arXiv subjects

Joseph T. Lizier

Publications and source records attributed to Joseph T. Lizier.

At least 19 recordsLinked to original sources

arXiv2026

Estimating measures of information processing during cognitive tasks using functional magnetic resonance imaging

Cognition is increasingly framed in terms of information processing, yet most fMRI analyses focus on activation or functional connectivity rather than quantifying how information is stored and transferred. To remedy this problem, we propose a framework for estimating measures of information processing: active information storage (AIS), transfer entropy (TE), and net synergy from task-based fMRI. AIS measures information maintained within a region, TE captures directed information flow, and net synergy contrasts higher-order synergistic to redundant interactions. Crucially, to enable this framework we utilised a recently developed approach for calculating information-theoretic measures: the cross mutual information. This approach combines resting-state and task data to address the challenges of limited sample size, non-stationarity and context in task-based fMRI. We applied this framework to the working memory (N-back) task from the Human Connectome Project (470 participants). Results show that AIS increases in fronto-parietal regions with working memory load, TE reveals enhanced directed information flows across control pathways, and net synergy indicates a global shift to redundancy. This work establishes a novel methodology for quantifying information processing in task-based fMRI.

q-bio.NC↗

arXiv2026

Unifying concepts in information-theoretic time-series analysis

Information theory is a powerful framework for quantifying complexity, uncertainty, and dynamical structure in time-series data, with widespread applicability across disciplines such as physics, finance, and neuroscience. However, the literature on these measures remains fragmented, with domain-specific terminologies, inconsistent mathematical notation, and disparate visualization conventions that hinder interdisciplinary integration. This work addresses these challenges by unifying key information-theoretic time-series measures through shared semantic definitions, standardized mathematical notation, and cohesive visual representations. We compare these measures in terms of their theoretical foundations, computational formulations, and practical interpretability -- mapping them onto a common conceptual space through an illustrative case study with functional magnetic resonance imaging time series in the brain. This case study exemplifies the complementary insights these measures offer in characterizing the dynamics of complex neural systems, such as signal complexity and information flow. By providing a structured synthesis, our work aims to enhance interdisciplinary dialogue and methodological adoption, which is particularly critical for reproducibility and interoperability in computational neuroscience. More broadly, our framework serves as a resource for researchers seeking to navigate and apply information-theoretic time-series measures to diverse complex systems.

cs.IT↗

arXiv2025

Cross Mutual Information

Mutual information (MI) is a useful information-theoretic measure to quantify the statistical dependence between two random variables: $X$ and $Y$. Often, we are interested in understanding how the dependence between $X$ and $Y$ in one set of samples compares to another. Although the dependence between $X$ and $Y$ in each set of samples can be measured separately using MI, these estimates cannot be compared directly if they are based on samples from a non-stationary distribution. Here, we propose an alternative measure for characterising how the dependence between $X$ and $Y$ as defined by one set of samples is expressed in another, \textit{cross mutual information}. We present a comprehensive set of simulation studies sampling data with $X$-$Y$ dependencies to explore this measure. Finally, we discuss how this relates to measures of model fit in linear regression, and some future applications in neuroimaging data analysis.

cs.IT↗

arXiv2024

Biological arrow of time: Emergence of tangled information hierarchies and self-modelling dynamics

We study open-ended evolution by focusing on computational and information-processing dynamics underlying major evolutionary transitions. In doing so, we consider biological organisms as hierarchical dynamical systems that generate regularities in their phase-spaces through interactions with their environment. These emergent information patterns can then be encoded within the organism's components, leading to self-modelling "tangled hierarchies". Our main conjecture is that when macro-scale patterns are encoded within micro-scale components, it creates fundamental tensions (computational inconsistencies) between what is encodable at a particular evolutionary stage and what is potentially realisable in the environment. A resolution of these tensions triggers an evolutionary transition which expands the problem-space, at the cost of generating new tensions in the expanded space, in a continual process. We argue that biological complexification can be interpreted computation-theoretically, within the Gödel--Turing--Post recursion-theoretic framework, as open-ended generation of computational novelty. In general, this process can be viewed as a meta-simulation performed by higher-order systems that successively simulate the computation carried out by lower-order systems. This computation-theoretic argument provides a basis for hypothesising the biological arrow of time.

q-bio.PE↗

arXiv2024

A feature-based information-theoretic approach for detecting interpretable, long-timescale pairwise interactions from time series

Quantifying relationships between components of a complex system is critical to understanding the rich network of interactions that characterize the behavior of the system. Traditional methods for detecting pairwise dependence of time series, such as Pearson correlation, Granger causality, and mutual information, are computed directly in the space of measured time-series values. But for systems in which interactions are mediated by statistical properties of the time series (`time-series features') over longer timescales, this approach can fail to capture the underlying dependence from limited and noisy time-series data, and can be challenging to interpret. Addressing these issues, here we introduce an information-theoretic method for detecting dependence between time series mediated by time-series features that provides interpretable insights into the nature of the interactions. Our method extracts a candidate set of time-series features from sliding windows of the source time series and assesses their role in mediating a relationship to values of the target process. Across simulations of three different generative processes, we demonstrate that our feature-based approach can outperform a traditional inference approach based on raw time-series values, especially in challenging scenarios characterized by short time-series lengths, high noise levels, and long interaction timescales. Our work introduces a new tool for inferring and interpreting feature-mediated interactions from time-series data, contributing to the broader landscape of quantitative analysis in complex systems research, with potential applications in various domains including but not limited to neuroscience, finance, climate science, and engineering.

physics.data-an↗

arXiv2023

On the information-theoretic formulation of network participation

The participation coefficient is a widely used metric of the diversity of a node's connections with respect to a modular partition of a network. An information-theoretic formulation of this concept of connection diversity, referred to here as participation entropy, has been introduced as the Shannon entropy of the distribution of module labels across a node's connected neighbors. While diversity metrics have been studied theoretically in other literatures, including to index species diversity in ecology, many of these results have not previously been applied to networks. Here we show that the participation coefficient is a first-order approximation to participation entropy and use the desirable additive properties of entropy to develop new metrics of connection diversity with respect to multiple labelings of nodes in a network, as joint and conditional participation entropies. The information-theoretic formalism developed here allows new and more subtle types of nodal connection patterns in complex networks to be studied.

physics.soc-ph↗

arXiv2023

Unifying Pairwise Interactions in Complex Dynamics

Scientists have developed hundreds of techniques to measure the interactions between pairs of processes in complex systems. But these computational methods, from correlation coefficients to causal inference, rely on distinct quantitative theories that remain largely disconnected. Here we introduce a library of 237 statistics of pairwise interactions and assess their behavior on 1053 multivariate time series from a wide range of real-world and model-generated systems. Our analysis highlights new commonalities between different mathematical formulations, providing a unified picture of a rich interdisciplinary literature. Using three real-world case studies, we then show that simultaneously leveraging diverse methods from across science can uncover those most suitable for addressing a given problem, yielding interpretable understanding of the conceptual formulations of pairwise dependence that drive successful performance. Our framework is provided in extendable open software, enabling comprehensive data-driven analysis by integrating decades of methodological advances.

physics.data-an↗

arXiv2023

Analytic relationship of relative synchronizability to network structure and motifs

Synchronization phenomena on networks have attracted much attention in studies of neural, social, economic, and biological systems, yet we still lack a systematic understanding of how relative synchronizability relates to underlying network structure. Indeed, this question is of central importance to the key theme of how dynamics on networks relate to their structure more generally. We present an analytic technique to directly measure the relative synchronizability of noise-driven time-series processes on networks, in terms of the directed network structure. We consider both discrete-time auto-regressive processes and continuous-time Ornstein-Uhlenbeck dynamics on networks. Our technique builds on computation of the network covariance matrix in the space orthogonal to the synchronized state, enabling it to be more general than previous work in not requiring either symmetric (undirected) or diagonalizable connectivity matrices, and allowing arbitrary self-link weights. More importantly, our approach quantifies the relative synchronisation specifically in terms of the contribution of process motif (walk) structures. We demonstrate that in general the relative abundance of process motifs with convergent directed walks (including feedback and feedforward loops) hinders synchronizability. We also reveal subtle differences between the motifs involved for discrete or continuous-time dynamics. Our insights analytically explain several known general results regarding synchronizability of networks, including that small-world and regular networks are less synchronizable than random networks.

cs.SI↗

arXiv2022

Disentangling high-order mechanisms and high-order behaviours in complex systems

Battiston et al. (arXiv:2110.06023) provide a comprehensive overview of how investigations of complex systems should take into account interactions between more than two elements, which can be modelled by hypergraphs and studied via topological data analysis. Following a separate line of enquiry, a broad literature has developed information-theoretic tools to characterize high-order interdependencies from observed data. While these could seem to be competing approaches aiming to address the same question, in this correspondence we clarify that this is not the case, and that a complete account of higher-order phenomena needs to embrace both.

cs.IT↗

arXiv2021

Assessing the Significance of Directed and Multivariate Measures of Linear Dependence Between Time Series

Inferring linear dependence between time series is central to our understanding of natural and artificial systems. Unfortunately, the hypothesis tests that are used to determine statistically significant directed or multivariate relationships from time-series data often yield spurious associations (Type I errors) or omit causal relationships (Type II errors). This is due to the autocorrelation present in the analysed time series -- a property that is ubiquitous across diverse applications, from brain dynamics to climate change. Here we show that, for limited data, this issue cannot be mediated by fitting a time-series model alone (e.g., in Granger causality or prewhitening approaches), and instead that the degrees of freedom in statistical tests should be altered to account for the effective sample size induced by cross-correlations in the observations. This insight enabled us to derive modified hypothesis tests for any multivariate correlation-based measures of linear dependence between covariance-stationary time series, including Granger causality and mutual information with Gaussian marginals. We use both numerical simulations (generated by autoregressive models and digital filtering) as well as recorded fMRI-neuroimaging data to show that our tests are unbiased for a variety of stationary time series. Our experiments demonstrate that the commonly used $F$- and $χ^2$-tests can induce significant false-positive rates of up to $100\%$ for both measures, with and without prewhitening of the signals. These findings suggest that many dependencies reported in the scientific literature may have been, and may continue to be, spuriously reported or missed if modified hypothesis tests are not used when analysing time series.

stat.ME↗

arXiv2020

Inferring network properties from time series using transfer entropy and mutual information: validation of multivariate versus bivariate approaches

Functional and effective networks inferred from time series are at the core of network neuroscience. Interpreting their properties requires inferred network models to reflect key underlying structural features; however, even a few spurious links can distort network measures, challenging functional connectomes. We study the extent to which micro- and macroscopic properties of underlying networks can be inferred by algorithms based on mutual information and bivariate/multivariate transfer entropy. The validation is performed on two macaque connectomes and on synthetic networks with various topologies (regular lattice, small-world, random, scale-free, modular). Simulations are based on a neural mass model and on autoregressive dynamics (employing Gaussian estimators for direct comparison to functional connectivity and Granger causality). We find that multivariate transfer entropy captures key properties of all networks for longer time series. Bivariate methods can achieve higher recall (sensitivity) for shorter time series but are unable to control false positives (lower specificity) as available data increases. This leads to overestimated clustering, small-world, and rich-club coefficients, underestimated shortest path lengths and hub centrality, and fattened degree distribution tails. Caution should therefore be used when interpreting network properties of functional connectomes obtained via correlation or pairwise statistical dependence measures, rather than more holistic (yet data-hungry) multivariate models.

q-bio.NC↗

arXiv2020

Deriving pairwise transfer entropy from network structure and motifs

Transfer entropy is an established method for quantifying directed statistical dependencies in neuroimaging and complex systems datasets. The pairwise (or bivariate) transfer entropy from a source to a target node in a network does not depend solely on the local source-target link weight, but on the wider network structure that the link is embedded in. This relationship is studied using a discrete-time linearly-coupled Gaussian model, which allows us to derive the transfer entropy for each link from the network topology. It is shown analytically that the dependence on the directed link weight is only a first approximation, valid for weak coupling. More generally, the transfer entropy increases with the in-degree of the source and decreases with the in-degree of the target, indicating an asymmetry of information transfer between hubs and low-degree nodes. In addition, the transfer entropy is directly proportional to weighted motif counts involving common parents or multiple walks from the source to the target, which are more abundant in networks with a high clustering coefficient than in random networks. Our findings also apply to Granger causality, which is equivalent to transfer entropy for Gaussian variables. Moreover, similar empirical results on random Boolean networks suggest that the dependence of the transfer entropy on the in-degree extends to nonlinear dynamics.

cs.IT↗

arXiv2019

Generalised Measures of Multivariate Information Content

The entropy of a pair of random variables is commonly depicted using a Venn diagram. This representation is potentially misleading, however, since the multivariate mutual information can be negative. This paper presents new measures of multivariate information content that can be accurately depicted using Venn diagrams for any number of random variables. These measures complement the existing measures of multivariate mutual information and are constructed by considering the algebraic structure of information sharing. It is shown that the distinct ways in which a set of marginal observers can share their information with a non-observing third party corresponds to the elements of a free distributive lattice. The redundancy lattice from partial information decomposition is then subsequently and independently derived by combining the algebraic structures of joint and shared information content.

cs.IT↗

arXiv2019

Large-scale directed network inference with multivariate transfer entropy and hierarchical statistical testing

Network inference algorithms are valuable tools for the study of large-scale neuroimaging datasets. Multivariate transfer entropy is well suited for this task, being a model-free measure that captures nonlinear and lagged dependencies between time series to infer a minimal directed network model. Greedy algorithms have been proposed to efficiently deal with high-dimensional datasets while avoiding redundant inferences and capturing synergistic effects. However, multiple statistical comparisons may inflate the false positive rate and are computationally demanding, which limited the size of previous validation studies. The algorithm we present---as implemented in the IDTxl open-source software---addresses these challenges by employing hierarchical statistical tests to control the family-wise error rate and to allow for efficient parallelisation. The method was validated on synthetic datasets involving random networks of increasing size (up to 100 nodes), for both linear and nonlinear dynamics. The performance increased with the length of the time series, reaching consistently high precision, recall, and specificity (>98% on average) for 10000 time samples. Varying the statistical significance threshold showed a more favourable precision-recall trade-off for longer time series. Both the network size and the sample size are one order of magnitude larger than previously demonstrated, showing feasibility for typical EEG and MEG experiments.

q-bio.NC↗

arXiv2019

IDTxl: The Information Dynamics Toolkit xl: a Python package for the efficient analysis of multivariate information dynamics in networks

The Information Dynamics Toolkit xl (IDTxl) is a comprehensive software package for efficient inference of networks and their node dynamics from multivariate time series data using information theory. IDTxl provides functionality to estimate the following measures: 1) For network inference: multivariate transfer entropy (TE)/Granger causality (GC), multivariate mutual information (MI), bivariate TE/GC, bivariate MI 2) For analysis of node dynamics: active information storage (AIS), partial information decomposition (PID) IDTxl implements estimators for discrete and continuous data with parallel computing engines for both GPU and CPU platforms. Written for Python3.4.3+.

cs.IT↗

arXiv2018

Entropy balance and Information processing in bipartite and non-bipartite composite systems

Information dynamics is an emerging description of information processing in complex systems which describes systems in terms of intrinsic computation, identifying computational primitives of information storage and transfer. In this paper we make a formal analogy between information dynamics and stochastic thermodynamics which describes the thermal behaviour of small irreversible systems. As stochastic dynamics is increasingly being utilized to quantify the thermodynamics associated with the processing of information we suggest such an analogy is instructive, highlighting that existing thermodynamic quantities can be described solely in terms of extant information theoretic measures related to information processing. In this contribution we construct irreversibility measures in terms of these quantities and relate them to the physical entropy productions that characterise the behaviour of single and composite systems in stochastic thermodynamics illustrating them with simple examples. Moreover, we can apply such a formalism to systems which do not have a bipartite structure. In particular we demonstrate that, given suitable non-bipartite processes, the heat flow in a subsystem can still be identified and one requires the present formalism to recover generalizations of the second law. In these systems residual irreversibility is associated with neither subsystem and this must be included in the these generalised second laws. This opens up the possibility of describing all physical systems in terms of computation allowing us to propose a framework for discussing the reversibility of systems traditionally out of scope of stochastic thermodynamics.

cond-mat.stat-mech↗

arXiv2018

Characterising information-theoretic storage and transfer in continuous time processes

The characterisation of information processing is an important task in complex systems science. Information dynamics is a quantitative methodology for modelling the intrinsic information processing conducted by a process represented as a time series, but to date has only been formulated in discrete time. Building on previous work which demonstrated how to formulate transfer entropy in continuous time, we give a total account of information processing in this setting, incorporating information storage. We find that a convergent rate of predictive capacity, comprised of the transfer entropy and active information storage, does not exist, arising through divergent rates of active information storage. We identify that active information storage can be decomposed into two separate quantities that characterise predictive capacity stored in a process: active memory utilisation and instantaneous predictive capacity. The latter involves prediction related to path regularity and so solely inherits the divergent properties of the active information storage, whilst the former permits definitions of pathwise and rate quantities. We formulate measures of memory utilisation for jump and neural spiking processes and illustrate measures of information processing in synthetic neural spiking models and coupled Ornstein-Uhlenbeck models. The application to synthetic neural spiking models demonstrates that active memory utilisation for point processes consists of discontinuous jump contributions (at spikes) interrupting a continuously varying contribution (relating to waiting times between spikes), complementing the behaviour previously demonstrated for transfer entropy in these processes.

cs.IT↗

arXiv2018

An interview based study of pioneering experiences in teaching and learning Complex Systems in Higher Education

Due to the interdisciplinary nature of complex systems as a field, students studying complex systems at University level have diverse disciplinary backgrounds. This brings challenges (e.g. wide range of computer programming skills) but also opportunities (e.g. facilitating interdisciplinary interactions and projects) for the classroom. However, there is little published regarding how these challenges and opportunities are handled in teaching and learning Complex Systems as an explicit subject in higher education, and how this differs in comparison to other subject areas. We seek to explore these particular challenges and opportunities via an interview-based study of pioneering teachers and learners (conducted amongst the authors) regarding their experiences. We compare and contrast those experiences, and analyse them with respect to the educational literature. Our discussions explored: approaches to curriculum design, how theories/models/frameworks of teaching and learning informed decisions and experience, how diversity in student backgrounds was addressed, and assessment task design. We found a striking level of commonality in the issues expressed as well as the strategies to handle them, for example a significant focus on problem-based learning, and the use of major student-led creative projects for both achieving and assessing learning outcomes.

physics.ed-ph↗