PaperlayerView exact revision on arXiv

Source-linked AI summary

Sample Dependence-Aware Blind Source Separation for Linear Causal Discovery

Cihan Eralp Kumbasar, Emin Erdem Kumbasar, Tulay Adali

arXiv:2610.06656v1eess.SP

TL;DR

Observational data often do not determine causal direction, and classical LiNGAM has limited identifiability when disturbances are Gaussian or temporally dependent. This paper extends its BSS formulation to independent disturbance processes and uses mutual information rate to exploit temporal structure alongside higher-order statistics. Joint use of both sources supports near-perfect synthetic recovery and improves bootstrap stability of ancestral directionality in fMRI data.

  • Problem

    Classical LiNGAM relies on non-Gaussianity under independent sampling, limiting identifiability with multiple Gaussian disturbances and leaving potentially informative temporal dependence unused.

    Source: §1 · p. 1

  • Method

    The paper models disturbances as mutually independent processes and uses mutual information rate to combine higher-order statistics with sample dependence for causal identification.

    Source: §1 · p. 1, §2.4 · p. 2

  • Results

    Joint higher-order statistics and sample dependence yield near-perfect synthetic causal recovery across tested disturbance settings and improve fMRI ancestral-direction bootstrap reproducibility.

    Source: §1 · p. 2, §4 · p. 4

  • Takeaways & Limitations

    Temporal structure can broaden causal identifiability to Gaussian disturbance processes when their covariance functions are sufficiently distinct.

    Source: §2.4 · p. 2, §4 · p. 4

    The fMRI interpretation is limited by the assumed common group-level structure, subject-boundary artifacts from concatenation, and unobserved confounders outside the SC/AU components.

    Source: §3.2.2 · p. 4

Abstract

from arXiv · show

Causal discovery seeks to determine directional relationships among variables in complex systems, yet observational data alone generally do not identify causal direction. Complete identification therefore requires assumptions beyond linearity and acyclicity. A key approach is the Linear Non-Gaussian Acyclic Model (LiNGAM), which formulates linear structural equation model estimation as a blind source separation (BSS) problem. LiNGAM treats disturbances as mutually independent random variables under independent sampling, relying on higher-order statistics (HOS) and non-Gaussianity for identifiability. This restricts identifiability when multiple disturbances are Gaussian and ignores potentially informative temporal dependence. To broaden causal identifiability, we formulate linear acyclic causal discovery with mutually independent disturbance processes and transfer established BSS identification conditions to causal structure recovery. Under this formulation, replacing the mutual information cost with mutual information rate enables identification under a broader class of disturbances, including Gaussian processes with nonproportional covariance functions. Synthetic experiments reveal the limitations of methods relying solely on HOS or sample dependence, while their joint exploitation provides near-perfect causal recovery across the tested disturbance settings. Experiments on real functional magnetic resonance imaging (fMRI) data further demonstrate that jointly exploiting HOS and sample dependence improves the bootstrap stability of estimated ancestral directionality.

1. INTRODUCTION

The paper broadens LiNGAM-style causal identification by using temporal dependence alongside non-Gaussianity, then evaluates recovery in simulations and fMRI data.

1. INTRODUCTION

  • ICA-based source separation can exploit either higher-order statistics or sample dependence as statistical diversity.FastICA commonly relies on non-Gaussianity and higher-order statistics, while other source separation strategies use sample dependence.Source: §1 · p. 1
  • Classical LiNGAM requires at most one Gaussian disturbance for identifiability and assumes independent sampling, leaving temporal dependence unused.With Gaussian disturbances, covariance information alone generally does not uniquely identify the directed graph.Source: §1 · p. 1
  • The proposed framework extends LiNGAM's BSS formulation to mutually independent disturbance processes and transfers dependence-aware BSS identifiability conditions to causal recovery.It targets Gaussian disturbance processes with distinguishable covariance functions.Source: §1 · p. 1
  • Joint use of higher-order statistics and sample dependence achieves near-perfect synthetic causal recovery across diverse disturbance settings.HOS-only methods fail with Gaussian processes, while sample-dependence-only methods suffer when temporal diversity is insufficient.Source: §1 · p. 2
  • On real fMRI data, joint use of both information sources yields more reproducible causal dependencies, while HOS-only methods show greater uncertainty in ancestral directionality.The evaluation uses bootstrap resampling of subjects to assess stability.Source: §1 · p. 2

2. BSS-BASED IDENTIFICATION OF LINEAR ACYCLIC SEMS

The section recasts linear acyclic SEM estimation as BSS, then extends identification from independent samples to dependent disturbance processes using mutual information rate.

2.1. Linear Acyclic SEM as a BSS Model

  • A linear acyclic SEM can be written as a BSS model, with independent disturbances as sources and the inverse causal transformation as the mixing matrix.The BSS demixing matrix estimates I − B; the method then aligns and normalizes it, estimates causal order, and selects parents with adaptive Lasso.Source: §2.1 · p. 2

2.2. Identification Under Independent Sampling

  • Under independent sampling, ICA minimizes mutual information among source estimates, exploiting higher-order statistics and requiring at most one Gaussian disturbance for identifiability.ICA-LiNGAM inherits this identifiability condition.Source: §2.2 · p. 2

2.3. Random Process Disturbance Model

  • The random-process formulation allows mutually independent disturbances to have temporal dependence while retaining temporally i.i.d. disturbances as a special case.Temporal structure adds statistical diversity alongside higher-order statistics.Source: §2.3 · p. 2

2.4. Sample Dependence-Aware Identification

  • For stationary processes with finite entropy rate, mutual information rate combines higher-order statistics and temporal diversity, identifying Gaussian sources with nonproportional autocovariance functions.When disturbances are identifiable up to permutation and scaling, acyclic SEM constraints yield the causal coefficient matrix.Source: §2.4 · p. 2

3. EXPERIMENTAL RESULTS

The experiments compare BSS strategies across disturbance-diversity settings and assess ancestral stability in real fMRI data. Joint use of HOS and sample dependence is more consistent across synthetic settings, while ERBM has the highest reported fMRI stability score.

3.1. Synthetic Simulations

  • Synthetic comparisons include HOS-only, temporal-only, and two mixed-diversity settings, using five BSS algorithms and assessing coefficient error and edge detection.The methods are FastICA, EBM, WASOBI, ERBM, and DirectLiNGAM; the simulations use N = 20 variables and report relative Frobenius error and AUPRC.Source: §3.1 · p. 3
  • Joint exploitation of HOS and sample dependence performs more consistently across heterogeneous disturbance settings, while either source alone can fail when its diversity is insufficient.Specialized methods can be more sample-efficient when their assumptions match the data: WASOBI approaches AUPRC near one around T = 2000 in Temporal-only, while ERBM approaches comparable ranking performance near T = 10000.Source: §3.1 · p. 3

3.2.1. Dataset Details

  • The fMRI analysis uses seven ICNs—five subcortical and two auditory—from 250 healthy BSNIP controls, each with 224 time points.The component time courses are standardized within subject and concatenated across subjects for group-level estimation.Source: §3.2.1 · pp. 3–4

3.2.2. Stability Analysis

  • Stability is estimated from 500 subject-level bootstrap samples, comparing ancestral relationships across resampled group estimates.Each bootstrap adjacency matrix is transitively closed; the score summarizes the mean absolute difference between opposing ancestral frequencies, and larger values indicate more reproducible directional preference.Source: §3.2.2 · p. 4
  • ERBM reports the highest ancestral stability (Sanc = 0.7330), followed by WASOBI (0.5721), DirectLiNGAM (0.4504), and FastICA (0.4170).ERBM places AU components downstream of SC with all SC-to-AU probabilities above 0.90, but ERBM and WASOBI favor opposite SC3/SC2 directions.Source: §3.2.2 · p. 4, Figure 2 · p. 4
  • Causal interpretation is limited by the assumed common group-level structure, concatenation-related subject-boundary artifacts, and unobserved confounders outside the selected SC/AU components.Source: §3.2.2 · p. 4

4. CONCLUSION

The proposed framework broadens linear causal-structure identification by jointly using higher-order statistics and sample dependence. Synthetic and fMRI experiments support the value of combining these sources of statistical diversity.

4. CONCLUSION

  • Jointly exploiting higher-order statistics and sample dependence improves synthetic causal-structure recovery across diverse disturbance settings.HOS-based methods fail when non-Gaussianity is insufficient, while sample-dependence-only methods perform poorly when temporal diversity is limited.Source: §4 · p. 4
  • On real fMRI data, methods combining higher-order statistics and sample dependence produce more stable causal relationships across bootstrap samples than HOS-only methods.Source: §4 · p. 4
  • Gaussian disturbance processes can support causal-structure identification when their covariance functions are sufficiently distinct.Source: §4 · p. 4
  • The random-process formulation extends BSS-based linear causal-structure estimation beyond LiNGAM's non-Gaussian disturbance assumption.Source: §4 · p. 4
Loading 2610.06656v1…