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Pathway Lasso: Estimate and Select Sparse Mediation Pathways with High Dimensional Mediators
Machine Learning · Submitted 24 Mar 2016
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim On both simulated data and a real fMRI dataset, the proposed approach yields higher pathway selection accuracy and lower estimation bias than other competing methods.
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The abstract, sentence by sentence
In many scientific studies, it becomes increasingly important to delineate the causal pathways through a large number of mediators, such as genetic and brain mediators. Structural equation modeling (SEM) is a popular technique to estimate the pathway effects, commonly expressed as products of coefficients. However, it becomes unstable to fit such models with high dimensional mediators, especially for a general setting where all the mediators are causally dependent but the exact causal relationships between them are unknown. This paper proposes a sparse mediation model using a regularized SEM approach, where sparsity here means that a small number of mediators have nonzero mediation effects between a treatment and an outcome. To address the model selection challenge, we innovate by introducing a new penalty called Pathway Lasso. This penalty function is a convex relaxation of the non-convex product function, and it enables a computationally tractable optimization criterion to estimate and select many pathway effects simultaneously. We develop a fast ADMM-type algorithm to compute the model parameters, and we show that the iterative updates can be expressed in closed form. On both simulated data and a real fMRI dataset, the proposed approach yields higher pathway selection accuracy and lower estimation bias than other competing methods.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | In many scientific studies, it becomes increasingly important to delineate the causal pathways through a large number of mediators, such as genetic and brain mediators. | background 1.00 | 0.04 | 0.02 | asserted 0.92 |
| s1 | Structural equation modeling (SEM) is a popular technique to estimate the pathway effects, commonly expressed as products of coefficients. | background 1.00 | 0.04 | 0.02 | asserted 1.00 |
| s2 | However, it becomes unstable to fit such models with high dimensional mediators, especially for a general setting where all the mediators are causally dependent but the exact causal relationships between them are unknown. | gap 0.61 | 0.09 | 0.02 | asserted 0.99 |
| s3 | This paper proposes a sparse mediation model using a regularized SEM approach, where sparsity here means that a small number of mediators have nonzero mediation effects between a treatment and an outcome. | contribution 0.68 | 0.75 | 0.10 | asserted 0.99 |
| s4 | To address the model selection challenge, we innovate by introducing a new penalty called Pathway Lasso. | contribution 0.98 | 0.94 | 0.05 | asserted 1.00 |
| s5 | This penalty function is a convex relaxation of the non-convex product function, and it enables a computationally tractable optimization criterion to estimate and select many pathway effects simultaneously. | method 0.72 | 0.89 | 0.10 | asserted 1.00 |
| s6 | We develop a fast ADMM-type algorithm to compute the model parameters, and we show that the iterative updates can be expressed in closed form. | method 0.97 | 0.97 | 0.04 | asserted 1.00 |
| s7 | On both simulated data and a real fMRI dataset, the proposed approach yields higher pathway selection accuracy and lower estimation bias than other competing methods. | result 1.00 | 0.96 | 0.85 | asserted 1.00 |
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The paper
Original abstract
In many scientific studies, it becomes increasingly important to delineate the causal pathways through a large number of mediators, such as genetic and brain mediators. Structural equation modeling (SEM) is a popular technique to estimate the pathway effects, commonly expressed as products of coefficients. However, it becomes unstable to fit such models with high dimensional mediators, especially for a general setting where all the mediators are causally dependent but the exact causal relationships between them are unknown. This paper proposes a sparse mediation model using a regularized SEM approach, where sparsity here means that a small number of mediators have nonzero mediation effects between a treatment and an outcome. To address the model selection challenge, we innovate by introducing a new penalty called Pathway Lasso. This penalty function is a convex relaxation of the non-convex product function, and it enables a computationally tractable optimization criterion to estimate and select many pathway effects simultaneously. We develop a fast ADMM-type algorithm to compute the model parameters, and we show that the iterative updates can be expressed in closed form. On both simulated data and a real fMRI dataset, the proposed approach yields higher pathway selection accuracy and lower estimation bias than other competing methods.
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References
How the literature uses it
11 arXiv papers cite this in 28 sentences
Papers citing it · 14 sentences without a confident label
Builds on it 2 papers
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It is a generalization of the pathway Lasso penalty of [ref] to $q$ exposure variables, and is to facilitate selection of individual mediators.
Multimodal Data Integration via Mediation Analysis with High-Dimensional Exposures and Mediators · Estimation · 0.94
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It extends that of [ref] from a single modality of mediators to multiple modalities of mediators.
Multimodal Neuroimaging Data Integration and Pathway Analysis · Model · 1.00
Uses its method or tool 2 papers
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To address this issue, we adopt the idea of [ref] and consider a marginal model, as depicted in Figure [ref] (b).
Multimodal Neuroimaging Data Integration and Pathway Analysis · Introduction · 0.89
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We use the algorithm from [ref] to fit Pathway Lasso.
Bayesian Sparse Mediation Analysis with Targeted Penalization of Natural Indirect Effects · Other Approaches for High-dimensional Mediation Analysis · 1.00
Compares with it 2 papers
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Moreover, the convergence rate of the total indirect effect $IE^1$ and $IE^2$ are $√(log(p_1)/n)$ and $√(log(p_2)/n)$, respectively, which are consistent with the rate under only one set of mediators as studied in [ref] .
Multimodal Neuroimaging Data Integration and Pathway Analysis · Theory · 0.91
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Model [ref] is similar to that used in [ref] , but none of those can handle multivariate exposure variables.
Multimodal Data Integration via Mediation Analysis with High-Dimensional Exposures and Mediators · Model · 0.82
Cites it as support 1 paper
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It is found that this additional penalty helps further improves the selection accuracy [ref] .
Multimodal Data Integration via Mediation Analysis with High-Dimensional Exposures and Mediators · Estimation · 0.97
Cites it as background 5 papers
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Some used regularization-based methods [ref] .
Model Selection for Exposure-Mediator Interaction · Introduction · 0.84
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For example, [ref] proposes sure independent screening and minimax concave penalty techniques to study how the high-dimensional DNAm mediate the effect of smoking on lung function; [ref] develops a new convex, Lasso-type penalty on the indirect effects to identify brain pathways from the language stimuli to the outcome region activity.
Bayesian Hierarchical Models for High-Dimensional Mediation Analysis with Coordinated Selection of Correlated Mediators · Introduction · 0.90
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It is now widely used in a large variety of scientific applications, including psychology [ref] , genomics [ref] , genetic epidemiology [ref] , and neuroscience [ref] .
Testing Mediation Effects Using Logic of Boolean Matrices · Introduction · 0.82
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