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Robust and highly scalable estimation of directional couplings from time-shifted signals

Louis Rouillard, Luca Ambrogioni, Demian Wassermann

TL;DR

This paper addresses estimating directed couplings in networks from indirect measurements with potentially unknown time-shifts $d$. It introduces a hybrid variational Bayes framework that marginalizes delays by employing a forward KL loss for hyperparameters and a scalable gradient-based reverse KL for couplings, enabling fast, large-scale inference. The model uses a latent linear dynamical system with region-specific HRFs and time-shifted observations, solved by a two-stage VI where $q_{HP}$ captures hyperparameters and $q_{P}$ captures latent states ${\bf X}$ and coupling ${\bf A}$. Empirical results on synthetic MDS-based data and human neuroimaging datasets demonstrate robust, conservative coupling estimates, reduced mode-collapse risk, and the ability to reveal driving regions while scaling to hundreds of regions.

Abstract

The estimation of directed couplings between the nodes of a network from indirect measurements is a central methodological challenge in scientific fields such as neuroscience, systems biology and economics. Unfortunately, the problem is generally ill-posed due to the possible presence of unknown delays in the measurements. In this paper, we offer a solution of this problem by using a variational Bayes framework, where the uncertainty over the delays is marginalized in order to obtain conservative coupling estimates. To overcome the well-known overconfidence of classical variational methods, we use a hybrid-VI scheme where the (possibly flat or multimodal) posterior over the measurement parameters is estimated using a forward KL loss while the (nearly convex) conditional posterior over the couplings is estimated using the highly scalable gradient-based VI. In our ground-truth experiments, we show that the network provides reliable and conservative estimates of the couplings, greatly outperforming similar methods such as regression DCM.

Robust and highly scalable estimation of directional couplings from time-shifted signals

TL;DR

This paper addresses estimating directed couplings in networks from indirect measurements with potentially unknown time-shifts . It introduces a hybrid variational Bayes framework that marginalizes delays by employing a forward KL loss for hyperparameters and a scalable gradient-based reverse KL for couplings, enabling fast, large-scale inference. The model uses a latent linear dynamical system with region-specific HRFs and time-shifted observations, solved by a two-stage VI where captures hyperparameters and captures latent states and coupling . Empirical results on synthetic MDS-based data and human neuroimaging datasets demonstrate robust, conservative coupling estimates, reduced mode-collapse risk, and the ability to reveal driving regions while scaling to hundreds of regions.

Abstract

The estimation of directed couplings between the nodes of a network from indirect measurements is a central methodological challenge in scientific fields such as neuroscience, systems biology and economics. Unfortunately, the problem is generally ill-posed due to the possible presence of unknown delays in the measurements. In this paper, we offer a solution of this problem by using a variational Bayes framework, where the uncertainty over the delays is marginalized in order to obtain conservative coupling estimates. To overcome the well-known overconfidence of classical variational methods, we use a hybrid-VI scheme where the (possibly flat or multimodal) posterior over the measurement parameters is estimated using a forward KL loss while the (nearly convex) conditional posterior over the couplings is estimated using the highly scalable gradient-based VI. In our ground-truth experiments, we show that the network provides reliable and conservative estimates of the couplings, greatly outperforming similar methods such as regression DCM.
Paper Structure (17 sections, 9 equations, 3 figures, 1 table)

This paper contains 17 sections, 9 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Related Work
  3. Methods
  4. Latent activation dynamics
  5. Time-shifted measurements
  6. Problem statement: inferring region coupling from the convolved signals
  7. Inferring parameters susceptible to yield the observed signal
  8. A practical hurdle for inference: multiple modes explaining the observed data
  9. Hybrid Variational Bayes
  10. Inference using parameter optimization: the automatic differentiation variational inference (ADVI) framework
  11. Hyper-parameter (HP) estimation
  12. Parameter (P) estimation
  13. Synthetic experiments
  14. Mode collapse in practice: effect on ground truth coupling coverage
  15. Application on a neurophysiological synthetic dataset: connection detection
  16. ...and 2 more sections

Figures (3)

  • Figure 1: Graphical representation for the MDS model, and general principle of our hybrid method. Parameters are separated into two groups. For the hyper-parameters (HP), we use the forward KL to obtain a well-calibrated estimator. The HP estimator is plugged into a scalable reverse-KL training to estimate the parameters (P).
  • Figure 2: Synthetic example inference Posterior marginal distributions of the hyper-parameter $\alpha$ and the parameter ${\bm{\mathsfit{A}}}$ ---as described in Section \ref{['sec:h-VB']}.
  • Figure 3: Full-brain analysis confirms the driving role of the r-AI in working memoryOn the left: directed outflow analysis on 11 pre-selected ROIs. Working memory regions are selected by an expert, which can incur confounding from unobserved regions. On the right: full-brain analysis, removing potential confounds. The r-AI was hypothesized to be a driving region in the 11-ROIs analysis (blue rectangle). The full-brain analysis confirms this analysis: the r-AI (blue arrow) appears as a hot spot of the directed outflow.