Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Simultaneous Inference in Multiple Matrix-Variate Graphs for High-Dimensional Neural Recordings

Zongge Liu, Heejong Bong, Zhao Ren, Matthew A. Smith, Robert E. Kass

TL;DR

This work addresses high-dimensional simultaneous inference for multiple matrix-variate Gaussian graphical models, motivated by spatiotemporal neural data collected across heterogeneous groups. It introduces a joint estimation approach using group Lasso to share sparsity patterns across groups, coupled with a Gaussian-approximation bootstrap to perform edge-set testing with validity under temporal dependence. Theoretical results establish non-asymptotic estimation guarantees and near-optimal detection boundaries for simultaneous testing, while simulations and neural-data analysis demonstrate improved power and meaningful brain connectivity insights across task stages. The method is computationally tractable, relying on convex optimization and parametric bootstrap, and is demonstrated on V4–PFC recordings to reveal stage-specific cross-area dynamics with potential cognitive relevance.

Abstract

We study simultaneous inference for multiple matrix-variate Gaussian graphical models in high-dimensional settings. Such models arise when spatiotemporal data are collected across multiple sample groups or experimental sessions, where each group is characterized by its own graphical structure but shares common sparsity patterns. A central challenge is to conduct valid inference on collections of graph edges while efficiently borrowing strength across groups under both high-dimensionality and temporal dependence. We propose a unified framework that combines joint estimation via group penalized regression with a high-dimensional Gaussian approximation bootstrap to enable global testing of edge subsets of arbitrary size. The proposed procedure accommodates temporally dependent observations and avoids naive pooling across heterogeneous groups. We establish theoretical guarantees for the validity of the simultaneous tests under mild conditions on sample size, dimensionality, and non-stationary autoregressive temporal dependence, and show that the resulting tests are nearly optimal in terms of the testable region boundary. The method relies only on convex optimization and parametric bootstrap, making it computationally tractable. Simulation studies and a neural recording example illustrate the efficacy of the proposed approach.

Simultaneous Inference in Multiple Matrix-Variate Graphs for High-Dimensional Neural Recordings

TL;DR

This work addresses high-dimensional simultaneous inference for multiple matrix-variate Gaussian graphical models, motivated by spatiotemporal neural data collected across heterogeneous groups. It introduces a joint estimation approach using group Lasso to share sparsity patterns across groups, coupled with a Gaussian-approximation bootstrap to perform edge-set testing with validity under temporal dependence. Theoretical results establish non-asymptotic estimation guarantees and near-optimal detection boundaries for simultaneous testing, while simulations and neural-data analysis demonstrate improved power and meaningful brain connectivity insights across task stages. The method is computationally tractable, relying on convex optimization and parametric bootstrap, and is demonstrated on V4–PFC recordings to reveal stage-specific cross-area dynamics with potential cognitive relevance.

Abstract

We study simultaneous inference for multiple matrix-variate Gaussian graphical models in high-dimensional settings. Such models arise when spatiotemporal data are collected across multiple sample groups or experimental sessions, where each group is characterized by its own graphical structure but shares common sparsity patterns. A central challenge is to conduct valid inference on collections of graph edges while efficiently borrowing strength across groups under both high-dimensionality and temporal dependence. We propose a unified framework that combines joint estimation via group penalized regression with a high-dimensional Gaussian approximation bootstrap to enable global testing of edge subsets of arbitrary size. The proposed procedure accommodates temporally dependent observations and avoids naive pooling across heterogeneous groups. We establish theoretical guarantees for the validity of the simultaneous tests under mild conditions on sample size, dimensionality, and non-stationary autoregressive temporal dependence, and show that the resulting tests are nearly optimal in terms of the testable region boundary. The method relies only on convex optimization and parametric bootstrap, making it computationally tractable. Simulation studies and a neural recording example illustrate the efficacy of the proposed approach.

Paper Structure

This paper contains 42 sections, 15 theorems, 162 equations, 9 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Matrix-variate Gaussian Graphical Model
  3. Simultaneous Inference Framework
  4. Estimation of Spatial Covariance Matrix
  5. Simultaneous Test by Parametric Bootstrap
  6. Single Edge Test
  7. Simultaneous Test
  8. Estimation of Temporal Covariance Matrix
  9. Theoretical Properties
  10. Non-asymptotic error bound for the group Lasso estimate
  11. Theoretical justification for the simultaneous edge testing
  12. Numerical Studies
  13. Simulation Studies
  14. Edge-wise Estimation Comparison
  15. Simultaneous Test
  16. ...and 27 more sections

Key Result

Theorem 4.1

Suppose that $\gamma_i$ satisfies $\frac{1}{C(\kappa_1,\kappa_3)}\sqrt{\frac{m+\log (mn_0pq)}{n_0 p}} \leq \gamma_i \leq C(\kappa_1,\kappa_3) \sqrt{\frac{m+\log (mn_0pq)}{n_0 p}}$ for some sufficiently large $C(\kappa_1,\kappa_3)$. Then, under assmp:balanced_sampleassmp:temporal_sample, for a sufficiently large $n_0$, where $\underline{\Delta}^{(\mathcal{S},l)}_j := \frac{\lVert X^{(\mathcal{S},l

Figures (9)

  • Figure 1: Simulated spatial graphs.
  • Figure 2: Simulation results are shown for different graph configurations and temporal dimensions with $n=5$ and $m=5$. Rows represent different graph types, while columns correspond to varying spatial and temporal dimensions. Curves represent our method (M0) and the other baseline methods.
  • Figure 3: (a) The positions of the analyzed cortical areas, V4 and PFC in a primate brain. The neuroelectrical activity in each area was recorded by a 96-electrode Utah array. (b) The timeline of one experimental trial. (c) LFP recordings for one experimental trial. Each x-axis indicates $96$ electrodes in each brain area, and the y-axis is time in ms. Time $t=0$ was aligned at the start of the delay period.
  • Figure 4: The averaged $\widehat{\rho}^{(\mathcal{S})}_{ij}$ within a group of spatially equidistant within-area edges during the late delay stage in V4.
  • Figure 5: Spatially smoothed within-area connectivity strength distribution over the spatial electrode array for PFC and V4 over the experimental stages. The connectivity within V4 decayed over the stages, while the level of within-connectivity in PFC was stable.
  • ...and 4 more figures

Theorems & Definitions (19)

  • Remark 3.1
  • Theorem 4.1
  • Proposition 4.2
  • Theorem 4.3
  • Theorem 4.4
  • Remark 4.5
  • Lemma C.1
  • Lemma C.2
  • Lemma C.3
  • Lemma C.4
  • ...and 9 more