Inference in conditioned dynamics through causality restoration

Area of Science:

• Computational Science
• Statistical Physics
• Dynamical Systems

Background:

• Estimating observables from conditioned dynamics is computationally challenging.
• Conditioning dynamics breaks causal properties, leading to inefficient sampling.
• Existing methods often discard many samples that do not meet imposed conditions.

Purpose of the Study:

• To propose a Causal Variational Approach for efficient generation of independent samples from conditioned distributions.
• To restore causality in conditioned dynamics for non-trivial sampling.
• To enable efficient computation of observables and provide interpretable results.

Main Methods:

• Learning parameters of a generalized dynamical model in a variational sense.
• Developing an effective, unconditioned dynamical model from conditioned dynamics.
• Applying the approximation to various dynamical systems, including epidemic inference.

Main Results:

• The Causal Variational Approach generates independent samples efficiently from conditioned distributions.
• The method effectively restores causality, simplifying sampling.
• Allows for efficient computation of observables via averaging over independent samples.
• Provides an interpretable, effective unconditioned distribution.

Conclusions:

• The proposed Causal Variational Approach offers an efficient and interpretable method for sampling conditioned dynamics.
• Promising results were observed when applied to epidemic inference, outperforming state-of-the-art methods.
• The approximation is broadly applicable to diverse dynamical systems.