Background

Causality is a philosophical endeavor formalizing knowledge about the world and its transformations. It has produced a refined mathematical framework, called Structural Causal Models (SCM), that has been instrumental in many scientific fields. The field of causal machine learning has been expanding in recent years as the questions of robustness and interpretability of algorithms became increasingly related to causality, which puts the focus on the data generating mechanisms and their possible changes.

Notably, it is now well accepted that powerful deep learning algorithms for image classification may deliver their predictions based on “spurious features”, not causally related to the relevant information, and as such may underperform when they are deployed in different environments. More recently, impressive results have been obtained by generative AI, allowing to produce highly-realistic novel texts and images. However, again, those algorithms are not guaranteed to behave according to basic causality principles (and even common sense) and may produce surprising mistakes.

Causality provides principled ways to study and improve AI algorithms. In particular, it can endow generative AI with the ability to emulate meaningful changes to the data generating mechanisms, called interventions, and produce “what-if” scenarios called counterfactuals. Leveraging causal generative AI thus carries the potential to explore the space of possible transformations of a system to anticipate failures, and inform decision makers.

Contributions

Data is often not enough to infer unambiguously the causal model that generated it. Our theoretical contributions to the field of causal machine learning have revolved around the question of causal model identifiability, establishing principles and assumptions under which we can recover information about the ground truth mechanisms based on data.

Answering this question is crucial for applications: only if mechanisms are correctly recovered can we expect interventions on the inferred causal model to be predictive of real-world changes. We have investigated the principle of Independence of Causal Mechanisms (ICM), according to which we assume that the different mechanisms forming a causal model do not inform each other. We have shown that it can be mathematically formulated and exploited in various ways to expand capabilities of causal inference to new settings [Besserve et al., AISTATS 2018]. In particular, this led to new causal model identification approaches in contexts ranging from robust inference of the direction of causation in multivariate time series [Shajarisales et al., ICML 2015; Besserve et al., CLeaR 2022], to analyzing the internal causal structure of generative AI trained on complex image datasets [Besserve et al., AAAI 2021] and generating counterfactual images able to assessing robustness of object classification algorithms [Besserve et al., ICLR 2020].

Recently, we were able to make a major breakthrough in the problem of identifiability of nonlinear generative models: ICM could be formulated as a restriction of the function class of such models, providing guarantees that the ground truth function can be identified based on unlabeled observational data [Gresele et al., NeurIPS 2021, Buchholz et al., NeurIPS 2022]. Moreover, we could demonstrate that such inductive bias is implicitly performed in Variational Autoencoders [Reizinger et al., 2022], providing an explanation for their empirical success at disentangling the factors of variations of image datasets.

On the applications side, we have pursued the goal of understanding brain function through the lens of causality, data science and biophysical modeling. We have used causal inference and machine learning to uncover information processing pathways of visual and memory systems which led to publications in major multidisciplinary and biology journals [Besserve et al., PLOS Biology 2015; Ramirez-Villegas et al., PNAS 2015; Ramirez-Villegas et al., Nature 2020]. We have developed biologically realistic computational models of cortical networks to study the precise mechanism underlying dynamical brain phenomena during information processing, notably leading to state-of-the-art realistic simulations of high frequency oscillations occurring in memory systems as we remember events [Ramirez-Villegas et al., Neuron 2018].

More recently, we broadened our investigation of complex systems by studying multiagent [Geiger et al., UAI 2019] and socio-economic systems [Besserve & Schölkopf, UAI 2022], which, similarly to brain networks, are characterized by their high dimensionality and recurrent interactions. Motivated by fostering the transition to sustainable economies, we developed theoretical foundations and algorithms to design optimal interventions in such systems [Besserve & Schölkopf, UAI 2022]. This approach merges causality, machine learning and scientific modeling by relying on a differentiable simulator of economic equilibrium.

Vision

Our current reseach aims at developping a Causal Computational Model (CCM) framework: learning digital representations of real-world systems integrating data, domain knowledge and an interpretable causal structure. This aims at improving robustness and interpretability of a broad range of highly detailed models that can be linked to empirical data: simulators of scientific models based on (partial) differential equations (e.g. general circulation models of the Earth atmosphere), digital twins of industrial systems (e.g. factories, bridges), computable general equilibrium models of the economy, multi-agent systems simulators (e.g. traffic models).

Due to their complexity, the causal structure of such models is not directly apparent to decision makers and hinders the ability of modelers to communicate constructively the limitations and impacts of their work. CCMs add a layer of causal abstraction: a simplified causal representation that aggregates variables of the low-level model into a high-level model with fewer variables. This allows users to switch between two different levels of description, the low-level describing the minute phenomena, and the high-level describing global behavior of the system. We have started to address how to build such abstraction from simulations in a recent preprint [Kekić et al., arXiv 2023].

This framework will lead to causal AIs that can address the complexity of real-world systems, while producing interpretable outcomes for decision makers.

Selection by topic

Machine Learning and Causality

Target Reduction of Causal Models, A. Kekić, B. Schölkopf and M. Besserve. arXiv preprint.

Information theoretic measures of causal influences during transient neural events, K. Shao, N. K. Logothetis and M. Besserve. Frontiers in Network Physiology, Section Information Theory 2023.

Embrace the Gap: VAEs Perform Independent Mechanism Analysis, P. Reizinger, L. Gresele, J. Brady, J. von Kügelgen, D. Zietlow, B. Schölkopf, G. Martius, W. Brendel, M. Besserve. NeurIPS 2022.

Learning soft interventions in complex equilibrium systems, M. Besserve and B. Schölkopf, UAI 2022 (oral).

Independent mechanism analysis, a new concept? L. Gresele, J. von Kügelgen, Vincent Stimper, Bernhard Schölkopf and M. Besserve, NeurIPS 2021.

Self-Supervised Learning with Data Augmentations Provably Isolates Content from Style J. von Kügelgen, Y. Sharma, L. Gresele, W. Brendel, B. Schölkopf, M. Besserve and Francesco Locatello, NeurIPS 2021.

A theory of independent mechanisms for extrapolation in generative models, M. Besserve, R. Sun, D. Janzing and B. Schölkopf, AAAI-2021.

Counterfactuals uncover the modular structure of deep generative models, M. Besserve, A. Merhjou, R. Sun and B. Schölkopf, ICLR 2020.

Group invariance principles for causal generative models, M. Besserve, N. Shajarisales, B. Schölkopf and D. Janzing, Proceedings of the 21st International Conference on Artificial Intelligence and Statistics (AISTATS) 2018.

Statistics and Stochastic Processes

Function Classes for Identifiable Nonlinear Independent Component Analysis, S. Buchholz, M. Besserve and B. Schölkopf. NeurIPS 2022.

Cause-effect inference through spectral independence in linear dynamical systems: theoretical foundations, M. Besserve, N. Shajarisales, D. Janzing, B. Schölkopf CLeaR 2022.

From univariate to multivariate coupling between continuous signals and point processes: a mathematical framework, S. Safavi, N. K. Logothetis and M. Besserve. Neural Computation 2021.

Compuational and Systems Neuroscience

Uncovering the Organization of Neural Circuits with Generalized Phase Locking Analysis, S. Safavi, T. I. Panagiotaropoulos, V. Kapoor, J. F. Ramirez-Villegas, N. K. Logothetis, M. Besserve. PLoS Computational Biology (accepted).

Coupling of hippocampal theta and ripples with pontogeniculooccipital waves, J. F. Ramirez-Villegas, M. Besserve, Y. Murayama, H. C. Evrard, A. Oeltermann, N. K. Logothetis. Nature 2020.

Dissecting the synapse- and frequency-dependent network mechanisms of in vivo hippocampal sharp wave-ripples, J. F. Ramirez-Villegas, K. F. Willeke, N. K. Logothetis and M. Besserve. Neuron 2018; 100:1016-19.

Diversity of sharp wave-ripple LFP signatures reveals differentiated brain-wide dynamical events, J. F. Ramirez-Villegas, N. K. Logothetis, M. Besserve. Proceedings of the National Academy of Sciences U.S.A 2015; 112:E6379-E6387.

Shifts of Gamma Phase across Primary Visual Cortical Sites Reflect Dynamic Stimulus-Modulated Information Transfer, M. Besserve, S. C. Lowe, N. K. Logothetis, B. Schölkopf, S. Panzeri. PLOS Biology 2015; 13, e1002257.

Collective and Multi-agent Systems

Coordination via predictive assistants: time series algorithms and game-theoretic analysis, P. Geiger, M. Besserve, J. Winkelmann, C. Proissl and B. Schölkopf. UAI 2019.

All topics (by publication type)

Preprints

Target Reduction of Causal Models, A. Kekić, B. Schölkopf and M. Besserve. arXiv preprint.

Conference papers

Nonparametric Identifiability of Causal Representations from Unknown Interventions, J. von Kügelgen, M. Besserve, W. Liang, L. Gresele, A. Kekić, E. Bareinboim, D. M. Blei and B. Schölkopf. NeurIPS 2023.

Causal Component Analysis, W. Liang, A. Kekić, J. von Kügelgen, S. Buchholz, M. Besserve, L. Gresele and B. Schölkopf, NeurIPS 2023.

Homomorphism AutoEncoder — Learning Group Structured Representations from Observed Transitions, H. Keurti, H. Pan, M. Besserve, B. F. Grewe and B. Schölkopf, ICML 2023.

Structure by Architecture: Structured Representations without Regularization, F. Leeb, G. Lanzillotta, Y. Annadani, M. Besserve, S. Bauer and B. Schölkopf, ICLR 2023.

Embrace the Gap: VAEs Perform Independent Mechanism Analysis, P. Reizinger, L. Gresele, J. Brady, J. von Kügelgen, D. Zietlow, B. Schölkopf, G. Martius, W. Brendel, M. Besserve. NeurIPS 2022.

Function Classes for Identifiable Nonlinear Independent Component Analysis, S. Buchholz, M. Besserve and B. Schölkopf. NeurIPS 2022.

Exploring the Latent Space of Autoencoders with Interventional Assays F. Leeb, S. Bauer, M. Besserve and B. Schölkopf. NeurIPS 2022.

Learning soft interventions in complex equilibrium systems, M. Besserve and B. Schölkopf, UAI 2022 (accepted).

Cause-effect inference through spectral independence in linear dynamical systems: theoretical foundations, M. Besserve, N. Shajarisales, D. Janzing, B. Schölkopf CLeaR 2022.

Independent mechanism analysis, a new concept? L. Gresele, J. von Kügelgen, Vincent Stimper, Bernhard Schölkopf and M. Besserve, NeurIPS 2021.

Self-Supervised Learning with Data Augmentations Provably Isolates Content from Style J. von Kügelgen, Y. Sharma, L. Gresele, W. Brendel, B. Schölkopf, M. Besserve and Francesco Locatello, NeurIPS 2021.

A theory of independent mechanisms for extrapolation in generative models, M. Besserve, R. Sun, D. Janzing and B. Schölkopf. AAAI-2021.

Counterfactuals uncover the modular structure of deep generative models, Besserve, A. Merhjou, R. Sun and B. Schölkopf. ICLR 2020.

Coordination via predictive assistants: time series algorithms and game-theoretic analysis, P. Geiger, M. Besserve, J. Winkelmann, C. Proissl and B. Schölkopf. UAI 2019.

Intrinsic disentanglement: an invariance view for deep generative models, M. Besserve, R. Sun and B. Schölkopf, Workshop on Theoretical Foundations and Applications of Deep Generative Models at ICML 2018.

Group invariance principles for causal generative models, M. Besserve, N. Shajarisales, B. Schölkopf and D. Janzing, Proceedings of the 21st International Conference on Artificial Intelligence and Statistics (AISTATS) 2018

Telling cause from effect in deterministic linear dynamical systems, N. Shajarisales, D. Janzing, B. Schölkopf and M. Besserve, ICML 2015.

Statistical analysis of coupled time series in the space of Kernel Cross-Spectral Density operators, M. Besserve, N.K. Logothetis and B. Schölkopf, NIPS 2013.

Towards a learning-theoretic analysis of spike-timing dependent plasticity. D. Balduzzi and M. Besserve, NIPS 2012.

Finding dependencies between frequencies with the kernel cross-spectral density, Besserve, M., D. Janzing, N. K. Logothetis & B. Schölkopf, International Conference on Acoustics, Speech and Signal Processing 2011.

Reconstructing the cortical functional network during imagery tasks for boosting asynchronous BCI, M. Besserve, J. Martinerie & L. Garnero, Second french conference on Computational Neuroscience, “Neurocomp08” 2008.

Non-invasive classification of cortical activities for Brain Computer Interface: A variable selection approach, M. Besserve, J. Martinerie & L. Garnero, 5th IEEE International Symposium on Biomedical Imaging (ISBI) 2008.

De l’estimation à la classification des activités corticales pour les Interfaces Cerveau-Machine, M. Besserve, L. Garnero & J. Martinerie, 21ème colloque GRETSI sur le traitement du signal et des images 2007.

Cross-spectral discriminant analysis for the classification of Brain Computer Interfaces, M. Besserve, L. Garnero & J. Martinerie, 3rd Internationnal IEEE EMBS Conference on Neural Engineering 2007.

Prediction of cognitive states using MEG and Blind Source Separation, M. Besserve, K. Jerbi, L. Garnero & J. Martinerie, Proceedings of the 15th International Conference on Biomagnetism, Vancouver, BC Canada, International Congress Series 2007 ;1300.

Journal Articles

Information theoretic measures of causal influences during transient neural events, K. Shao, N. K. Logothetis and M. Besserve. Frontiers in Network Physiology, Section Information Theory 2023.

Uncovering the Organization of Neural Circuits with Generalized Phase Locking Analysis, S. Safavi, T. I. Panagiotaropoulos, V. Kapoor, J. F. Ramirez-Villegas, N. K. Logothetis and M. Besserve. PLoS Computational Biology 2023.

Causal Feature Selection via Orthogonal Search, A. Soleymani, A. Raj, S. Bauer, B. Schölkopf and M. Besserve, Transactions on Machine Learning Research 2022.

Decoding internally generated transitions of conscious contents in the prefrontal cortex without subjective reports, V. Kapoor, A. Dwarakanath, S. Safavi, J. Werner, M. Besserve, T. I. Panagiotaropoulos and N. K. Logothetis. Nature Communications 2022.

From univariate to multivariate coupling between continuous signals and point processes: a mathematical framework, S. Safavi, N. K. Logothetis and M. Besserve. Neural Computation 2021.

Coupling of hippocampal theta and ripples with pontogeniculooccipital waves, J. F. Ramirez-Villegas, M. Besserve, Y. Murayama, H. C. Evrard, A. Oeltermann and N. K. Logothetis. Nature 2020.

Dissecting the synapse- and frequency-dependent network mechanisms of in vivo hippocampal sharp wave-ripples, J. F. Ramirez-Villegas, K. F. Willeke, N. K. Logothetis and M. Besserve. Neuron 2018; 100:1016-19.

Parallel and functionally segregated processing of task phase and conscious content in the prefrontal cortex, V. Kapoor, M. Besserve, N.K. Logothetis and F. Panagiotaropoulos. Communications Biology 2018; 1.

Diversity of sharp wave-ripple LFP signatures reveals differentiated brain-wide dynamical events, J. F. Ramirez-Villegas, N. K. Logothetis, M. Besserve. Proceedings of the National Academy of Sciences U.S.A 2015; 112:E6379-E6387

Shifts of Gamma Phase across Primary Visual Cortical Sites Reflect Dynamic Stimulus-Modulated Information Transfer, M. Besserve, S. C. Lowe, N. K. Logothetis, B. Schölkopf, S. Panzeri. PLOS Biology 2015; 13, e1002257

Metabolic cost as an organizing principle for cooperative learning, D. Balduzzi, P.A. Ortega and M. Besserve. Advances in Complex Systems 2013; 16 :1350012

Multimodal information improves the rapid detection of mental fatigue, F. Laurent , M. Valderrama, M. Besserve, M. Guillard, J.-P. Lachaux, J. Martinerie and G. Florence. Biomedical Signal Processing and Control 2013; 8 :400-8.

Hippocampal-Cortical Interaction during Periods of Subcortical Silence, N. K. Logothetis, O. Eschenko, Y. Murayama, M. Augath, T. Steudel, H. C. Evrard, M. Besserve and & A. Oeltermann. Nature 2012; 491 :547-53.

Extraction of functional information from ongoing brain electrical activity, M. Besserve & J. Martinerie. IRBM 2011; 32 :27-34.

Dynamics of excitable neural networks with heterogeneous connectivity, M. Chavez , M. Besserve & M. Le Van Quyen. Progress in Biophysics and Molecular Biology 2011; 105 :29-33

Improving quantification of functional networks with EEG inverse problem: evidence from a decoding point of view, M. Besserve, J. Martinerie & L. Garnero, Neuroimage 2011; 55 :1536-1547.

Causal relationships between frequency bands of extracellular signals in visual cortex revealed by an information theoretic analysis, M. Besserve, B. Schölkopf, N. K. Logothetis and S. Panzeri. Journal of Computational Neuroscience 2010; 29 :547-566.

Source reconstruction and synchrony measurements for revealing functional brain networks and classifying mental states, Laurent F , Besserve M, Garnero L, Philippe M, Florence G and Martinerie J., International Journal of Bifurcation and Chaos 2010; 20 :1703-1721.

Classification methods for ongoing EEG and MEG signals, M. Besserve, K. Jerbi, F. Laurent, S. Baillet, J. Martinerie & L. Garnero. Biological Research 2007; 40 :415-437.

Prediction of performance level during a cognitive task from ongoing EEG oscillatory activities, M. Besserve, M. Phillipe, G. Florence, L. Garnero & J. Martinerie, Clinical Neurophysiology 2008 ; 119 :897-908.

Towards a proper estimation of phase synchronization from time series, M. Chavez, M. Besserve, C. Adam & J. Martinerie, Journal of Neuroscience Methods 2006 ;154 :149-160.

Reports and dissertations

Analyse de la dynamique neuronale pour les Interfaces Cerveau-Machine : un retour aux sources, M. Besserve, PhD dissertation (in french)/Thèse de doctorat. Université Paris-Sud 11 22 Novembre 2007.