Bayesian Optimization for Likelihood-Free Inference of Simulator-Based Statistical Models (1501.03291v3)

Abstract: Our paper deals with inferring simulator-based statistical models given some observed data. A simulator-based model is a parametrized mechanism which specifies how data are generated. It is thus also referred to as generative model. We assume that only a finite number of parameters are of interest and allow the generative process to be very general; it may be a noisy nonlinear dynamical system with an unrestricted number of hidden variables. This weak assumption is useful for devising realistic models but it renders statistical inference very difficult. The main challenge is the intractability of the likelihood function. Several likelihood-free inference methods have been proposed which share the basic idea of identifying the parameters by finding values for which the discrepancy between simulated and observed data is small. A major obstacle to using these methods is their computational cost. The cost is largely due to the need to repeatedly simulate data sets and the lack of knowledge about how the parameters affect the discrepancy. We propose a strategy which combines probabilistic modeling of the discrepancy with optimization to facilitate likelihood-free inference. The strategy is implemented using Bayesian optimization and is shown to accelerate the inference through a reduction in the number of required simulations by several orders of magnitude.

• The paper introduces a Bayesian optimization approach that leverages Gaussian process surrogate models for efficient likelihood-free inference in simulator-based statistical models.
• The experimental results show that the method significantly reduces simulator evaluations while enhancing parameter estimation accuracy compared to traditional ABC techniques.
• The approach offers a scalable framework for various scientific fields, addressing computational challenges in complex simulation-based models.

Bayesian Optimization for Likelihood-Free Inference of Simulator-Based Statistical Models

The paper, titled "Bayesian Optimization for Likelihood-Free Inference of Simulator-Based Statistical Models," authored by Michael U. Gutmann, presents an advanced methodology for parameter inference when the likelihood function is intractable. This addresses a common challenge within the domain of simulator-based models, which are extensively used across various scientific disciplines.

Simulator-based models, while powerful, often lack analytical or computationally feasible forms for their likelihood functions. Traditional methods like Approximate Bayesian Computation (ABC) have been employed to circumvent these difficulties, but they typically require substantial computational resources. Gutmann introduces a novel approach leveraging Bayesian optimization to perform likelihood-free inference more efficiently and effectively.

Methodology and Techniques

The proposed method integrates Bayesian optimization into the inference process, treating it as a search problem over the parameter space. This allows for optimization in cases where the objective function, i.e., the likelihood, is not directly available. The method emphasizes utilizing Gaussian processes to build a surrogate model of the simulator output, permitting fast and efficient exploration of the parameter space.

Key features of the methodology include:

• Surrogate Models: Implementation of Gaussian processes as surrogate models that allow rapid evaluations of the simulator outputs, significantly reducing computational cost.
• Acquisition Functions: Utilization of acquisition functions to strategically explore and exploit the parameter space, directing computational efforts toward promising regions that maximize information gain about the parameters.

Experimental Results

The paper presents a series of experiments demonstrating the efficacy of the approach across a range of benchmark problems traditionally tackled by simulator-based models. The method consistently outperformed conventional ABC algorithms in terms of both computational efficiency and accuracy of parameter estimates. In scenarios where prior methods would require thousands of simulator evaluations, Bayesian optimization required markedly fewer iterations, showcasing its computational advantage.

Implications and Future Directions

This research provides a robust framework for addressing likelihood-free inference challenges, with significant implications for fields reliant on complex simulators, such as physics, ecology, and cosmology. By reducing the computational burden typically associated with these models, the method opens avenues for more frequent and dynamic model refinements based on real-world data.

The primary theoretical implication lies in the seamless integration of Bayesian optimization with statistical estimation processes, highlighting potential advancements in surrogate modeling and optimization strategies.

Future research could extend this framework by exploring alternative surrogate models and acquisition functions tailored to specific classes of simulator-based models. Additionally, a deeper investigation into the scalability of this approach for high-dimensional parameter spaces could further enhance its utility across various domains.

In summary, the paper provides a substantive contribution to the computational methodologies available for likelihood-free inference, broadening the scope and efficiency of simulator-based statistical modeling.