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Application of Granger Causality Analysis of the Directed Functional Connection in Alzheimer's Disease and Mild Cognitive Impairment

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Inference in conditioned dynamics through causality restoration.

Alfredo Braunstein^1,2,3, Giovanni Catania⁴, Luca Dall'Asta^1,2,3,5

¹DISAT, Politecnico di Torino, Corso Duca Degli Abruzzi 24, 10129, Turin, Italy.

Scientific Reports

|May 5, 2023

Summary

This summary is machine-generated.

A new Causal Variational Approach generates independent samples from conditioned dynamics efficiently. This method restores causality, enabling easier computation of observables and interpretation of results, with promising applications in epidemic inference.

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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.