Estimation of Directed Acyclic Graphs Through Two-Stage Adaptive Lasso for Gene Network Inference

Han, Sung Won; Chen, Gong; Cheon, Myun Seok; Zhong, Hua

doi:10.1080/01621459.2016.1142880

Cited by 42 publications

(68 citation statements)

References 69 publications

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“…Since there are many approaches in each of these categories we refer the reader to Han et al . (), Drton and Maathuis () and Heinze‐Deml et al . () for a more detailed overview and simulation studies.…”

Section: Problem Statement and Suggested Workmentioning

confidence: 97%

Robust Causal Structure Learning with Some Hidden Variables

Frot

Nandy

Maathuis

2019

Journal of the Royal Statistical Society Series B: Statistical Methodology

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Summary We introduce a new method to estimate the Markov equivalence class of a directed acyclic graph (DAG) in the presence of hidden variables, in settings where the underlying DAG among the observed variables is sparse, and there are a few hidden variables that have a direct effect on many of the observed variables. Building on the so‐called low rank plus sparse framework, we suggest a two‐stage approach which first removes the effect of the hidden variables and then estimates the Markov equivalence class of the underlying DAG under the assumption that there are no remaining hidden variables. This approach is consistent in certain high dimensional regimes and performs favourably when compared with the state of the art, in terms of both graphical structure recovery and total causal effect estimation.

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Section: Problem Statement and Suggested Workmentioning

confidence: 97%

Robust Causal Structure Learning with Some Hidden Variables

Frot

Nandy

Maathuis

2019

Journal of the Royal Statistical Society Series B: Statistical Methodology

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“…Let

T_{A}

denote the structure matrix induced by A , where the

false(i, j {false)}_{th}

entry of

T_{A}

is 1 if

A_{ij} \neq 0

. The following lemma proposed in Han et al () conveniently establishes the relationship between A and the acyclic restriction.Lemma The adjacency matrix A is acyclic if and only if

\sum_{l = 1}^{italicmin false(italicCard false(T_{A} false), p false)} \sum_{m = 1}^{p} false[T_{A}^{l} {false]}_{m, m} = 0,

where

italicmin false(false)

means a minimum value function, and

italicCard false(T_{A} false)

is the number of nonzero entries indicating a cardinality of

T_{A}

T_{A}^{l}

indicates l times the product of

T_{A}

matrix, and

false[T_{A}^{l} {false]}_{m, m}

indicates the

false(m, m false)

entry of the matrix

T_{A}^{l}

.For many applications, it is often the case that the underlying DAG structure is sparse.…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…This problem of minimizing function with the acyclic constraint is very similar to the optimization of function . We propose to use the DIST algorithm detailed in Han et al () and in Web Appendix B of web‐based Supplementary Materials. Last, we update

{\overset{D}{true}}^{false(t + 1 false)}

{\overset{D}{true}}^{false(t + 1 false)} = diag false[\sum_{j = 1}^{n} \frac{1}{n} false(I - {\overset{A}{true}}^{false(t + 1 false)} false) {\overset{χ}{true}}_{j}^{false(t false)} false(false(I - {\overset{A}{true}}^{false(t + 1 false)} false) {\overset{χ}{true}}_{j}^{false(t false)} {false)}^{T} false] .

…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…Note that log‐transformation is a widely applied approach for multivariate count data. For both approaches, to find the solution to minimize the

L_{1}

‐penalized likelihood objective function under a multivariate normal distribution, we use the DIST search algorithm by Han et al (), which shows improvements in performances over the coordinate descent search algorithm (Fu and Zhou, ). The DIST algorithm is also used to estimate equation in the proposed plnDAG algorithm.…”

Section: Simulation Studymentioning

confidence: 99%

“…The proposed objective function has a log term, which causes nonconvexity. Han et al () used an approximated convex objective function based on the

L_{1}

‐penalized likelihood to estimate DAGs given an unknown order of variables.…”

Section: Introductionmentioning

confidence: 99%

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Estimation of Sparse Directed Acyclic Graphs for Multivariate Counts Data

Han

Zhong

2016

Biometrics

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Summary The next-generation sequencing data, called high throughput sequencing data, are recorded as count data, which is generally far from normal distribution. Under the assumption that the count data follow the Poisson log-normal distribution, this paper provides an L1-penalized likelihood framework and an efficient search algorithm to estimate the structure of sparse directed acyclic graphs (DAGs) for multivariate counts data. In searching for the solution, we use iterative optimization procedures to estimate the adjacency matrix and the variance matrix of the latent variables. The simulation result shows that our proposed method outperforms the approach which assumes multivariate normal distributions, and the log-transformation approach. It also shows that the proposed method outperforms the rank-based PC method under sparse network or hub network structures. As a real data example, we demonstrate the efficiency of the proposed method in estimating the gene regulatory networks of the ovarian cancer study.

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