A Unified Stochastic Gradient Approach to Designing Bayesian-Optimal Experiments (1911.00294v2)

Abstract: We introduce a fully stochastic gradient based approach to Bayesian optimal experimental design (BOED). Our approach utilizes variational lower bounds on the expected information gain (EIG) of an experiment that can be simultaneously optimized with respect to both the variational and design parameters. This allows the design process to be carried out through a single unified stochastic gradient ascent procedure, in contrast to existing approaches that typically construct a pointwise EIG estimator, before passing this estimator to a separate optimizer. We provide a number of different variational objectives including the novel adaptive contrastive estimation (ACE) bound. Finally, we show that our gradient-based approaches are able to provide effective design optimization in substantially higher dimensional settings than existing approaches.

• The paper introduces a unified stochastic gradient approach for Bayesian optimal experimental design, optimizing expected information gain using variational bounds like ACE.
• Evaluations show the stochastic gradient approach outperforms traditional methods in maximizing expected information gain, especially in higher dimensions like biomolecular docking.
• This scalable approach provides a potent framework for enhancing experimental efficiency in large-scale and complex domains like drug discovery and behavioral studies.

Bayesian-Optimal Experimental Design Using Stochastic Gradient Approach

This paper presents a novel approach to Bayesian optimal experimental design (OED) by introducing a fully stochastic gradient methodology to optimize the expected information gain (EIG). The proposed method enables simultaneous optimization with respect to variational and design parameters, which contrasts sharply with traditional approaches that separate the design evaluation from optimization processes.

Overview

The design of experiments in scientific inquiry often requires choosing configurations that provide the most informative data about the underlying phenomena while minimizing costs. In Bayesian OED, this pursuit is structured as maximizing the EIG of a design, denoted as $I(\xi)$, which quantifies the expected reduction in uncertainty about latent variables $\theta$ from observed outcomes $y$ after experimenting with design $\xi$.

Traditional methods often face high computational challenges due to the nested expectations involved in calculating $I(\xi)$. This has typically necessitated a two-stage process: estimation of EIG and optimization over potential designs using gradient-free strategies, which do not scale effectively to high-dimensional design spaces.

Methodology

The core innovation of this paper is the unification of gradient-based approaches with OED, which facilitates optimization using stochastic gradient ascent. Several variational lower bounds on EIG are constructed, notably:

• Barber-Agakov (BA) Bound: Provides a posterior-based lower bound used in variational inference scenarios.
• Adaptive Contrastive Estimation (ACE) Bound: Introduces contrasts within sampling to provide more reliable lower bounds even when inference networks deviate from true posteriors.
• Prior Contrastive Estimation (PCE) Bound: Utilizes the priors directly for contrastive sample generation, simplifying computations especially when prior distributions adequately approximate posteriors.

These bounds are designed to be optimized jointly over variational parameters and design parameters, simplifying the optimization process and allowing the use of stochastic gradients.

Results

The paper evaluates its proposed methodology across various experimental design problems, including epidemiological models, high-dimensional regression tasks, advertising budget allocation, biomolecular docking, and iterated designs in behavioral economics. Findings suggest that the gradient-based methods, particularly ACE, outperform traditional strategies in terms of EIG maximization, especially in higher dimensional spaces:

• Death Process Model: Demonstrated superior performance of gradient-based methods over Bayesian optimization in lower-dimensional settings.
• Biomolecular Docking: Showed that automated design via ACE exceeded expert-crafted designs in specificity and informativeness.
• Iterated CES Model: Highlighted the effectiveness of ACE in reducing posterior uncertainty over multiple experimental cycles as compared to marginal upper bound approaches.

Implications and Future Directions

This paper's approach provides a scalable solution to experimental design problems, particularly in large-scale and complex domains by leveraging stochastic gradients. The implications are significant for scientific fields requiring efficient data acquisition strategies, potentially enabling experiments in circuitry mapping, drug discovery, and large-scale behavioral studies to be more adaptively and cost-effectively optimized.

Future exploration could extend these methodologies to discrete design spaces where gradient approaches are non-trivial, through techniques such as continuous relaxations or hybrid optimization strategies. Integrating the unified approach to experimental design with machine learning models and probabilistic programming systems promises further enhancements in automated scientific inquiry and decision-making processes.

In summary, this unified stochastic gradient approach to Bayesian optimal experimental design introduces a potent framework for enhancing the efficiency and effectiveness of experimental schemes, paving the way for rapid advancements in data-driven domains.