All-in-one simulation-based inference (2404.09636v3)

Abstract: Amortized Bayesian inference trains neural networks to solve stochastic inference problems using model simulations, thereby making it possible to rapidly perform Bayesian inference for any newly observed data. However, current simulation-based amortized inference methods are simulation-hungry and inflexible: They require the specification of a fixed parametric prior, simulator, and inference tasks ahead of time. Here, we present a new amortized inference method -- the Simformer -- which overcomes these limitations. By training a probabilistic diffusion model with transformer architectures, the Simformer outperforms current state-of-the-art amortized inference approaches on benchmark tasks and is substantially more flexible: It can be applied to models with function-valued parameters, it can handle inference scenarios with missing or unstructured data, and it can sample arbitrary conditionals of the joint distribution of parameters and data, including both posterior and likelihood. We showcase the performance and flexibility of the Simformer on simulators from ecology, epidemiology, and neuroscience, and demonstrate that it opens up new possibilities and application domains for amortized Bayesian inference on simulation-based models.

An Expert Overview of "All-in-one Simulation-based Inference"

The paper "All-in-one simulation-based inference" introduces a novel approach to Amortized Bayesian Inference (ABI) aimed at addressing the limitations present in existing simulation-based methods. The authors propose the Simformer, which integrates transformers and probabilistic diffusion models to significantly enhance both the flexibility and efficiency of simulation-based inference (SBI). This offering represents an advance in the capacity to perform Bayesian inference across various scientific models without the constraints imposed by fixed inference tasks or parametric assumptions.

Methodological Innovations

The primary innovation of the paper is the development of the Simformer, which leverages transformer architectures combined with probabilistic diffusion models. Transformatively, the approach presents the following capabilities:

• Holistic Flexibility: Unlike existing methods that bind the inference process to predetermined parametric priors and simulators, the Simformer can handle unstructured data and function-valued parameters. This flexibility allows it to operate across a broader array of data types and simulator configurations, including nonparametric scenarios.
• Multitask Inference: The Simformer is not restricted to a single type of inference task. It enables sampling from arbitrary conditionals of the joint distribution, which encompasses both posterior and likelihood estimates. This versatility provides salient advantages in scenarios that call for exploratory analysis of data and parameter subsets or varying prior conditions.
• Efficient Utilization of Domain Knowledge: By coding known dependency structures directly into the attention mechanism of transformers, this approach exploits simulator architectures to elevate prediction accuracy while improving simulation efficiency. This capability stands to significantly reduce the computational cost often associated with ABI.

Empirical Outcomes

The Simformer was validated on an array of benchmark tasks derived from domains such as ecology, epidemiology, and neuroscience. The results demonstrated a notable performance advantage over state-of-the-art ABI methods. Specifically, when applied to these tasks, the Simformer exhibited superior accuracy and required fewer simulations. This delineation of performance was quantified using metrics like the Classifier Two-Sample Test (C2ST) accuracy, which showed reliably low scores, indicative of improved alignment with true posterior distributions.

The authors also underscored the unique ability of the Simformer to estimate arbitrary conditionals robustly. Tests on conditional distributions outside the field of posteriors confirmed the method's capacity to yield accurate inferences, even under constraints emerging from interval structuring on parameters.

Practical and Theoretical Implications

The introduction of the Simformer carries substantial implications for both practical applications and theoretical developments in the field of AI. Practically, the Simformer reduces the barrier to entry for deploying flexible and efficient Bayesian inference to real-world problems with complex, unstructured data. It affords practitioners and researchers the capacity to engage with inferential tasks without being bounded to inflexible parametric models, enhancing the applicability across divergent scientific domains.

Theoretically, the work propels the frontier of SBI by demonstrating that transformers equipped with probabilistic diffusion models can adeptly tackle the non-trivial task of Bayesian inference over multidimensional parameter landscapes. Moreover, it underlines the potential of leveraging structural knowledge within data to refine the efficiency of neural-based inference models.

Future Directions

Anticipated developments include refining the computational aspects to balance the complexity and processing power inherent in transformer evaluations. Adaptation to more efficient models for joint and marginal distribution evaluations is paramount, given the quadratic scaling of transformers. Furthermore, expanding the reach of the Simformer to encompass even more complex simulator architectures, with possibly larger and more dynamic parameter spaces, could enhance current capabilities substantially.

Overall, this paper constitutes a significant addition to the SBI literature, offering a versatile and powerful tool for tackling a broad spectrum of inference challenges encountered across scientific disciplines.