Likelihood-free inference via classification.

Area of Science:

• Computational Statistics
• Machine Learning
• Generative Models

Background:

• Complex generative models offer realistic data characterization but face computational challenges for likelihood-based inference.
• Likelihood-free inference (LFI) identifies parameters by matching simulated to observed data, but measuring data discrepancy is difficult.
• Existing LFI methods struggle with quantifying the difference between simulated and real-world data.

Purpose of the Study:

• To develop a novel approach for discrepancy measurement in likelihood-free inference.
• To leverage classification methods for parameter inference in generative models with intractable likelihoods.
• To demonstrate the applicability of classification accuracy as a discrepancy metric in LFI.

Main Methods:

• Transformed the problem of discrepancy measurement into a binary classification task: distinguishing simulated from observed data.
• Utilized classification accuracy as a direct measure of the discrepancy between simulated and observed datasets.
• Applied this classification-based discrepancy metric to perform both point estimation and Bayesian inference for generative models.

Main Results:

• Demonstrated that classification accuracy effectively quantifies the discrepancy between simulated and observed data.
• Validated the approach through theoretical analysis and simulations for parameter estimation.
• Successfully inferred an individual-based epidemiological model for bacterial infections using real-world data.

Conclusions:

• Classification accuracy provides a powerful and versatile metric for discrepancy measurement in likelihood-free inference.
• This approach broadens the applicability of machine learning classification techniques to statistical inference problems.
• The method offers a computationally efficient alternative for analyzing complex generative models across various scientific domains.