Mutual Information Disentangles Interactions from Changing Environments

Nicoletti, Giorgio; Busiello, Daniel Maria

doi:10.1103/physrevlett.127.228301

Cited by 23 publications

(24 citation statements)

References 42 publications

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“…This framework is analogous to the one introduced in [13]. It is described by the following Fokker-Planck equation,…”

Section: Time-scale Separation Approachmentioning

confidence: 99%

“…The multidimensional generalization is straightforward. In [13], we showed that, in the presence of linear interactions -i.e., when Eq. ( 5) corresponds to a Gaussian mixture -the mutual information can be exactly disentangled into two independent contributions.…”

Section: Mutual Information: Dependencies and Boundsmentioning

confidence: 99%

“…12 is the mutual information associated with the i-th component P st i (x 1 , x 2 ) of the joint distribution. These bounds can be greatly improved [13,18], provided our ability to compute some suitable information distances both between the components of the mixture distribution in Eq. ( 5) and the components of the two corresponding marginalization.…”

Section: Mutual Information: Dependencies and Boundsmentioning

confidence: 99%

“…I quantifies the overall dependency between x 1 and x 2 . Recently, we showed that the mutual information of systems with linear interactions and a switching discrete-state environment receive disentangled contributions from environmental and internal interactions [13]. This result revealed that the properties of the information content of complex systems can be particularly informative, and that tools from information theory may greatly help to capture their essential features [14].…”

Section: Introductionmentioning

confidence: 97%

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Mutual information in changing environments: non-linear interactions, out-of-equilibrium systems, and continuously-varying diffusivities

Nicoletti,

Busiello

2022

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Biochemistry, ecology, and neuroscience are examples of prominent fields aiming at describing interacting systems that exhibit non-trivial couplings to complex, ever-changing environments. We have recently shown that linear interactions and a switching environment are encoded separately in the mutual information of the overall system. Here, we first generalize these findings to a broad class of non-linear interacting models. We find that a new term in the mutual information appears, quantifying the interplay between non-linear interactions and environmental changes, and leading to either constructive or destructive information interference. Furthermore, we show that a higher mutual information emerges in out-of-equilibrium environments with respect to an equilibrium scenario. Finally, we generalize our framework to the case of continuously varying environments. We find that environmental changes can be mapped exactly into an effective spatially-varying diffusion coefficient, shedding light on modeling and information structure of biophysical systems in inhomogeneous media.

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“…This framework is analogous to the one introduced in [13]. It is described by the following Fokker-Planck equation,…”

Section: Time-scale Separation Approachmentioning

confidence: 99%

Section: Mutual Information: Dependencies and Boundsmentioning

confidence: 99%

Section: Mutual Information: Dependencies and Boundsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

See 2 more Smart Citations

Mutual information in changing environments: non-linear interactions, out-of-equilibrium systems, and continuously-varying diffusivities

Nicoletti,

Busiello

2022

Preprint

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“…As information theory has proven to be a promising framework to capture essential features of complex stochastic systems [22][23][24], we build an optimal model that captures the maximum amount of information on possibly short-time trajectories in the x-space. Hence, we relax the stationarity assumption and include the effect of the initial conditions.…”

mentioning

confidence: 99%

Information-driven transitions in projections of underdamped dynamics

Nicoletti,

Maritan,

Busiello

2022

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Low-dimensional representations of underdamped systems often provide insightful grasps and analytical tractability. Here, we build such representations via information projections, obtaining an optimal model that captures the most information on observed spatial trajectories. We show that, in paradigmatic systems, the minimization of the information loss drives the appearance of a discontinuous transition in the optimal model parameters. Our results raise serious warnings for general inference approaches and unravel fundamental properties of effective dynamical representations, impacting several fields, from biophysics to dimensionality reduction.

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