Tian-Le Yang

Joe Suzuki, Tian-Le Yang

LiNGAM determines the variable order from cause to effect using additive noise models, but it faces challenges with confounding. Previous methods maintained LiNGAM's fundamental structure while trying to identify and address variables affected by confounding. As a result, these methods required significant computational resources regardless of the presence of confounding, and they did not ensure the detection of all confounding types. In contrast, this paper enhances LiNGAM by introducing LiNGAM-MMI, a method that quantifies the magnitude of confounding using KL divergence and arranges the variables to minimize its impact. This method efficiently achieves a globally optimal variable order through the shortest path problem formulation. LiNGAM-MMI processes data as efficiently as traditional LiNGAM in scenarios without confounding while effectively addressing confounding situations. Our experimental results suggest that LiNGAM-MMI more accurately determines the correct variable order, both in the presence and absence of confounding. The code is in the supplementary file in this link: https://github.com/SkyJoyTianle/ISIT2024.

Tian-Le Yang, Kuang-Yao Lee, Kun Zhang et al.

In causal discovery, non-Gaussianity has been used to characterize the complete configuration of a Linear Non-Gaussian Acyclic Model (LiNGAM), encompassing both the causal ordering of variables and their respective connection strengths. However, LiNGAM can only deal with the finite-dimensional case. To expand this concept, we extend the notion of variables to encompass vectors and even functions, leading to the Functional Linear Non-Gaussian Acyclic Model (Func-LiNGAM). Our motivation stems from the desire to identify causal relationships in brain-effective connectivity tasks involving, for example, fMRI and EEG datasets. We demonstrate why the original LiNGAM fails to handle these inherently infinite-dimensional datasets and explain the availability of functional data analysis from both empirical and theoretical perspectives. {We establish theoretical guarantees of the identifiability of the causal relationship among non-Gaussian random vectors and even random functions in infinite-dimensional Hilbert spaces.} To address the issue of sparsity in discrete time points within intrinsic infinite-dimensional functional data, we propose optimizing the coordinates of the vectors using functional principal component analysis. Experimental results on synthetic data verify the ability of the proposed framework to identify causal relationships among multivariate functions using the observed samples. For real data, we focus on analyzing the brain connectivity patterns derived from fMRI data.

Tian-Le Yang, Joe Suzuki

This study demonstrates that double descent can be mitigated by adding a dropout layer adjacent to the fully connected linear layer. The unexpected double-descent phenomenon garnered substantial attention in recent years, resulting in fluctuating prediction error rates as either sample size or model size increases. Our paper posits that the optimal test error, in terms of the dropout rate, shows a monotonic decrease in linear regression with increasing sample size. Although we do not provide a precise mathematical proof of this statement, we empirically validate through experiments that the test error decreases for each dropout rate. The statement we prove is that the expected test error for each dropout rate within a certain range decreases when the dropout rate is fixed. Our experimental results substantiate our claim, showing that dropout with an optimal dropout rate can yield a monotonic test error curve in nonlinear neural networks. These experiments were conducted using the Fashion-MNIST and CIFAR-10 datasets. These findings imply the potential benefit of incorporating dropout into risk curve scaling to address the peak phenomenon. To our knowledge, this study represents the first investigation into the relationship between dropout and double descent.