times larger than traditional methods.

The implications of this research extend into both theoretical and practical domains. Theoretically, the paper underscores the importance of posterior geometry in inference efficiency, highlighting a fertile ground for further exploration in automatic transformations. Practically, the automation of these processes simplifies the workflow for practitioners, reducing the need for trial-and-error adjustments and allowing for more consistent and reproducible model development.

Future Progressions

Looking ahead, potential future research could focus on enhancing these methods by integrating them with black-box optimization techniques, ensuring broader applicability across different PPLs. Another promising direction is the exploration of joint reparameterisation and structure-learning techniques that adapt not just parameterisations, but the underlying probabilistic structures concurrently.

In conclusion, the automatic reparameterisation of probabilistic programs presented in this paper represents a significant stride toward more efficient inference techniques. By automating what once required intricate domain knowledge, this work paves the way for more accessible and robust applications of probabilistic programming in statistical and machine learning contexts.