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Register a new userQuantifying dynamical high-order interdependencies from the O-information: an application to neural spiking dynamics
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We address the problem of efficiently and informatively quantifying how multiplets of variables carry information about the future of the dynamical system they belong to. In particular we want to identify groups of variables carrying redundant or synergistic information, and track how the size and the composition of these multiplets changes as the collective behavior of the system evolves. In order to afford a parsimonious expansion of shared information, and at the same time control for lagged interactions and common effect, we develop a dynamical, conditioned version of the O-information, a framework recently proposed to quantify high-order interdependencies via multivariate extension of the mutual information. We thus obtain an expansion of the transfer entropy in which synergistic and redundant effects are separated. We apply this framework to a dataset of spiking neurons from a monkey performing a perceptual discrimination task. The method identifies synergistic multiplets that include neurons previously categorized as containing little relevant information individually.
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Research showed that, the information transmitted in biological neurons is encoded in the instants of successive action potentials or their firing rate. In addition to that, in-vivo operation of the neuron makes measurement difficult and thus continuous data collection is restricted. Due to those reasons, classical mean square estimation techniques that are frequently used in neural network training is very difficult to apply. In such situations, point processes and related likelihood methods may be beneficial. In this study, we will present how one can apply certain methods to use the stimulus-response data obtained from a neural process in the mathematical modeling of a neuron. The study is theoretical in nature and it will be supported by simulations. In addition it will be compared to a similar study performed on the same network model.
This article introduces a model-agnostic approach to study statistical synergy, a form of emergence in which patterns at large scales are not traceable from lower scales. Our framework leverages various multivariate extensions of Shannons mutual information, and introduces the O-information as a metric capable of characterising synergy- and redundancy-dominated systems. We develop key analytical properties of the O-information, and study how it relates to other metrics of high-order interactions from the statistical mechanics and neuroscience literature. Finally, as a proof of concept, we use the proposed framework to explore the relevance of statistical synergy in Baroque music scores.
High-order, beyond-pairwise interdependencies are at the core of biological, economic, and social complex systems, and their adequate analysis is paramount to understand, engineer, and control such systems. This paper presents a framework to measure high-order interdependence that disentangles their effect on each individual pattern exhibited by a multivariate system. The approach is centred on the local O-information, a new measure that assesses the balance between synergistic and redundant interdependencies at each pattern. To illustrate the potential of this framework, we present a detailed analysis of music scores from J.S. Bach, which reveals how high-order interdependence is deeply connected with highly non-trivial aspects of the musical discourse. Our results place the local O-information as a promising tool of wide applicability, which opens new perspectives for analysing high-order relationships in the patterns exhibited by complex systems.
This study presents a comprehensive analytic description in terms of the empirical whole minus sum version of Integrated Information in comparison to the decoder based version for the spiking-bursting discrete-time, discrete-state stochastic model, which was recently introduced to describe a specific type of dynamics in a neuron-astrocyte network. The whole minus sum information may change sign, and an interpretation of this transition in terms of net synergy is available in the literature. This motivates our particular interest to the sign of the whole minus sum information in our analytical consideration. The behavior of the whole minus sum and decoder based information measures are found to bear a lot of similarity, showing their mutual asymptotic convergence as time-uncorrelated activity is increased, with the sign transition of the whole minus sum information associated to a rapid growth in the decoder based information. The study aims at creating a theoretical base for using the spiking-bursting model as a well understood reference point for applying Integrated Information concepts to systems exhibiting similar bursting behavior (in particular, to neuron-astrocyte networks). The model can also be of interest as a new discrete-state test bench for different formulations of Integrated Information.
Determining how much of the sensory information carried by a neural code contributes to behavioral performance is key to understand sensory function and neural information flow. However, there are as yet no analytical tools to compute this information that lies at the intersection between sensory coding and behavioral readout. Here we develop a novel measure, termed the information-theoretic intersection information $I_{II}(S;R;C)$, that quantifies how much of the sensory information carried by a neural response R is used for behavior during perceptual discrimination tasks. Building on the Partial Information Decomposition framework, we define $I_{II}(S;R;C)$ as the part of the mutual information between the stimulus S and the response R that also informs the consequent behavioral choice C. We compute $I_{II}(S;R;C)$ in the analysis of two experimental cortical datasets, to show how this measure can be used to compare quantitatively the contributions of spike timing and spike rates to task performance, and to identify brain areas or neural populations that specifically transform sensory information into choice.
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