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  1. Article ; Online: Information theoretic measures of causal influences during transient neural events.

    Shao, Kaidi / Logothetis, Nikos K / Besserve, Michel

    Frontiers in network physiology

    2023  Volume 3, Page(s) 1085347

    Abstract: Introduction: ...

    Abstract Introduction:
    Language English
    Publishing date 2023-05-31
    Publishing country Switzerland
    Document type Journal Article
    ISSN 2674-0109
    ISSN (online) 2674-0109
    DOI 10.3389/fnetp.2023.1085347
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  2. Book ; Online: Targeted Reduction of Causal Models

    Kekić, Armin / Schölkopf, Bernhard / Besserve, Michel

    2023  

    Abstract: Why does a phenomenon occur? Addressing this question is central to most scientific inquiries based on empirical observations, and often heavily relies on simulations of scientific models. As models become more intricate, deciphering the causes behind ... ...

    Abstract Why does a phenomenon occur? Addressing this question is central to most scientific inquiries based on empirical observations, and often heavily relies on simulations of scientific models. As models become more intricate, deciphering the causes behind these phenomena in high-dimensional spaces of interconnected variables becomes increasingly challenging. Causal machine learning may assist scientists in the discovery of relevant and interpretable patterns of causation in simulations. We introduce Targeted Causal Reduction (TCR), a method for turning complex models into a concise set of causal factors that explain a specific target phenomenon. We derive an information theoretic objective to learn TCR from interventional data or simulations and propose algorithms to optimize this objective efficiently. TCR's ability to generate interpretable high-level explanations from complex models is demonstrated on toy and mechanical systems, illustrating its potential to assist scientists in the study of complex phenomena in a broad range of disciplines.
    Keywords Statistics - Machine Learning ; Computer Science - Machine Learning
    Subject code 501
    Publishing date 2023-11-30
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  3. Book ; Online: Learning soft interventions in complex equilibrium systems

    Besserve, Michel / Schölkopf, Bernhard

    2021  

    Abstract: Complex systems often contain feedback loops that can be described as cyclic causal models. Intervening in such systems may lead to counterintuitive effects, which cannot be inferred directly from the graph structure. After establishing a framework for ... ...

    Abstract Complex systems often contain feedback loops that can be described as cyclic causal models. Intervening in such systems may lead to counterintuitive effects, which cannot be inferred directly from the graph structure. After establishing a framework for differentiable soft interventions based on Lie groups, we take advantage of modern automatic differentiation techniques and their application to implicit functions in order to optimize interventions in cyclic causal models. We illustrate the use of this framework by investigating scenarios of transition to sustainable economies.
    Keywords Computer Science - Machine Learning
    Publishing date 2021-12-10
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  4. Article ; Online: From Univariate to Multivariate Coupling Between Continuous Signals and Point Processes: A Mathematical Framework.

    Safavi, Shervin / Logothetis, Nikos K / Besserve, Michel

    Neural computation

    2021  Volume 33, Issue 7, Page(s) 1751–1817

    Abstract: Time series data sets often contain heterogeneous signals, composed of both continuously changing quantities and discretely occurring events. The coupling between these measurements may provide insights into key underlying mechanisms of the systems under ...

    Abstract Time series data sets often contain heterogeneous signals, composed of both continuously changing quantities and discretely occurring events. The coupling between these measurements may provide insights into key underlying mechanisms of the systems under study. To better extract this information, we investigate the asymptotic statistical properties of coupling measures between continuous signals and point processes. We first introduce martingale stochastic integration theory as a mathematical model for a family of statistical quantities that include the phase locking value, a classical coupling measure to characterize complex dynamics. Based on the martingale central limit theorem, we can then derive the asymptotic gaussian distribution of estimates of such coupling measure that can be exploited for statistical testing. Second, based on multivariate extensions of this result and random matrix theory, we establish a principled way to analyze the low-rank coupling between a large number of point processes and continuous signals. For a null hypothesis of no coupling, we establish sufficient conditions for the empirical distribution of squared singular values of the matrix to converge, as the number of measured signals increases, to the well-known Marchenko-Pastur (MP) law, and the largest squared singular value converges to the upper end of the MP support. This justifies a simple thresholding approach to assess the significance of multivariate coupling. Finally, we illustrate with simulations the relevance of our univariate and multivariate results in the context of neural time series, addressing how to reliably quantify the interplay between multichannel local field potential signals and the spiking activity of a large population of neurons.
    MeSH term(s) Mathematics ; Models, Theoretical ; Neurons
    Language English
    Publishing date 2021-08-19
    Publishing country United States
    Document type Journal Article ; Research Support, Non-U.S. Gov't
    ZDB-ID 1025692-1
    ISSN 1530-888X ; 0899-7667
    ISSN (online) 1530-888X
    ISSN 0899-7667
    DOI 10.1162/neco_a_01389
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    In stock of ZB MED Cologne/Königswinter

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    bis Jg. 1994: Bestellungen von Artikeln über das Online-Bestellformular
    Jg. 1995 - 2021: Lesesall (2.OG)
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  5. Book ; Online: Function Classes for Identifiable Nonlinear Independent Component Analysis

    Buchholz, Simon / Besserve, Michel / Schölkopf, Bernhard

    2022  

    Abstract: Unsupervised learning of latent variable models (LVMs) is widely used to represent data in machine learning. When such models reflect the ground truth factors and the mechanisms mapping them to observations, there is reason to expect that they allow ... ...

    Abstract Unsupervised learning of latent variable models (LVMs) is widely used to represent data in machine learning. When such models reflect the ground truth factors and the mechanisms mapping them to observations, there is reason to expect that they allow generalization in downstream tasks. It is however well known that such identifiability guaranties are typically not achievable without putting constraints on the model class. This is notably the case for nonlinear Independent Component Analysis, in which the LVM maps statistically independent variables to observations via a deterministic nonlinear function. Several families of spurious solutions fitting perfectly the data, but that do not correspond to the ground truth factors can be constructed in generic settings. However, recent work suggests that constraining the function class of such models may promote identifiability. Specifically, function classes with constraints on their partial derivatives, gathered in the Jacobian matrix, have been proposed, such as orthogonal coordinate transformations (OCT), which impose orthogonality of the Jacobian columns. In the present work, we prove that a subclass of these transformations, conformal maps, is identifiable and provide novel theoretical results suggesting that OCTs have properties that prevent families of spurious solutions to spoil identifiability in a generic setting.

    Comment: 43 pages
    Keywords Statistics - Machine Learning ; Computer Science - Machine Learning
    Publishing date 2022-08-12
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  6. Book ; Online: Bayesian Information Criterion for Event-based Multi-trial Ensemble data

    Shao, Kaidi / Logothetis, Nikos K. / Besserve, Michel

    2022  

    Abstract: Transient recurring phenomena are ubiquitous in many scientific fields like neuroscience and meteorology. Time inhomogenous Vector Autoregressive Models (VAR) may be used to characterize peri-event system dynamics associated with such phenomena, and can ... ...

    Abstract Transient recurring phenomena are ubiquitous in many scientific fields like neuroscience and meteorology. Time inhomogenous Vector Autoregressive Models (VAR) may be used to characterize peri-event system dynamics associated with such phenomena, and can be learned by exploiting multi-dimensional data gathering samples of the evolution of the system in multiple time windows comprising, each associated with one occurrence of the transient phenomenon, that we will call "trial". However, optimal VAR model order selection methods, commonly relying on the Akaike or Bayesian Information Criteria (AIC/BIC), are typically not designed for multi-trial data. Here we derive the BIC methods for multi-trial ensemble data which are gathered after the detection of the events. We show using simulated bivariate AR models that the multi-trial BIC is able to recover the real model order. We also demonstrate with simulated transient events and real data that the multi-trial BIC is able to estimate a sufficiently small model order for dynamic system modeling.

    Comment: 12 pages, 4 figures
    Keywords Statistics - Machine Learning ; Computer Science - Machine Learning ; Quantitative Biology - Quantitative Methods ; Statistics - Applications
    Subject code 310
    Publishing date 2022-04-29
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  7. Article ; Online: Uncovering the organization of neural circuits with Generalized Phase Locking Analysis.

    Safavi, Shervin / Panagiotaropoulos, Theofanis I / Kapoor, Vishal / Ramirez-Villegas, Juan F / Logothetis, Nikos K / Besserve, Michel

    PLoS computational biology

    2023  Volume 19, Issue 4, Page(s) e1010983

    Abstract: Despite the considerable progress of in vivo neural recording techniques, inferring the biophysical mechanisms underlying large scale coordination of brain activity from neural data remains challenging. One obstacle is the difficulty to link high ... ...

    Abstract Despite the considerable progress of in vivo neural recording techniques, inferring the biophysical mechanisms underlying large scale coordination of brain activity from neural data remains challenging. One obstacle is the difficulty to link high dimensional functional connectivity measures to mechanistic models of network activity. We address this issue by investigating spike-field coupling (SFC) measurements, which quantify the synchronization between, on the one hand, the action potentials produced by neurons, and on the other hand mesoscopic "field" signals, reflecting subthreshold activities at possibly multiple recording sites. As the number of recording sites gets large, the amount of pairwise SFC measurements becomes overwhelmingly challenging to interpret. We develop Generalized Phase Locking Analysis (GPLA) as an interpretable dimensionality reduction of this multivariate SFC. GPLA describes the dominant coupling between field activity and neural ensembles across space and frequencies. We show that GPLA features are biophysically interpretable when used in conjunction with appropriate network models, such that we can identify the influence of underlying circuit properties on these features. We demonstrate the statistical benefits and interpretability of this approach in various computational models and Utah array recordings. The results suggest that GPLA, used jointly with biophysical modeling, can help uncover the contribution of recurrent microcircuits to the spatio-temporal dynamics observed in multi-channel experimental recordings.
    MeSH term(s) Nerve Net/physiology ; Models, Neurological ; Neurons/physiology ; Action Potentials/physiology
    Language English
    Publishing date 2023-04-03
    Publishing country United States
    Document type Journal Article ; Research Support, Non-U.S. Gov't
    ZDB-ID 2193340-6
    ISSN 1553-7358 ; 1553-734X
    ISSN (online) 1553-7358
    ISSN 1553-734X
    DOI 10.1371/journal.pcbi.1010983
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  8. Book ; Online: Independent Mechanism Analysis and the Manifold Hypothesis

    Ghosh, Shubhangi / Gresele, Luigi / von Kügelgen, Julius / Besserve, Michel / Schölkopf, Bernhard

    2023  

    Abstract: Independent Mechanism Analysis (IMA) seeks to address non-identifiability in nonlinear Independent Component Analysis (ICA) by assuming that the Jacobian of the mixing function has orthogonal columns. As typical in ICA, previous work focused on the case ... ...

    Abstract Independent Mechanism Analysis (IMA) seeks to address non-identifiability in nonlinear Independent Component Analysis (ICA) by assuming that the Jacobian of the mixing function has orthogonal columns. As typical in ICA, previous work focused on the case with an equal number of latent components and observed mixtures. Here, we extend IMA to settings with a larger number of mixtures that reside on a manifold embedded in a higher-dimensional than the latent space -- in line with the manifold hypothesis in representation learning. For this setting, we show that IMA still circumvents several non-identifiability issues, suggesting that it can also be a beneficial principle for higher-dimensional observations when the manifold hypothesis holds. Further, we prove that the IMA principle is approximately satisfied with high probability (increasing with the number of observed mixtures) when the directions along which the latent components influence the observations are chosen independently at random. This provides a new and rigorous statistical interpretation of IMA.

    Comment: 6 pages, Accepted at Neurips Causal Representation Learning 2023
    Keywords Statistics - Machine Learning ; Computer Science - Machine Learning
    Subject code 006
    Publishing date 2023-12-20
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  9. Book ; Online: Exploring the Latent Space of Autoencoders with Interventional Assays

    Leeb, Felix / Bauer, Stefan / Besserve, Michel / Schölkopf, Bernhard

    2021  

    Abstract: Autoencoders exhibit impressive abilities to embed the data manifold into a low-dimensional latent space, making them a staple of representation learning methods. However, without explicit supervision, which is often unavailable, the representation is ... ...

    Abstract Autoencoders exhibit impressive abilities to embed the data manifold into a low-dimensional latent space, making them a staple of representation learning methods. However, without explicit supervision, which is often unavailable, the representation is usually uninterpretable, making analysis and principled progress challenging. We propose a framework, called latent responses, which exploits the locally contractive behavior exhibited by variational autoencoders to explore the learned manifold. More specifically, we develop tools to probe the representation using interventions in the latent space to quantify the relationships between latent variables. We extend the notion of disentanglement to take the learned generative process into account and consequently avoid the limitations of existing metrics that may rely on spurious correlations. Our analyses underscore the importance of studying the causal structure of the representation to improve performance on downstream tasks such as generation, interpolation, and inference of the factors of variation.

    Comment: Published in NeurIPS 2022 Conference Proceedings
    Keywords Computer Science - Machine Learning ; Computer Science - Computer Vision and Pattern Recognition
    Subject code 006
    Publishing date 2021-06-30
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  10. Article ; Online: Uncovering the organization of neural circuits with Generalized Phase Locking Analysis.

    Shervin Safavi / Theofanis I Panagiotaropoulos / Vishal Kapoor / Juan F Ramirez-Villegas / Nikos K Logothetis / Michel Besserve

    PLoS Computational Biology, Vol 19, Iss 4, p e

    2023  Volume 1010983

    Abstract: Despite the considerable progress of in vivo neural recording techniques, inferring the biophysical mechanisms underlying large scale coordination of brain activity from neural data remains challenging. One obstacle is the difficulty to link high ... ...

    Abstract Despite the considerable progress of in vivo neural recording techniques, inferring the biophysical mechanisms underlying large scale coordination of brain activity from neural data remains challenging. One obstacle is the difficulty to link high dimensional functional connectivity measures to mechanistic models of network activity. We address this issue by investigating spike-field coupling (SFC) measurements, which quantify the synchronization between, on the one hand, the action potentials produced by neurons, and on the other hand mesoscopic "field" signals, reflecting subthreshold activities at possibly multiple recording sites. As the number of recording sites gets large, the amount of pairwise SFC measurements becomes overwhelmingly challenging to interpret. We develop Generalized Phase Locking Analysis (GPLA) as an interpretable dimensionality reduction of this multivariate SFC. GPLA describes the dominant coupling between field activity and neural ensembles across space and frequencies. We show that GPLA features are biophysically interpretable when used in conjunction with appropriate network models, such that we can identify the influence of underlying circuit properties on these features. We demonstrate the statistical benefits and interpretability of this approach in various computational models and Utah array recordings. The results suggest that GPLA, used jointly with biophysical modeling, can help uncover the contribution of recurrent microcircuits to the spatio-temporal dynamics observed in multi-channel experimental recordings.
    Keywords Biology (General) ; QH301-705.5
    Subject code 612
    Language English
    Publishing date 2023-04-01T00:00:00Z
    Publisher Public Library of Science (PLoS)
    Document type Article ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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