simule
A Constrained L1 Minimization Approach for Estimating Multiple Sparse Gaussian or Nonparanormal Graphical Models
v1.3.0
·
Jul 2, 2018
·
GPL-2
Description
This is an R implementation of a constrained l1 minimization approach for estimating multiple Sparse Gaussian or Nonparanormal Graphical Models (SIMULE). The SIMULE algorithm can be used to estimate multiple related precision matrices. For instance, it can identify context-specific gene networks from multi-context gene expression datasets. By performing data-driven network inference from high-dimensional and heterogenous data sets, this tool can help users effectively translate aggregated data into knowledge that take the form of graphs among entities. Please run demo(simuleDemo) to learn the basic functions provided by this package. For further details, please read the original paper: Beilun Wang, Ritambhara Singh, Yanjun Qi (2017) <DOI:10.1007/s10994-017-5635-7>.
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NOTE
r-devel-linux-x86_64-debian-clang
CRAN incoming feasibility
Maintainer: ‘Beilun Wang <bw4mw@virginia.edu>’ The BugReports field in DESCRIPTION has https://github.com/QData/SIMULE which should likely be https://github.com/QData/SIMULE/issues instead.
NOTE
r-devel-linux-x86_64-debian-clang
Rd files
checkRd: (-1) simule-package.Rd:18: Lost braces; missing escapes or markup?
18 | Identifying context-specific entity networks from aggregated data is an important task, often arising in bioinformatics and neuroimaging. Computationally, this task can be formulated as jointly estimating multiple different, but related, sparse Undirected Graphical Models (UGM) from aggregated samples across several contexts. Previous joint-UGM studies have mostly focused on sparse Gaussian Graphical Models (sGGMs) and can't identify context-specific edge patterns directly. We, therefore, propose a novel approach, SIMULE (detecting Shared and Individual parts of MULtiple graphs Explicitly) to learn multi-UGM via a constrained L1 minimization. SIMULE automatically infers both specific edge patterns that are unique to each context and shared interactions preserved among all the contexts. Through the L1 constrained formulation, this problem is cast as multiple independent subtasks of linear programming that can be solved efficiently in parallel. In addition to Gaussian data, SIMULE can also handle multivariate nonparanormal data that greatly relaxes the normality assumption that many real-world applications do not follow. We provide a novel theoretical proof showing that SIMULE achieves a consistent result at the rate O(log(Kp)/n_{tot}). On multiple synthetic datasets and two biomedical datasets, SIMULE shows significant improvement over state-of-the-art multi-sGGM and single-UGM baselines.
| ^
checkRd: (-1) simule.Rd:18: Lost braces
18 | level of the matrices. The \\eqn{\\lambda_n} in the following section:
| ^
checkRd: (-1) simule.Rd:23: Lost braces
23 | of each graph. The \\eqn{\\epsilon} in the following section: Details. If
| ^
checkRd: (-1) simule.Rd:62-65: Lost braces
62 | following equation: \\deqn{ \\hat{\\Omega}^{(1)}_I, \\hat{\\Omega}^{(2)}_I,
| ^
checkRd: (-1) simule.Rd:62: Lost braces
62 | following equation: \\deqn{ \\hat{\\Omega}^{(1)}_I, \\hat{\\Omega}^{(2)}_I,
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checkRd: (-1) simule.Rd:62: Lost braces; missing escapes or markup?
62 | following equation: \\deqn{ \\hat{\\Omega}^{(1)}_I, \\hat{\\Omega}^{(2)}_I,
| ^
checkRd: (-1) simule.Rd:62: Lost braces
62 | following equation: \\deqn{ \\hat{\\Omega}^{(1)}_I, \\hat{\\Omega}^{(2)}_I,
| ^
checkRd: (-1) simule.Rd:62: Lost braces; missing escapes or markup?
62 | following equation: \\deqn{ \\hat{\\Omega}^{(1)}_I, \\hat{\\Omega}^{(2)}_I,
| ^
checkRd: (-1) simule.Rd:63: Lost braces
63 | \\dots, \\hat{\\Omega}^{(K)}_I, \\hat{\\Omega}_S =
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checkRd: (-1) simule.Rd:63: Lost braces; missing escapes or markup?
63 | \\dots, \\hat{\\Omega}^{(K)}_I, \\hat{\\Omega}_S =
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checkRd: (-1) simule.Rd:63: Lost braces
63 | \\dots, \\hat{\\Omega}^{(K)}_I, \\hat{\\Omega}_S =
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checkRd: (-1) simule.Rd:64: Lost braces
64 | \\min\\limits_{\\Omega^{(i)}_I,\\Omega_S}\\sum\\limits_i ||\\Omega^{(i)}_I||_1+
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checkRd: (-1) simule.Rd:64: Lost braces; missing escapes or markup?
64 | \\min\\limits_{\\Omega^{(i)}_I,\\Omega_S}\\sum\\limits_i ||\\Omega^{(i)}_I||_1+
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checkRd: (-1) simule.Rd:64: Lost braces; missing escapes or markup?
64 | \\min\\limits_{\\Omega^{(i)}_I,\\Omega_S}\\sum\\limits_i ||\\Omega^{(i)}_I||_1+
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checkRd: (-1) simule.Rd:65-67: Lost braces
65 | \\epsilon K||\\Omega_S||_1 } Subject to : \\deqn{
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checkRd: (-1) simule.Rd:66: Lost braces; missing escapes or markup?
66 | ||\\Sigma^{(i)}(\\Omega^{(i)}_I + \\Omega_S) - I||_{\\infty} \\le \\lambda_{n}, i
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checkRd: (-1) simule.Rd:66: Lost braces; missing escapes or markup?
66 | ||\\Sigma^{(i)}(\\Omega^{(i)}_I + \\Omega_S) - I||_{\\infty} \\le \\lambda_{n}, i
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checkRd: (-1) simule.Rd:66: Lost braces; missing escapes or markup?
66 | ||\\Sigma^{(i)}(\\Omega^{(i)}_I + \\Omega_S) - I||_{\\infty} \\le \\lambda_{n}, i
| ^
checkRd: (-1) simule.Rd:66: Lost braces; missing escapes or markup?
66 | ||\\Sigma^{(i)}(\\Omega^{(i)}_I + \\Omega_S) - I||_{\\infty} \\le \\lambda_{n}, i
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checkRd: (-1) simule.Rd:68: Lost braces
68 | \\eqn{\\lambda_n} is the hyperparameter controlling the sparsity level of the
| ^
checkRd: (-1) simule.Rd:69: Lost braces
69 | matrices and it is the \\code{lambda} in our function. The \\eqn{\\epsilon} is
| ^
checkRd: (-1) simule.Rd:69: Lost braces
69 | matrices and it is the \\code{lambda} in our function. The \\eqn{\\epsilon} is
| ^
checkRd: (-1) simule.Rd:72: Lost braces
72 | \\code{epsilon} parameter in our function and the default value is 1. For
| ^
checkRd: (-1) simule.Rd:47: Lost braces
47 | \\item{Graphs}{A list of the estimated inverse
| ^
checkRd: (-1) simule.Rd:47-48: Lost braces
47 | \\item{Graphs}{A list of the estimated inverse
| ^
checkRd: (-1) simule.Rd:48: Lost braces
48 | covariance/correlation matrices.} \\item{share}{The share graph among
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checkRd: (-1) simule.Rd:48-49: Lost braces
48 | covariance/correlation matrices.} \\item{share}{The share graph among
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NOTE
r-devel-linux-x86_64-debian-gcc
CRAN incoming feasibility
Maintainer: ‘Beilun Wang <bw4mw@virginia.edu>’ The BugReports field in DESCRIPTION has https://github.com/QData/SIMULE which should likely be https://github.com/QData/SIMULE/issues instead.
NOTE
r-devel-linux-x86_64-debian-gcc
Rd files
checkRd: (-1) simule-package.Rd:18: Lost braces; missing escapes or markup?
18 | Identifying context-specific entity networks from aggregated data is an important task, often arising in bioinformatics and neuroimaging. Computationally, this task can be formulated as jointly estimating multiple different, but related, sparse Undirected Graphical Models (UGM) from aggregated samples across several contexts. Previous joint-UGM studies have mostly focused on sparse Gaussian Graphical Models (sGGMs) and can't identify context-specific edge patterns directly. We, therefore, propose a novel approach, SIMULE (detecting Shared and Individual parts of MULtiple graphs Explicitly) to learn multi-UGM via a constrained L1 minimization. SIMULE automatically infers both specific edge patterns that are unique to each context and shared interactions preserved among all the contexts. Through the L1 constrained formulation, this problem is cast as multiple independent subtasks of linear programming that can be solved efficiently in parallel. In addition to Gaussian data, SIMULE can also handle multivariate nonparanormal data that greatly relaxes the normality assumption that many real-world applications do not follow. We provide a novel theoretical proof showing that SIMULE achieves a consistent result at the rate O(log(Kp)/n_{tot}). On multiple synthetic datasets and two biomedical datasets, SIMULE shows significant improvement over state-of-the-art multi-sGGM and single-UGM baselines.
| ^
checkRd: (-1) simule.Rd:18: Lost braces
18 | level of the matrices. The \\eqn{\\lambda_n} in the following section:
| ^
checkRd: (-1) simule.Rd:23: Lost braces
23 | of each graph. The \\eqn{\\epsilon} in the following section: Details. If
| ^
checkRd: (-1) simule.Rd:62-65: Lost braces
62 | following equation: \\deqn{ \\hat{\\Omega}^{(1)}_I, \\hat{\\Omega}^{(2)}_I,
| ^
checkRd: (-1) simule.Rd:62: Lost braces
62 | following equation: \\deqn{ \\hat{\\Omega}^{(1)}_I, \\hat{\\Omega}^{(2)}_I,
| ^
checkRd: (-1) simule.Rd:62: Lost braces; missing escapes or markup?
62 | following equation: \\deqn{ \\hat{\\Omega}^{(1)}_I, \\hat{\\Omega}^{(2)}_I,
| ^
checkRd: (-1) simule.Rd:62: Lost braces
62 | following equation: \\deqn{ \\hat{\\Omega}^{(1)}_I, \\hat{\\Omega}^{(2)}_I,
| ^
checkRd: (-1) simule.Rd:62: Lost braces; missing escapes or markup?
62 | following equation: \\deqn{ \\hat{\\Omega}^{(1)}_I, \\hat{\\Omega}^{(2)}_I,
| ^
checkRd: (-1) simule.Rd:63: Lost braces
63 | \\dots, \\hat{\\Omega}^{(K)}_I, \\hat{\\Omega}_S =
| ^
checkRd: (-1) simule.Rd:63: Lost braces; missing escapes or markup?
63 | \\dots, \\hat{\\Omega}^{(K)}_I, \\hat{\\Omega}_S =
| ^
checkRd: (-1) simule.Rd:63: Lost braces
63 | \\dots, \\hat{\\Omega}^{(K)}_I, \\hat{\\Omega}_S =
| ^
checkRd: (-1) simule.Rd:64: Lost braces
64 | \\min\\limits_{\\Omega^{(i)}_I,\\Omega_S}\\sum\\limits_i ||\\Omega^{(i)}_I||_1+
| ^
checkRd: (-1) simule.Rd:64: Lost braces; missing escapes or markup?
64 | \\min\\limits_{\\Omega^{(i)}_I,\\Omega_S}\\sum\\limits_i ||\\Omega^{(i)}_I||_1+
| ^
checkRd: (-1) simule.Rd:64: Lost braces; missing escapes or markup?
64 | \\min\\limits_{\\Omega^{(i)}_I,\\Omega_S}\\sum\\limits_i ||\\Omega^{(i)}_I||_1+
| ^
checkRd: (-1) simule.Rd:65-67: Lost braces
65 | \\epsilon K||\\Omega_S||_1 } Subject to : \\deqn{
| ^
checkRd: (-1) simule.Rd:66: Lost braces; missing escapes or markup?
66 | ||\\Sigma^{(i)}(\\Omega^{(i)}_I + \\Omega_S) - I||_{\\infty} \\le \\lambda_{n}, i
| ^
checkRd: (-1) simule.Rd:66: Lost braces; missing escapes or markup?
66 | ||\\Sigma^{(i)}(\\Omega^{(i)}_I + \\Omega_S) - I||_{\\infty} \\le \\lambda_{n}, i
| ^
checkRd: (-1) simule.Rd:66: Lost braces; missing escapes or markup?
66 | ||\\Sigma^{(i)}(\\Omega^{(i)}_I + \\Omega_S) - I||_{\\infty} \\le \\lambda_{n}, i
| ^
checkRd: (-1) simule.Rd:66: Lost braces; missing escapes or markup?
66 | ||\\Sigma^{(i)}(\\Omega^{(i)}_I + \\Omega_S) - I||_{\\infty} \\le \\lambda_{n}, i
| ^
checkRd: (-1) simule.Rd:68: Lost braces
68 | \\eqn{\\lambda_n} is the hyperparameter controlling the sparsity level of the
| ^
checkRd: (-1) simule.Rd:69: Lost braces
69 | matrices and it is the \\code{lambda} in our function. The \\eqn{\\epsilon} is
| ^
checkRd: (-1) simule.Rd:69: Lost braces
69 | matrices and it is the \\code{lambda} in our function. The \\eqn{\\epsilon} is
| ^
checkRd: (-1) simule.Rd:72: Lost braces
72 | \\code{epsilon} parameter in our function and the default value is 1. For
| ^
checkRd: (-1) simule.Rd:47: Lost braces
47 | \\item{Graphs}{A list of the estimated inverse
| ^
checkRd: (-1) simule.Rd:47-48: Lost braces
47 | \\item{Graphs}{A list of the estimated inverse
| ^
checkRd: (-1) simule.Rd:48: Lost braces
48 | covariance/correlation matrices.} \\item{share}{The share graph among
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checkRd: (-1) simule.Rd:48-49: Lost braces
48 | covariance/correlation matrices.} \\item{share}{The share graph among
| ^
NOTE
r-devel-linux-x86_64-fedora-clang
Rd files
checkRd: (-1) simule-package.Rd:18: Lost braces; missing escapes or markup?
18 | Identifying context-specific entity networks from aggregated data is an important task, often arising in bioinformatics and neuroimaging. Computationally, this task can be formulated as jointly estimating multiple different, but related, sparse Undirected Graphical Models (UGM) from aggregated samples across several contexts. Previous joint-UGM studies have mostly focused on sparse Gaussian Graphical Models (sGGMs) and can't identify context-specific edge patterns directly. We, therefore, propose a novel approach, SIMULE (detecting Shared and Individual parts of MULtiple graphs Explicitly) to learn multi-UGM via a constrained L1 minimization. SIMULE automatically infers both specific edge patterns that are unique to each context and shared interactions preserved among all the contexts. Through the L1 constrained formulation, this problem is cast as multiple independent subtasks of linear programming that can be solved efficiently in parallel. In addition to Gaussian data, SIMULE can also handle multivariate nonparanormal data that greatly relaxes the normality assumption that many real-world applications do not follow. We provide a novel theoretical proof showing that SIMULE achieves a consistent result at the rate O(log(Kp)/n_{tot}). On multiple synthetic datasets and two biomedical datasets, SIMULE shows significant improvement over state-of-the-art multi-sGGM and single-UGM baselines.
| ^
checkRd: (-1) simule.Rd:18: Lost braces
18 | level of the matrices. The \\eqn{\\lambda_n} in the following section:
| ^
checkRd: (-1) simule.Rd:23: Lost braces
23 | of each graph. The \\eqn{\\epsilon} in the following section: Details. If
| ^
checkRd: (-1) simule.Rd:62-65: Lost braces
62 | following equation: \\deqn{ \\hat{\\Omega}^{(1)}_I, \\hat{\\Omega}^{(2)}_I,
| ^
checkRd: (-1) simule.Rd:62: Lost braces
62 | following equation: \\deqn{ \\hat{\\Omega}^{(1)}_I, \\hat{\\Omega}^{(2)}_I,
| ^
checkRd: (-1) simule.Rd:62: Lost braces; missing escapes or markup?
62 | following equation: \\deqn{ \\hat{\\Omega}^{(1)}_I, \\hat{\\Omega}^{(2)}_I,
| ^
checkRd: (-1) simule.Rd:62: Lost braces
62 | following equation: \\deqn{ \\hat{\\Omega}^{(1)}_I, \\hat{\\Omega}^{(2)}_I,
| ^
checkRd: (-1) simule.Rd:62: Lost braces; missing escapes or markup?
62 | following equation: \\deqn{ \\hat{\\Omega}^{(1)}_I, \\hat{\\Omega}^{(2)}_I,
| ^
checkRd: (-1) simule.Rd:63: Lost braces
63 | \\dots, \\hat{\\Omega}^{(K)}_I, \\hat{\\Omega}_S =
| ^
checkRd: (-1) simule.Rd:63: Lost braces; missing escapes or markup?
63 | \\dots, \\hat{\\Omega}^{(K)}_I, \\hat{\\Omega}_S =
| ^
checkRd: (-1) simule.Rd:63: Lost braces
63 | \\dots, \\hat{\\Omega}^{(K)}_I, \\hat{\\Omega}_S =
| ^
checkRd: (-1) simule.Rd:64: Lost braces
64 | \\min\\limits_{\\Omega^{(i)}_I,\\Omega_S}\\sum\\limits_i ||\\Omega^{(i)}_I||_1+
| ^
checkRd: (-1) simule.Rd:64: Lost braces; missing escapes or markup?
64 | \\min\\limits_{\\Omega^{(i)}_I,\\Omega_S}\\sum\\limits_i ||\\Omega^{(i)}_I||_1+
| ^
checkRd: (-1) simule.Rd:64: Lost braces; missing escapes or markup?
64 | \\min\\limits_{\\Omega^{(i)}_I,\\Omega_S}\\sum\\limits_i ||\\Omega^{(i)}_I||_1+
| ^
checkRd: (-1) simule.Rd:65-67: Lost braces
65 | \\epsilon K||\\Omega_S||_1 } Subject to : \\deqn{
| ^
checkRd: (-1) simule.Rd:66: Lost braces; missing escapes or markup?
66 | ||\\Sigma^{(i)}(\\Omega^{(i)}_I + \\Omega_S) - I||_{\\infty} \\le \\lambda_{n}, i
| ^
checkRd: (-1) simule.Rd:66: Lost braces; missing escapes or markup?
66 | ||\\Sigma^{(i)}(\\Omega^{(i)}_I + \\Omega_S) - I||_{\\infty} \\le \\lambda_{n}, i
| ^
checkRd: (-1) simule.Rd:66: Lost braces; missing escapes or markup?
66 | ||\\Sigma^{(i)}(\\Omega^{(i)}_I + \\Omega_S) - I||_{\\infty} \\le \\lambda_{n}, i
| ^
checkRd: (-1) simule.Rd:66: Lost braces; missing escapes or markup?
66 | ||\\Sigma^{(i)}(\\Omega^{(i)}_I + \\Omega_S) - I||_{\\infty} \\le \\lambda_{n}, i
| ^
checkRd: (-1) simule.Rd:68: Lost braces
68 | \\eqn{\\lambda_n} is the hyperparameter controlling the sparsity level of the
| ^
checkRd: (-1) simule.Rd:69: Lost braces
69 | matrices and it is the \\code{lambda} in our function. The \\eqn{\\epsilon} is
| ^
checkRd: (-1) simule.Rd:69: Lost braces
69 | matrices and it is the \\code{lambda} in our function. The \\eqn{\\epsilon} is
| ^
checkRd: (-1) simule.Rd:72: Lost braces
72 | \\code{epsilon} parameter in our function and the default value is 1. For
| ^
checkRd: (-1) simule.Rd:47: Lost braces
47 | \\item{Graphs}{A list of the estimated inverse
| ^
checkRd: (-1) simule.Rd:47-48: Lost braces
47 | \\item{Graphs}{A list of the estimated inverse
| ^
checkRd: (-1) simule.Rd:48: Lost braces
48 | covariance/correlation matrices.} \\item{share}{The share graph among
| ^
checkRd: (-1) simule.Rd:48-49: Lost braces
48 | covariance/correlation matrices.} \\item{share}{The share graph among
| ^
NOTE
r-devel-linux-x86_64-fedora-gcc
Rd files
checkRd: (-1) simule-package.Rd:18: Lost braces; missing escapes or markup?
18 | Identifying context-specific entity networks from aggregated data is an important task, often arising in bioinformatics and neuroimaging. Computationally, this task can be formulated as jointly estimating multiple different, but related, sparse Undirected Graphical Models (UGM) from aggregated samples across several contexts. Previous joint-UGM studies have mostly focused on sparse Gaussian Graphical Models (sGGMs) and can't identify context-specific edge patterns directly. We, therefore, propose a novel approach, SIMULE (detecting Shared and Individual parts of MULtiple graphs Explicitly) to learn multi-UGM via a constrained L1 minimization. SIMULE automatically infers both specific edge patterns that are unique to each context and shared interactions preserved among all the contexts. Through the L1 constrained formulation, this problem is cast as multiple independent subtasks of linear programming that can be solved efficiently in parallel. In addition to Gaussian data, SIMULE can also handle multivariate nonparanormal data that greatly relaxes the normality assumption that many real-world applications do not follow. We provide a novel theoretical proof showing that SIMULE achieves a consistent result at the rate O(log(Kp)/n_{tot}). On multiple synthetic datasets and two biomedical datasets, SIMULE shows significant improvement over state-of-the-art multi-sGGM and single-UGM baselines.
| ^
checkRd: (-1) simule.Rd:18: Lost braces
18 | level of the matrices. The \\eqn{\\lambda_n} in the following section:
| ^
checkRd: (-1) simule.Rd:23: Lost braces
23 | of each graph. The \\eqn{\\epsilon} in the following section: Details. If
| ^
checkRd: (-1) simule.Rd:62-65: Lost braces
62 | following equation: \\deqn{ \\hat{\\Omega}^{(1)}_I, \\hat{\\Omega}^{(2)}_I,
| ^
checkRd: (-1) simule.Rd:62: Lost braces
62 | following equation: \\deqn{ \\hat{\\Omega}^{(1)}_I, \\hat{\\Omega}^{(2)}_I,
| ^
checkRd: (-1) simule.Rd:62: Lost braces; missing escapes or markup?
62 | following equation: \\deqn{ \\hat{\\Omega}^{(1)}_I, \\hat{\\Omega}^{(2)}_I,
| ^
checkRd: (-1) simule.Rd:62: Lost braces
62 | following equation: \\deqn{ \\hat{\\Omega}^{(1)}_I, \\hat{\\Omega}^{(2)}_I,
| ^
checkRd: (-1) simule.Rd:62: Lost braces; missing escapes or markup?
62 | following equation: \\deqn{ \\hat{\\Omega}^{(1)}_I, \\hat{\\Omega}^{(2)}_I,
| ^
checkRd: (-1) simule.Rd:63: Lost braces
63 | \\dots, \\hat{\\Omega}^{(K)}_I, \\hat{\\Omega}_S =
| ^
checkRd: (-1) simule.Rd:63: Lost braces; missing escapes or markup?
63 | \\dots, \\hat{\\Omega}^{(K)}_I, \\hat{\\Omega}_S =
| ^
checkRd: (-1) simule.Rd:63: Lost braces
63 | \\dots, \\hat{\\Omega}^{(K)}_I, \\hat{\\Omega}_S =
| ^
checkRd: (-1) simule.Rd:64: Lost braces
64 | \\min\\limits_{\\Omega^{(i)}_I,\\Omega_S}\\sum\\limits_i ||\\Omega^{(i)}_I||_1+
| ^
checkRd: (-1) simule.Rd:64: Lost braces; missing escapes or markup?
64 | \\min\\limits_{\\Omega^{(i)}_I,\\Omega_S}\\sum\\limits_i ||\\Omega^{(i)}_I||_1+
| ^
checkRd: (-1) simule.Rd:64: Lost braces; missing escapes or markup?
64 | \\min\\limits_{\\Omega^{(i)}_I,\\Omega_S}\\sum\\limits_i ||\\Omega^{(i)}_I||_1+
| ^
checkRd: (-1) simule.Rd:65-67: Lost braces
65 | \\epsilon K||\\Omega_S||_1 } Subject to : \\deqn{
| ^
checkRd: (-1) simule.Rd:66: Lost braces; missing escapes or markup?
66 | ||\\Sigma^{(i)}(\\Omega^{(i)}_I + \\Omega_S) - I||_{\\infty} \\le \\lambda_{n}, i
| ^
checkRd: (-1) simule.Rd:66: Lost braces; missing escapes or markup?
66 | ||\\Sigma^{(i)}(\\Omega^{(i)}_I + \\Omega_S) - I||_{\\infty} \\le \\lambda_{n}, i
| ^
checkRd: (-1) simule.Rd:66: Lost braces; missing escapes or markup?
66 | ||\\Sigma^{(i)}(\\Omega^{(i)}_I + \\Omega_S) - I||_{\\infty} \\le \\lambda_{n}, i
| ^
checkRd: (-1) simule.Rd:66: Lost braces; missing escapes or markup?
66 | ||\\Sigma^{(i)}(\\Omega^{(i)}_I + \\Omega_S) - I||_{\\infty} \\le \\lambda_{n}, i
| ^
checkRd: (-1) simule.Rd:68: Lost braces
68 | \\eqn{\\lambda_n} is the hyperparameter controlling the sparsity level of the
| ^
checkRd: (-1) simule.Rd:69: Lost braces
69 | matrices and it is the \\code{lambda} in our function. The \\eqn{\\epsilon} is
| ^
checkRd: (-1) simule.Rd:69: Lost braces
69 | matrices and it is the \\code{lambda} in our function. The \\eqn{\\epsilon} is
| ^
checkRd: (-1) simule.Rd:72: Lost braces
72 | \\code{epsilon} parameter in our function and the default value is 1. For
| ^
checkRd: (-1) simule.Rd:47: Lost braces
47 | \\item{Graphs}{A list of the estimated inverse
| ^
checkRd: (-1) simule.Rd:47-48: Lost braces
47 | \\item{Graphs}{A list of the estimated inverse
| ^
checkRd: (-1) simule.Rd:48: Lost braces
48 | covariance/correlation matrices.} \\item{share}{The share graph among
| ^
checkRd: (-1) simule.Rd:48-49: Lost braces
48 | covariance/correlation matrices.} \\item{share}{The share graph among
| ^
NOTE
r-devel-macos-arm64
Rd files
checkRd: (-1) simule-package.Rd:18: Lost braces; missing escapes or markup?
18 | Identifying context-specific entity networks from aggregated data is an important task, often arising in bioinformatics and neuroimaging. Computationally, this task can be formulated as jointly estimating multiple different, but related, sparse Undirected Graphical Models (UGM) from aggregated samples across several contexts. Previous joint-UGM studies have mostly focused on sparse Gaussian Graphical Models (sGGMs) and can't identify context-specific edge patterns directly. We, therefore, propose a novel approach, SIMULE (detecting Shared and Individual parts of MULtiple graphs Explicitly) to learn multi-UGM via a constrained L1 minimization. SIMULE automatically infers both specific edge patterns that are unique to each context and shared interactions preserved among all the contexts. Through the L1 constrained formulation, this problem is cast as multiple independent subtasks of linear programming that can be solved efficiently in parallel. In addition to Gaussian data, SIMULE can also handle multivariate nonparanormal data that greatly relaxes the normality assumption that many real-world applications do not follow. We provide a novel theoretical proof showing that SIMULE achieves a consistent result at the rate O(log(Kp)/n_{tot}). On multiple synthetic datasets and two biomedical datasets, SIMULE shows significant improvement over state-of-the-art multi-sGGM and single-UGM baselines.
| ^
checkRd: (-1) simule.Rd:18: Lost braces
18 | level of the matrices. The \\eqn{\\lambda_n} in the following section:
| ^
checkRd: (-1) simule.Rd:23: Lost braces
23 | of each graph. The \\eqn{\\epsilon} in the following section: Details. If
| ^
checkRd: (-1) simule.Rd:62-65: Lost braces
62 | following equation: \\deqn{ \\hat{\\Omega}^{(1)}_I, \\hat{\\Omega}^{(2)}_I,
| ^
checkRd: (-1) simule.Rd:62: Lost braces
62 | following equation: \\deqn{ \\hat{\\Omega}^{(1)}_I, \\hat{\\Omega}^{(2)}_I,
| ^
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62 | following equation: \\deqn{ \\hat{\\Omega}^{(1)}_I, \\hat{\\Omega}^{(2)}_I,
| ^
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62 | following equation: \\deqn{ \\hat{\\Omega}^{(1)}_I, \\hat{\\Omega}^{(2)}_I,
| ^
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62 | following equation: \\deqn{ \\hat{\\Omega}^{(1)}_I, \\hat{\\Omega}^{(2)}_I,
| ^
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63 | \\dots, \\hat{\\Omega}^{(K)}_I, \\hat{\\Omega}_S =
| ^
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63 | \\dots, \\hat{\\Omega}^{(K)}_I, \\hat{\\Omega}_S =
| ^
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63 | \\dots, \\hat{\\Omega}^{(K)}_I, \\hat{\\Omega}_S =
| ^
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64 | \\min\\limits_{\\Omega^{(i)}_I,\\Omega_S}\\sum\\limits_i ||\\Omega^{(i)}_I||_1+
| ^
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64 | \\min\\limits_{\\Omega^{(i)}_I,\\Omega_S}\\sum\\limits_i ||\\Omega^{(i)}_I||_1+
| ^
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64 | \\min\\limits_{\\Omega^{(i)}_I,\\Omega_S}\\sum\\limits_i ||\\Omega^{(i)}_I||_1+
| ^
checkRd: (-1) simule.Rd:65-67: Lost braces
65 | \\epsilon K||\\Omega_S||_1 } Subject to : \\deqn{
| ^
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66 | ||\\Sigma^{(i)}(\\Omega^{(i)}_I + \\Omega_S) - I||_{\\infty} \\le \\lambda_{n}, i
| ^
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66 | ||\\Sigma^{(i)}(\\Omega^{(i)}_I + \\Omega_S) - I||_{\\infty} \\le \\lambda_{n}, i
| ^
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66 | ||\\Sigma^{(i)}(\\Omega^{(i)}_I + \\Omega_S) - I||_{\\infty} \\le \\lambda_{n}, i
| ^
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66 | ||\\Sigma^{(i)}(\\Omega^{(i)}_I + \\Omega_S) - I||_{\\infty} \\le \\lambda_{n}, i
| ^
checkRd: (-1) simule.Rd:68: Lost braces
68 | \\eqn{\\lambda_n} is the hyperparameter controlling the sparsity level of the
| ^
checkRd: (-1) simule.Rd:69: Lost braces
69 | matrices and it is the \\code{lambda} in our function. The \\eqn{\\epsilon} is
| ^
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69 | matrices and it is the \\code{lambda} in our function. The \\eqn{\\epsilon} is
| ^
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72 | \\code{epsilon} parameter in our function and the default value is 1. For
| ^
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47 | \\item{Graphs}{A list of the estimated inverse
| ^
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47 | \\item{Graphs}{A list of the estimated inverse
| ^
checkRd: (-1) simule.Rd:48: Lost braces
48 | covariance/correlation matrices.} \\item{share}{The share graph among
| ^
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48 | covariance/correlation matrices.} \\item{share}{The share graph among
| ^
NOTE
r-devel-windows-x86_64
Rd files
checkRd: (-1) simule-package.Rd:18: Lost braces; missing escapes or markup?
18 | Identifying context-specific entity networks from aggregated data is an important task, often arising in bioinformatics and neuroimaging. Computationally, this task can be formulated as jointly estimating multiple different, but related, sparse Undirected Graphical Models (UGM) from aggregated samples across several contexts. Previous joint-UGM studies have mostly focused on sparse Gaussian Graphical Models (sGGMs) and can't identify context-specific edge patterns directly. We, therefore, propose a novel approach, SIMULE (detecting Shared and Individual parts of MULtiple graphs Explicitly) to learn multi-UGM via a constrained L1 minimization. SIMULE automatically infers both specific edge patterns that are unique to each context and shared interactions preserved among all the contexts. Through the L1 constrained formulation, this problem is cast as multiple independent subtasks of linear programming that can be solved efficiently in parallel. In addition to Gaussian data, SIMULE can also handle multivariate nonparanormal data that greatly relaxes the normality assumption that many real-world applications do not follow. We provide a novel theoretical proof showing that SIMULE achieves a consistent result at the rate O(log(Kp)/n_{tot}). On multiple synthetic datasets and two biomedical datasets, SIMULE shows significant improvement over state-of-the-art multi-sGGM and single-UGM baselines.
| ^
checkRd: (-1) simule.Rd:18: Lost braces
18 | level of the matrices. The \\eqn{\\lambda_n} in the following section:
| ^
checkRd: (-1) simule.Rd:23: Lost braces
23 | of each graph. The \\eqn{\\epsilon} in the following section: Details. If
| ^
checkRd: (-1) simule.Rd:62-65: Lost braces
62 | following equation: \\deqn{ \\hat{\\Omega}^{(1)}_I, \\hat{\\Omega}^{(2)}_I,
| ^
checkRd: (-1) simule.Rd:62: Lost braces
62 | following equation: \\deqn{ \\hat{\\Omega}^{(1)}_I, \\hat{\\Omega}^{(2)}_I,
| ^
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62 | following equation: \\deqn{ \\hat{\\Omega}^{(1)}_I, \\hat{\\Omega}^{(2)}_I,
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62 | following equation: \\deqn{ \\hat{\\Omega}^{(1)}_I, \\hat{\\Omega}^{(2)}_I,
| ^
checkRd: (-1) simule.Rd:62: Lost braces; missing escapes or markup?
62 | following equation: \\deqn{ \\hat{\\Omega}^{(1)}_I, \\hat{\\Omega}^{(2)}_I,
| ^
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63 | \\dots, \\hat{\\Omega}^{(K)}_I, \\hat{\\Omega}_S =
| ^
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63 | \\dots, \\hat{\\Omega}^{(K)}_I, \\hat{\\Omega}_S =
| ^
checkRd: (-1) simule.Rd:63: Lost braces
63 | \\dots, \\hat{\\Omega}^{(K)}_I, \\hat{\\Omega}_S =
| ^
checkRd: (-1) simule.Rd:64: Lost braces
64 | \\min\\limits_{\\Omega^{(i)}_I,\\Omega_S}\\sum\\limits_i ||\\Omega^{(i)}_I||_1+
| ^
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64 | \\min\\limits_{\\Omega^{(i)}_I,\\Omega_S}\\sum\\limits_i ||\\Omega^{(i)}_I||_1+
| ^
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64 | \\min\\limits_{\\Omega^{(i)}_I,\\Omega_S}\\sum\\limits_i ||\\Omega^{(i)}_I||_1+
| ^
checkRd: (-1) simule.Rd:65-67: Lost braces
65 | \\epsilon K||\\Omega_S||_1 } Subject to : \\deqn{
| ^
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66 | ||\\Sigma^{(i)}(\\Omega^{(i)}_I + \\Omega_S) - I||_{\\infty} \\le \\lambda_{n}, i
| ^
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66 | ||\\Sigma^{(i)}(\\Omega^{(i)}_I + \\Omega_S) - I||_{\\infty} \\le \\lambda_{n}, i
| ^
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66 | ||\\Sigma^{(i)}(\\Omega^{(i)}_I + \\Omega_S) - I||_{\\infty} \\le \\lambda_{n}, i
| ^
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66 | ||\\Sigma^{(i)}(\\Omega^{(i)}_I + \\Omega_S) - I||_{\\infty} \\le \\lambda_{n}, i
| ^
checkRd: (-1) simule.Rd:68: Lost braces
68 | \\eqn{\\lambda_n} is the hyperparameter controlling the sparsity level of the
| ^
checkRd: (-1) simule.Rd:69: Lost braces
69 | matrices and it is the \\code{lambda} in our function. The \\eqn{\\epsilon} is
| ^
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69 | matrices and it is the \\code{lambda} in our function. The \\eqn{\\epsilon} is
| ^
checkRd: (-1) simule.Rd:72: Lost braces
72 | \\code{epsilon} parameter in our function and the default value is 1. For
| ^
checkRd: (-1) simule.Rd:47: Lost braces
47 | \\item{Graphs}{A list of the estimated inverse
| ^
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47 | \\item{Graphs}{A list of the estimated inverse
| ^
checkRd: (-1) simule.Rd:48: Lost braces
48 | covariance/correlation matrices.} \\item{share}{The share graph among
| ^
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48 | covariance/correlation matrices.} \\item{share}{The share graph among
| ^
NOTE
r-oldrel-macos-arm64
Rd files
checkRd: (-1) simule-package.Rd:18: Lost braces; missing escapes or markup?
18 | Identifying context-specific entity networks from aggregated data is an important task, often arising in bioinformatics and neuroimaging. Computationally, this task can be formulated as jointly estimating multiple different, but related, sparse Undirected Graphical Models (UGM) from aggregated samples across several contexts. Previous joint-UGM studies have mostly focused on sparse Gaussian Graphical Models (sGGMs) and can't identify context-specific edge patterns directly. We, therefore, propose a novel approach, SIMULE (detecting Shared and Individual parts of MULtiple graphs Explicitly) to learn multi-UGM via a constrained L1 minimization. SIMULE automatically infers both specific edge patterns that are unique to each context and shared interactions preserved among all the contexts. Through the L1 constrained formulation, this problem is cast as multiple independent subtasks of linear programming that can be solved efficiently in parallel. In addition to Gaussian data, SIMULE can also handle multivariate nonparanormal data that greatly relaxes the normality assumption that many real-world applications do not follow. We provide a novel theoretical proof showing that SIMULE achieves a consistent result at the rate O(log(Kp)/n_{tot}). On multiple synthetic datasets and two biomedical datasets, SIMULE shows significant improvement over state-of-the-art multi-sGGM and single-UGM baselines.
| ^
checkRd: (-1) simule.Rd:18: Lost braces
18 | level of the matrices. The \\eqn{\\lambda_n} in the following section:
| ^
checkRd: (-1) simule.Rd:23: Lost braces
23 | of each graph. The \\eqn{\\epsilon} in the following section: Details. If
| ^
checkRd: (-1) simule.Rd:62-65: Lost braces
62 | following equation: \\deqn{ \\hat{\\Omega}^{(1)}_I, \\hat{\\Omega}^{(2)}_I,
| ^
checkRd: (-1) simule.Rd:62: Lost braces
62 | following equation: \\deqn{ \\hat{\\Omega}^{(1)}_I, \\hat{\\Omega}^{(2)}_I,
| ^
checkRd: (-1) simule.Rd:62: Lost braces; missing escapes or markup?
62 | following equation: \\deqn{ \\hat{\\Omega}^{(1)}_I, \\hat{\\Omega}^{(2)}_I,
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checkRd: (-1) simule.Rd:62: Lost braces
62 | following equation: \\deqn{ \\hat{\\Omega}^{(1)}_I, \\hat{\\Omega}^{(2)}_I,
| ^
checkRd: (-1) simule.Rd:62: Lost braces; missing escapes or markup?
62 | following equation: \\deqn{ \\hat{\\Omega}^{(1)}_I, \\hat{\\Omega}^{(2)}_I,
| ^
checkRd: (-1) simule.Rd:63: Lost braces
63 | \\dots, \\hat{\\Omega}^{(K)}_I, \\hat{\\Omega}_S =
| ^
checkRd: (-1) simule.Rd:63: Lost braces; missing escapes or markup?
63 | \\dots, \\hat{\\Omega}^{(K)}_I, \\hat{\\Omega}_S =
| ^
checkRd: (-1) simule.Rd:63: Lost braces
63 | \\dots, \\hat{\\Omega}^{(K)}_I, \\hat{\\Omega}_S =
| ^
checkRd: (-1) simule.Rd:64: Lost braces
64 | \\min\\limits_{\\Omega^{(i)}_I,\\Omega_S}\\sum\\limits_i ||\\Omega^{(i)}_I||_1+
| ^
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64 | \\min\\limits_{\\Omega^{(i)}_I,\\Omega_S}\\sum\\limits_i ||\\Omega^{(i)}_I||_1+
| ^
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64 | \\min\\limits_{\\Omega^{(i)}_I,\\Omega_S}\\sum\\limits_i ||\\Omega^{(i)}_I||_1+
| ^
checkRd: (-1) simule.Rd:65-67: Lost braces
65 | \\epsilon K||\\Omega_S||_1 } Subject to : \\deqn{
| ^
checkRd: (-1) simule.Rd:66: Lost braces; missing escapes or markup?
66 | ||\\Sigma^{(i)}(\\Omega^{(i)}_I + \\Omega_S) - I||_{\\infty} \\le \\lambda_{n}, i
| ^
checkRd: (-1) simule.Rd:66: Lost braces; missing escapes or markup?
66 | ||\\Sigma^{(i)}(\\Omega^{(i)}_I + \\Omega_S) - I||_{\\infty} \\le \\lambda_{n}, i
| ^
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66 | ||\\Sigma^{(i)}(\\Omega^{(i)}_I + \\Omega_S) - I||_{\\infty} \\le \\lambda_{n}, i
| ^
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66 | ||\\Sigma^{(i)}(\\Omega^{(i)}_I + \\Omega_S) - I||_{\\infty} \\le \\lambda_{n}, i
| ^
checkRd: (-1) simule.Rd:68: Lost braces
68 | \\eqn{\\lambda_n} is the hyperparameter controlling the sparsity level of the
| ^
checkRd: (-1) simule.Rd:69: Lost braces
69 | matrices and it is the \\code{lambda} in our function. The \\eqn{\\epsilon} is
| ^
checkRd: (-1) simule.Rd:69: Lost braces
69 | matrices and it is the \\code{lambda} in our function. The \\eqn{\\epsilon} is
| ^
checkRd: (-1) simule.Rd:72: Lost braces
72 | \\code{epsilon} parameter in our function and the default value is 1. For
| ^
checkRd: (-1) simule.Rd:47: Lost braces
47 | \\item{Graphs}{A list of the estimated inverse
| ^
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47 | \\item{Graphs}{A list of the estimated inverse
| ^
checkRd: (-1) simule.Rd:48: Lost braces
48 | covariance/correlation matrices.} \\item{share}{The share graph among
| ^
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48 | covariance/correlation matrices.} \\item{share}{The share graph among
| ^
NOTE
r-oldrel-macos-x86_64
Rd files
checkRd: (-1) simule-package.Rd:18: Lost braces; missing escapes or markup?
18 | Identifying context-specific entity networks from aggregated data is an important task, often arising in bioinformatics and neuroimaging. Computationally, this task can be formulated as jointly estimating multiple different, but related, sparse Undirected Graphical Models (UGM) from aggregated samples across several contexts. Previous joint-UGM studies have mostly focused on sparse Gaussian Graphical Models (sGGMs) and can't identify context-specific edge patterns directly. We, therefore, propose a novel approach, SIMULE (detecting Shared and Individual parts of MULtiple graphs Explicitly) to learn multi-UGM via a constrained L1 minimization. SIMULE automatically infers both specific edge patterns that are unique to each context and shared interactions preserved among all the contexts. Through the L1 constrained formulation, this problem is cast as multiple independent subtasks of linear programming that can be solved efficiently in parallel. In addition to Gaussian data, SIMULE can also handle multivariate nonparanormal data that greatly relaxes the normality assumption that many real-world applications do not follow. We provide a novel theoretical proof showing that SIMULE achieves a consistent result at the rate O(log(Kp)/n_{tot}). On multiple synthetic datasets and two biomedical datasets, SIMULE shows significant improvement over state-of-the-art multi-sGGM and single-UGM baselines.
| ^
checkRd: (-1) simule.Rd:18: Lost braces
18 | level of the matrices. The \\eqn{\\lambda_n} in the following section:
| ^
checkRd: (-1) simule.Rd:23: Lost braces
23 | of each graph. The \\eqn{\\epsilon} in the following section: Details. If
| ^
checkRd: (-1) simule.Rd:62-65: Lost braces
62 | following equation: \\deqn{ \\hat{\\Omega}^{(1)}_I, \\hat{\\Omega}^{(2)}_I,
| ^
checkRd: (-1) simule.Rd:62: Lost braces
62 | following equation: \\deqn{ \\hat{\\Omega}^{(1)}_I, \\hat{\\Omega}^{(2)}_I,
| ^
checkRd: (-1) simule.Rd:62: Lost braces; missing escapes or markup?
62 | following equation: \\deqn{ \\hat{\\Omega}^{(1)}_I, \\hat{\\Omega}^{(2)}_I,
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checkRd: (-1) simule.Rd:62: Lost braces
62 | following equation: \\deqn{ \\hat{\\Omega}^{(1)}_I, \\hat{\\Omega}^{(2)}_I,
| ^
checkRd: (-1) simule.Rd:62: Lost braces; missing escapes or markup?
62 | following equation: \\deqn{ \\hat{\\Omega}^{(1)}_I, \\hat{\\Omega}^{(2)}_I,
| ^
checkRd: (-1) simule.Rd:63: Lost braces
63 | \\dots, \\hat{\\Omega}^{(K)}_I, \\hat{\\Omega}_S =
| ^
checkRd: (-1) simule.Rd:63: Lost braces; missing escapes or markup?
63 | \\dots, \\hat{\\Omega}^{(K)}_I, \\hat{\\Omega}_S =
| ^
checkRd: (-1) simule.Rd:63: Lost braces
63 | \\dots, \\hat{\\Omega}^{(K)}_I, \\hat{\\Omega}_S =
| ^
checkRd: (-1) simule.Rd:64: Lost braces
64 | \\min\\limits_{\\Omega^{(i)}_I,\\Omega_S}\\sum\\limits_i ||\\Omega^{(i)}_I||_1+
| ^
checkRd: (-1) simule.Rd:64: Lost braces; missing escapes or markup?
64 | \\min\\limits_{\\Omega^{(i)}_I,\\Omega_S}\\sum\\limits_i ||\\Omega^{(i)}_I||_1+
| ^
checkRd: (-1) simule.Rd:64: Lost braces; missing escapes or markup?
64 | \\min\\limits_{\\Omega^{(i)}_I,\\Omega_S}\\sum\\limits_i ||\\Omega^{(i)}_I||_1+
| ^
checkRd: (-1) simule.Rd:65-67: Lost braces
65 | \\epsilon K||\\Omega_S||_1 } Subject to : \\deqn{
| ^
checkRd: (-1) simule.Rd:66: Lost braces; missing escapes or markup?
66 | ||\\Sigma^{(i)}(\\Omega^{(i)}_I + \\Omega_S) - I||_{\\infty} \\le \\lambda_{n}, i
| ^
checkRd: (-1) simule.Rd:66: Lost braces; missing escapes or markup?
66 | ||\\Sigma^{(i)}(\\Omega^{(i)}_I + \\Omega_S) - I||_{\\infty} \\le \\lambda_{n}, i
| ^
checkRd: (-1) simule.Rd:66: Lost braces; missing escapes or markup?
66 | ||\\Sigma^{(i)}(\\Omega^{(i)}_I + \\Omega_S) - I||_{\\infty} \\le \\lambda_{n}, i
| ^
checkRd: (-1) simule.Rd:66: Lost braces; missing escapes or markup?
66 | ||\\Sigma^{(i)}(\\Omega^{(i)}_I + \\Omega_S) - I||_{\\infty} \\le \\lambda_{n}, i
| ^
checkRd: (-1) simule.Rd:68: Lost braces
68 | \\eqn{\\lambda_n} is the hyperparameter controlling the sparsity level of the
| ^
checkRd: (-1) simule.Rd:69: Lost braces
69 | matrices and it is the \\code{lambda} in our function. The \\eqn{\\epsilon} is
| ^
checkRd: (-1) simule.Rd:69: Lost braces
69 | matrices and it is the \\code{lambda} in our function. The \\eqn{\\epsilon} is
| ^
checkRd: (-1) simule.Rd:72: Lost braces
72 | \\code{epsilon} parameter in our function and the default value is 1. For
| ^
checkRd: (-1) simule.Rd:47: Lost braces
47 | \\item{Graphs}{A list of the estimated inverse
| ^
checkRd: (-1) simule.Rd:47-48: Lost braces
47 | \\item{Graphs}{A list of the estimated inverse
| ^
checkRd: (-1) simule.Rd:48: Lost braces
48 | covariance/correlation matrices.} \\item{share}{The share graph among
| ^
checkRd: (-1) simule.Rd:48-49: Lost braces
48 | covariance/correlation matrices.} \\item{share}{The share graph among
| ^
NOTE
r-oldrel-windows-x86_64
Rd files
checkRd: (-1) simule-package.Rd:18: Lost braces; missing escapes or markup?
18 | Identifying context-specific entity networks from aggregated data is an important task, often arising in bioinformatics and neuroimaging. Computationally, this task can be formulated as jointly estimating multiple different, but related, sparse Undirected Graphical Models (UGM) from aggregated samples across several contexts. Previous joint-UGM studies have mostly focused on sparse Gaussian Graphical Models (sGGMs) and can't identify context-specific edge patterns directly. We, therefore, propose a novel approach, SIMULE (detecting Shared and Individual parts of MULtiple graphs Explicitly) to learn multi-UGM via a constrained L1 minimization. SIMULE automatically infers both specific edge patterns that are unique to each context and shared interactions preserved among all the contexts. Through the L1 constrained formulation, this problem is cast as multiple independent subtasks of linear programming that can be solved efficiently in parallel. In addition to Gaussian data, SIMULE can also handle multivariate nonparanormal data that greatly relaxes the normality assumption that many real-world applications do not follow. We provide a novel theoretical proof showing that SIMULE achieves a consistent result at the rate O(log(Kp)/n_{tot}). On multiple synthetic datasets and two biomedical datasets, SIMULE shows significant improvement over state-of-the-art multi-sGGM and single-UGM baselines.
| ^
checkRd: (-1) simule.Rd:18: Lost braces
18 | level of the matrices. The \\eqn{\\lambda_n} in the following section:
| ^
checkRd: (-1) simule.Rd:23: Lost braces
23 | of each graph. The \\eqn{\\epsilon} in the following section: Details. If
| ^
checkRd: (-1) simule.Rd:62-65: Lost braces
62 | following equation: \\deqn{ \\hat{\\Omega}^{(1)}_I, \\hat{\\Omega}^{(2)}_I,
| ^
checkRd: (-1) simule.Rd:62: Lost braces
62 | following equation: \\deqn{ \\hat{\\Omega}^{(1)}_I, \\hat{\\Omega}^{(2)}_I,
| ^
checkRd: (-1) simule.Rd:62: Lost braces; missing escapes or markup?
62 | following equation: \\deqn{ \\hat{\\Omega}^{(1)}_I, \\hat{\\Omega}^{(2)}_I,
| ^
checkRd: (-1) simule.Rd:62: Lost braces
62 | following equation: \\deqn{ \\hat{\\Omega}^{(1)}_I, \\hat{\\Omega}^{(2)}_I,
| ^
checkRd: (-1) simule.Rd:62: Lost braces; missing escapes or markup?
62 | following equation: \\deqn{ \\hat{\\Omega}^{(1)}_I, \\hat{\\Omega}^{(2)}_I,
| ^
checkRd: (-1) simule.Rd:63: Lost braces
63 | \\dots, \\hat{\\Omega}^{(K)}_I, \\hat{\\Omega}_S =
| ^
checkRd: (-1) simule.Rd:63: Lost braces; missing escapes or markup?
63 | \\dots, \\hat{\\Omega}^{(K)}_I, \\hat{\\Omega}_S =
| ^
checkRd: (-1) simule.Rd:63: Lost braces
63 | \\dots, \\hat{\\Omega}^{(K)}_I, \\hat{\\Omega}_S =
| ^
checkRd: (-1) simule.Rd:64: Lost braces
64 | \\min\\limits_{\\Omega^{(i)}_I,\\Omega_S}\\sum\\limits_i ||\\Omega^{(i)}_I||_1+
| ^
checkRd: (-1) simule.Rd:64: Lost braces; missing escapes or markup?
64 | \\min\\limits_{\\Omega^{(i)}_I,\\Omega_S}\\sum\\limits_i ||\\Omega^{(i)}_I||_1+
| ^
checkRd: (-1) simule.Rd:64: Lost braces; missing escapes or markup?
64 | \\min\\limits_{\\Omega^{(i)}_I,\\Omega_S}\\sum\\limits_i ||\\Omega^{(i)}_I||_1+
| ^
checkRd: (-1) simule.Rd:65-67: Lost braces
65 | \\epsilon K||\\Omega_S||_1 } Subject to : \\deqn{
| ^
checkRd: (-1) simule.Rd:66: Lost braces; missing escapes or markup?
66 | ||\\Sigma^{(i)}(\\Omega^{(i)}_I + \\Omega_S) - I||_{\\infty} \\le \\lambda_{n}, i
| ^
checkRd: (-1) simule.Rd:66: Lost braces; missing escapes or markup?
66 | ||\\Sigma^{(i)}(\\Omega^{(i)}_I + \\Omega_S) - I||_{\\infty} \\le \\lambda_{n}, i
| ^
checkRd: (-1) simule.Rd:66: Lost braces; missing escapes or markup?
66 | ||\\Sigma^{(i)}(\\Omega^{(i)}_I + \\Omega_S) - I||_{\\infty} \\le \\lambda_{n}, i
| ^
checkRd: (-1) simule.Rd:66: Lost braces; missing escapes or markup?
66 | ||\\Sigma^{(i)}(\\Omega^{(i)}_I + \\Omega_S) - I||_{\\infty} \\le \\lambda_{n}, i
| ^
checkRd: (-1) simule.Rd:68: Lost braces
68 | \\eqn{\\lambda_n} is the hyperparameter controlling the sparsity level of the
| ^
checkRd: (-1) simule.Rd:69: Lost braces
69 | matrices and it is the \\code{lambda} in our function. The \\eqn{\\epsilon} is
| ^
checkRd: (-1) simule.Rd:69: Lost braces
69 | matrices and it is the \\code{lambda} in our function. The \\eqn{\\epsilon} is
| ^
checkRd: (-1) simule.Rd:72: Lost braces
72 | \\code{epsilon} parameter in our function and the default value is 1. For
| ^
checkRd: (-1) simule.Rd:47: Lost braces
47 | \\item{Graphs}{A list of the estimated inverse
| ^
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47 | \\item{Graphs}{A list of the estimated inverse
| ^
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48 | covariance/correlation matrices.} \\item{share}{The share graph among
| ^
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48 | covariance/correlation matrices.} \\item{share}{The share graph among
| ^
NOTE
r-patched-linux-x86_64
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18 | Identifying context-specific entity networks from aggregated data is an important task, often arising in bioinformatics and neuroimaging. Computationally, this task can be formulated as jointly estimating multiple different, but related, sparse Undirected Graphical Models (UGM) from aggregated samples across several contexts. Previous joint-UGM studies have mostly focused on sparse Gaussian Graphical Models (sGGMs) and can't identify context-specific edge patterns directly. We, therefore, propose a novel approach, SIMULE (detecting Shared and Individual parts of MULtiple graphs Explicitly) to learn multi-UGM via a constrained L1 minimization. SIMULE automatically infers both specific edge patterns that are unique to each context and shared interactions preserved among all the contexts. Through the L1 constrained formulation, this problem is cast as multiple independent subtasks of linear programming that can be solved efficiently in parallel. In addition to Gaussian data, SIMULE can also handle multivariate nonparanormal data that greatly relaxes the normality assumption that many real-world applications do not follow. We provide a novel theoretical proof showing that SIMULE achieves a consistent result at the rate O(log(Kp)/n_{tot}). On multiple synthetic datasets and two biomedical datasets, SIMULE shows significant improvement over state-of-the-art multi-sGGM and single-UGM baselines.
| ^
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18 | level of the matrices. The \\eqn{\\lambda_n} in the following section:
| ^
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23 | of each graph. The \\eqn{\\epsilon} in the following section: Details. If
| ^
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62 | following equation: \\deqn{ \\hat{\\Omega}^{(1)}_I, \\hat{\\Omega}^{(2)}_I,
| ^
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62 | following equation: \\deqn{ \\hat{\\Omega}^{(1)}_I, \\hat{\\Omega}^{(2)}_I,
| ^
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62 | following equation: \\deqn{ \\hat{\\Omega}^{(1)}_I, \\hat{\\Omega}^{(2)}_I,
| ^
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62 | following equation: \\deqn{ \\hat{\\Omega}^{(1)}_I, \\hat{\\Omega}^{(2)}_I,
| ^
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62 | following equation: \\deqn{ \\hat{\\Omega}^{(1)}_I, \\hat{\\Omega}^{(2)}_I,
| ^
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63 | \\dots, \\hat{\\Omega}^{(K)}_I, \\hat{\\Omega}_S =
| ^
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63 | \\dots, \\hat{\\Omega}^{(K)}_I, \\hat{\\Omega}_S =
| ^
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63 | \\dots, \\hat{\\Omega}^{(K)}_I, \\hat{\\Omega}_S =
| ^
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64 | \\min\\limits_{\\Omega^{(i)}_I,\\Omega_S}\\sum\\limits_i ||\\Omega^{(i)}_I||_1+
| ^
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64 | \\min\\limits_{\\Omega^{(i)}_I,\\Omega_S}\\sum\\limits_i ||\\Omega^{(i)}_I||_1+
| ^
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64 | \\min\\limits_{\\Omega^{(i)}_I,\\Omega_S}\\sum\\limits_i ||\\Omega^{(i)}_I||_1+
| ^
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65 | \\epsilon K||\\Omega_S||_1 } Subject to : \\deqn{
| ^
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66 | ||\\Sigma^{(i)}(\\Omega^{(i)}_I + \\Omega_S) - I||_{\\infty} \\le \\lambda_{n}, i
| ^
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66 | ||\\Sigma^{(i)}(\\Omega^{(i)}_I + \\Omega_S) - I||_{\\infty} \\le \\lambda_{n}, i
| ^
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66 | ||\\Sigma^{(i)}(\\Omega^{(i)}_I + \\Omega_S) - I||_{\\infty} \\le \\lambda_{n}, i
| ^
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66 | ||\\Sigma^{(i)}(\\Omega^{(i)}_I + \\Omega_S) - I||_{\\infty} \\le \\lambda_{n}, i
| ^
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68 | \\eqn{\\lambda_n} is the hyperparameter controlling the sparsity level of the
| ^
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69 | matrices and it is the \\code{lambda} in our function. The \\eqn{\\epsilon} is
| ^
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69 | matrices and it is the \\code{lambda} in our function. The \\eqn{\\epsilon} is
| ^
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72 | \\code{epsilon} parameter in our function and the default value is 1. For
| ^
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47 | \\item{Graphs}{A list of the estimated inverse
| ^
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47 | \\item{Graphs}{A list of the estimated inverse
| ^
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48 | covariance/correlation matrices.} \\item{share}{The share graph among
| ^
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48 | covariance/correlation matrices.} \\item{share}{The share graph among
| ^
NOTE
r-release-linux-x86_64
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checkRd: (-1) simule-package.Rd:18: Lost braces; missing escapes or markup?
18 | Identifying context-specific entity networks from aggregated data is an important task, often arising in bioinformatics and neuroimaging. Computationally, this task can be formulated as jointly estimating multiple different, but related, sparse Undirected Graphical Models (UGM) from aggregated samples across several contexts. Previous joint-UGM studies have mostly focused on sparse Gaussian Graphical Models (sGGMs) and can't identify context-specific edge patterns directly. We, therefore, propose a novel approach, SIMULE (detecting Shared and Individual parts of MULtiple graphs Explicitly) to learn multi-UGM via a constrained L1 minimization. SIMULE automatically infers both specific edge patterns that are unique to each context and shared interactions preserved among all the contexts. Through the L1 constrained formulation, this problem is cast as multiple independent subtasks of linear programming that can be solved efficiently in parallel. In addition to Gaussian data, SIMULE can also handle multivariate nonparanormal data that greatly relaxes the normality assumption that many real-world applications do not follow. We provide a novel theoretical proof showing that SIMULE achieves a consistent result at the rate O(log(Kp)/n_{tot}). On multiple synthetic datasets and two biomedical datasets, SIMULE shows significant improvement over state-of-the-art multi-sGGM and single-UGM baselines.
| ^
checkRd: (-1) simule.Rd:18: Lost braces
18 | level of the matrices. The \\eqn{\\lambda_n} in the following section:
| ^
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23 | of each graph. The \\eqn{\\epsilon} in the following section: Details. If
| ^
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62 | following equation: \\deqn{ \\hat{\\Omega}^{(1)}_I, \\hat{\\Omega}^{(2)}_I,
| ^
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62 | following equation: \\deqn{ \\hat{\\Omega}^{(1)}_I, \\hat{\\Omega}^{(2)}_I,
| ^
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62 | following equation: \\deqn{ \\hat{\\Omega}^{(1)}_I, \\hat{\\Omega}^{(2)}_I,
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62 | following equation: \\deqn{ \\hat{\\Omega}^{(1)}_I, \\hat{\\Omega}^{(2)}_I,
| ^
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62 | following equation: \\deqn{ \\hat{\\Omega}^{(1)}_I, \\hat{\\Omega}^{(2)}_I,
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63 | \\dots, \\hat{\\Omega}^{(K)}_I, \\hat{\\Omega}_S =
| ^
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63 | \\dots, \\hat{\\Omega}^{(K)}_I, \\hat{\\Omega}_S =
| ^
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63 | \\dots, \\hat{\\Omega}^{(K)}_I, \\hat{\\Omega}_S =
| ^
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64 | \\min\\limits_{\\Omega^{(i)}_I,\\Omega_S}\\sum\\limits_i ||\\Omega^{(i)}_I||_1+
| ^
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64 | \\min\\limits_{\\Omega^{(i)}_I,\\Omega_S}\\sum\\limits_i ||\\Omega^{(i)}_I||_1+
| ^
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64 | \\min\\limits_{\\Omega^{(i)}_I,\\Omega_S}\\sum\\limits_i ||\\Omega^{(i)}_I||_1+
| ^
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65 | \\epsilon K||\\Omega_S||_1 } Subject to : \\deqn{
| ^
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66 | ||\\Sigma^{(i)}(\\Omega^{(i)}_I + \\Omega_S) - I||_{\\infty} \\le \\lambda_{n}, i
| ^
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66 | ||\\Sigma^{(i)}(\\Omega^{(i)}_I + \\Omega_S) - I||_{\\infty} \\le \\lambda_{n}, i
| ^
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66 | ||\\Sigma^{(i)}(\\Omega^{(i)}_I + \\Omega_S) - I||_{\\infty} \\le \\lambda_{n}, i
| ^
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66 | ||\\Sigma^{(i)}(\\Omega^{(i)}_I + \\Omega_S) - I||_{\\infty} \\le \\lambda_{n}, i
| ^
checkRd: (-1) simule.Rd:68: Lost braces
68 | \\eqn{\\lambda_n} is the hyperparameter controlling the sparsity level of the
| ^
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69 | matrices and it is the \\code{lambda} in our function. The \\eqn{\\epsilon} is
| ^
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69 | matrices and it is the \\code{lambda} in our function. The \\eqn{\\epsilon} is
| ^
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72 | \\code{epsilon} parameter in our function and the default value is 1. For
| ^
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47 | \\item{Graphs}{A list of the estimated inverse
| ^
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47 | \\item{Graphs}{A list of the estimated inverse
| ^
checkRd: (-1) simule.Rd:48: Lost braces
48 | covariance/correlation matrices.} \\item{share}{The share graph among
| ^
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48 | covariance/correlation matrices.} \\item{share}{The share graph among
| ^
NOTE
r-release-macos-arm64
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checkRd: (-1) simule-package.Rd:18: Lost braces; missing escapes or markup?
18 | Identifying context-specific entity networks from aggregated data is an important task, often arising in bioinformatics and neuroimaging. Computationally, this task can be formulated as jointly estimating multiple different, but related, sparse Undirected Graphical Models (UGM) from aggregated samples across several contexts. Previous joint-UGM studies have mostly focused on sparse Gaussian Graphical Models (sGGMs) and can't identify context-specific edge patterns directly. We, therefore, propose a novel approach, SIMULE (detecting Shared and Individual parts of MULtiple graphs Explicitly) to learn multi-UGM via a constrained L1 minimization. SIMULE automatically infers both specific edge patterns that are unique to each context and shared interactions preserved among all the contexts. Through the L1 constrained formulation, this problem is cast as multiple independent subtasks of linear programming that can be solved efficiently in parallel. In addition to Gaussian data, SIMULE can also handle multivariate nonparanormal data that greatly relaxes the normality assumption that many real-world applications do not follow. We provide a novel theoretical proof showing that SIMULE achieves a consistent result at the rate O(log(Kp)/n_{tot}). On multiple synthetic datasets and two biomedical datasets, SIMULE shows significant improvement over state-of-the-art multi-sGGM and single-UGM baselines.
| ^
checkRd: (-1) simule.Rd:18: Lost braces
18 | level of the matrices. The \\eqn{\\lambda_n} in the following section:
| ^
checkRd: (-1) simule.Rd:23: Lost braces
23 | of each graph. The \\eqn{\\epsilon} in the following section: Details. If
| ^
checkRd: (-1) simule.Rd:62-65: Lost braces
62 | following equation: \\deqn{ \\hat{\\Omega}^{(1)}_I, \\hat{\\Omega}^{(2)}_I,
| ^
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62 | following equation: \\deqn{ \\hat{\\Omega}^{(1)}_I, \\hat{\\Omega}^{(2)}_I,
| ^
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62 | following equation: \\deqn{ \\hat{\\Omega}^{(1)}_I, \\hat{\\Omega}^{(2)}_I,
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62 | following equation: \\deqn{ \\hat{\\Omega}^{(1)}_I, \\hat{\\Omega}^{(2)}_I,
| ^
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62 | following equation: \\deqn{ \\hat{\\Omega}^{(1)}_I, \\hat{\\Omega}^{(2)}_I,
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63 | \\dots, \\hat{\\Omega}^{(K)}_I, \\hat{\\Omega}_S =
| ^
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63 | \\dots, \\hat{\\Omega}^{(K)}_I, \\hat{\\Omega}_S =
| ^
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63 | \\dots, \\hat{\\Omega}^{(K)}_I, \\hat{\\Omega}_S =
| ^
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64 | \\min\\limits_{\\Omega^{(i)}_I,\\Omega_S}\\sum\\limits_i ||\\Omega^{(i)}_I||_1+
| ^
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64 | \\min\\limits_{\\Omega^{(i)}_I,\\Omega_S}\\sum\\limits_i ||\\Omega^{(i)}_I||_1+
| ^
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64 | \\min\\limits_{\\Omega^{(i)}_I,\\Omega_S}\\sum\\limits_i ||\\Omega^{(i)}_I||_1+
| ^
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65 | \\epsilon K||\\Omega_S||_1 } Subject to : \\deqn{
| ^
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66 | ||\\Sigma^{(i)}(\\Omega^{(i)}_I + \\Omega_S) - I||_{\\infty} \\le \\lambda_{n}, i
| ^
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66 | ||\\Sigma^{(i)}(\\Omega^{(i)}_I + \\Omega_S) - I||_{\\infty} \\le \\lambda_{n}, i
| ^
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66 | ||\\Sigma^{(i)}(\\Omega^{(i)}_I + \\Omega_S) - I||_{\\infty} \\le \\lambda_{n}, i
| ^
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66 | ||\\Sigma^{(i)}(\\Omega^{(i)}_I + \\Omega_S) - I||_{\\infty} \\le \\lambda_{n}, i
| ^
checkRd: (-1) simule.Rd:68: Lost braces
68 | \\eqn{\\lambda_n} is the hyperparameter controlling the sparsity level of the
| ^
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69 | matrices and it is the \\code{lambda} in our function. The \\eqn{\\epsilon} is
| ^
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69 | matrices and it is the \\code{lambda} in our function. The \\eqn{\\epsilon} is
| ^
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72 | \\code{epsilon} parameter in our function and the default value is 1. For
| ^
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47 | \\item{Graphs}{A list of the estimated inverse
| ^
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47 | \\item{Graphs}{A list of the estimated inverse
| ^
checkRd: (-1) simule.Rd:48: Lost braces
48 | covariance/correlation matrices.} \\item{share}{The share graph among
| ^
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48 | covariance/correlation matrices.} \\item{share}{The share graph among
| ^
NOTE
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checkRd: (-1) simule-package.Rd:18: Lost braces; missing escapes or markup?
18 | Identifying context-specific entity networks from aggregated data is an important task, often arising in bioinformatics and neuroimaging. Computationally, this task can be formulated as jointly estimating multiple different, but related, sparse Undirected Graphical Models (UGM) from aggregated samples across several contexts. Previous joint-UGM studies have mostly focused on sparse Gaussian Graphical Models (sGGMs) and can't identify context-specific edge patterns directly. We, therefore, propose a novel approach, SIMULE (detecting Shared and Individual parts of MULtiple graphs Explicitly) to learn multi-UGM via a constrained L1 minimization. SIMULE automatically infers both specific edge patterns that are unique to each context and shared interactions preserved among all the contexts. Through the L1 constrained formulation, this problem is cast as multiple independent subtasks of linear programming that can be solved efficiently in parallel. In addition to Gaussian data, SIMULE can also handle multivariate nonparanormal data that greatly relaxes the normality assumption that many real-world applications do not follow. We provide a novel theoretical proof showing that SIMULE achieves a consistent result at the rate O(log(Kp)/n_{tot}). On multiple synthetic datasets and two biomedical datasets, SIMULE shows significant improvement over state-of-the-art multi-sGGM and single-UGM baselines.
| ^
checkRd: (-1) simule.Rd:18: Lost braces
18 | level of the matrices. The \\eqn{\\lambda_n} in the following section:
| ^
checkRd: (-1) simule.Rd:23: Lost braces
23 | of each graph. The \\eqn{\\epsilon} in the following section: Details. If
| ^
checkRd: (-1) simule.Rd:62-65: Lost braces
62 | following equation: \\deqn{ \\hat{\\Omega}^{(1)}_I, \\hat{\\Omega}^{(2)}_I,
| ^
checkRd: (-1) simule.Rd:62: Lost braces
62 | following equation: \\deqn{ \\hat{\\Omega}^{(1)}_I, \\hat{\\Omega}^{(2)}_I,
| ^
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62 | following equation: \\deqn{ \\hat{\\Omega}^{(1)}_I, \\hat{\\Omega}^{(2)}_I,
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62 | following equation: \\deqn{ \\hat{\\Omega}^{(1)}_I, \\hat{\\Omega}^{(2)}_I,
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checkRd: (-1) simule.Rd:62: Lost braces; missing escapes or markup?
62 | following equation: \\deqn{ \\hat{\\Omega}^{(1)}_I, \\hat{\\Omega}^{(2)}_I,
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63 | \\dots, \\hat{\\Omega}^{(K)}_I, \\hat{\\Omega}_S =
| ^
checkRd: (-1) simule.Rd:63: Lost braces; missing escapes or markup?
63 | \\dots, \\hat{\\Omega}^{(K)}_I, \\hat{\\Omega}_S =
| ^
checkRd: (-1) simule.Rd:63: Lost braces
63 | \\dots, \\hat{\\Omega}^{(K)}_I, \\hat{\\Omega}_S =
| ^
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64 | \\min\\limits_{\\Omega^{(i)}_I,\\Omega_S}\\sum\\limits_i ||\\Omega^{(i)}_I||_1+
| ^
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64 | \\min\\limits_{\\Omega^{(i)}_I,\\Omega_S}\\sum\\limits_i ||\\Omega^{(i)}_I||_1+
| ^
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64 | \\min\\limits_{\\Omega^{(i)}_I,\\Omega_S}\\sum\\limits_i ||\\Omega^{(i)}_I||_1+
| ^
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65 | \\epsilon K||\\Omega_S||_1 } Subject to : \\deqn{
| ^
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66 | ||\\Sigma^{(i)}(\\Omega^{(i)}_I + \\Omega_S) - I||_{\\infty} \\le \\lambda_{n}, i
| ^
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66 | ||\\Sigma^{(i)}(\\Omega^{(i)}_I + \\Omega_S) - I||_{\\infty} \\le \\lambda_{n}, i
| ^
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66 | ||\\Sigma^{(i)}(\\Omega^{(i)}_I + \\Omega_S) - I||_{\\infty} \\le \\lambda_{n}, i
| ^
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66 | ||\\Sigma^{(i)}(\\Omega^{(i)}_I + \\Omega_S) - I||_{\\infty} \\le \\lambda_{n}, i
| ^
checkRd: (-1) simule.Rd:68: Lost braces
68 | \\eqn{\\lambda_n} is the hyperparameter controlling the sparsity level of the
| ^
checkRd: (-1) simule.Rd:69: Lost braces
69 | matrices and it is the \\code{lambda} in our function. The \\eqn{\\epsilon} is
| ^
checkRd: (-1) simule.Rd:69: Lost braces
69 | matrices and it is the \\code{lambda} in our function. The \\eqn{\\epsilon} is
| ^
checkRd: (-1) simule.Rd:72: Lost braces
72 | \\code{epsilon} parameter in our function and the default value is 1. For
| ^
checkRd: (-1) simule.Rd:47: Lost braces
47 | \\item{Graphs}{A list of the estimated inverse
| ^
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47 | \\item{Graphs}{A list of the estimated inverse
| ^
checkRd: (-1) simule.Rd:48: Lost braces
48 | covariance/correlation matrices.} \\item{share}{The share graph among
| ^
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48 | covariance/correlation matrices.} \\item{share}{The share graph among
| ^
NOTE
r-release-windows-x86_64
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checkRd: (-1) simule-package.Rd:18: Lost braces; missing escapes or markup?
18 | Identifying context-specific entity networks from aggregated data is an important task, often arising in bioinformatics and neuroimaging. Computationally, this task can be formulated as jointly estimating multiple different, but related, sparse Undirected Graphical Models (UGM) from aggregated samples across several contexts. Previous joint-UGM studies have mostly focused on sparse Gaussian Graphical Models (sGGMs) and can't identify context-specific edge patterns directly. We, therefore, propose a novel approach, SIMULE (detecting Shared and Individual parts of MULtiple graphs Explicitly) to learn multi-UGM via a constrained L1 minimization. SIMULE automatically infers both specific edge patterns that are unique to each context and shared interactions preserved among all the contexts. Through the L1 constrained formulation, this problem is cast as multiple independent subtasks of linear programming that can be solved efficiently in parallel. In addition to Gaussian data, SIMULE can also handle multivariate nonparanormal data that greatly relaxes the normality assumption that many real-world applications do not follow. We provide a novel theoretical proof showing that SIMULE achieves a consistent result at the rate O(log(Kp)/n_{tot}). On multiple synthetic datasets and two biomedical datasets, SIMULE shows significant improvement over state-of-the-art multi-sGGM and single-UGM baselines.
| ^
checkRd: (-1) simule.Rd:18: Lost braces
18 | level of the matrices. The \\eqn{\\lambda_n} in the following section:
| ^
checkRd: (-1) simule.Rd:23: Lost braces
23 | of each graph. The \\eqn{\\epsilon} in the following section: Details. If
| ^
checkRd: (-1) simule.Rd:62-65: Lost braces
62 | following equation: \\deqn{ \\hat{\\Omega}^{(1)}_I, \\hat{\\Omega}^{(2)}_I,
| ^
checkRd: (-1) simule.Rd:62: Lost braces
62 | following equation: \\deqn{ \\hat{\\Omega}^{(1)}_I, \\hat{\\Omega}^{(2)}_I,
| ^
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62 | following equation: \\deqn{ \\hat{\\Omega}^{(1)}_I, \\hat{\\Omega}^{(2)}_I,
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62 | following equation: \\deqn{ \\hat{\\Omega}^{(1)}_I, \\hat{\\Omega}^{(2)}_I,
| ^
checkRd: (-1) simule.Rd:62: Lost braces; missing escapes or markup?
62 | following equation: \\deqn{ \\hat{\\Omega}^{(1)}_I, \\hat{\\Omega}^{(2)}_I,
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63 | \\dots, \\hat{\\Omega}^{(K)}_I, \\hat{\\Omega}_S =
| ^
checkRd: (-1) simule.Rd:63: Lost braces; missing escapes or markup?
63 | \\dots, \\hat{\\Omega}^{(K)}_I, \\hat{\\Omega}_S =
| ^
checkRd: (-1) simule.Rd:63: Lost braces
63 | \\dots, \\hat{\\Omega}^{(K)}_I, \\hat{\\Omega}_S =
| ^
checkRd: (-1) simule.Rd:64: Lost braces
64 | \\min\\limits_{\\Omega^{(i)}_I,\\Omega_S}\\sum\\limits_i ||\\Omega^{(i)}_I||_1+
| ^
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64 | \\min\\limits_{\\Omega^{(i)}_I,\\Omega_S}\\sum\\limits_i ||\\Omega^{(i)}_I||_1+
| ^
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64 | \\min\\limits_{\\Omega^{(i)}_I,\\Omega_S}\\sum\\limits_i ||\\Omega^{(i)}_I||_1+
| ^
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65 | \\epsilon K||\\Omega_S||_1 } Subject to : \\deqn{
| ^
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66 | ||\\Sigma^{(i)}(\\Omega^{(i)}_I + \\Omega_S) - I||_{\\infty} \\le \\lambda_{n}, i
| ^
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66 | ||\\Sigma^{(i)}(\\Omega^{(i)}_I + \\Omega_S) - I||_{\\infty} \\le \\lambda_{n}, i
| ^
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66 | ||\\Sigma^{(i)}(\\Omega^{(i)}_I + \\Omega_S) - I||_{\\infty} \\le \\lambda_{n}, i
| ^
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66 | ||\\Sigma^{(i)}(\\Omega^{(i)}_I + \\Omega_S) - I||_{\\infty} \\le \\lambda_{n}, i
| ^
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68 | \\eqn{\\lambda_n} is the hyperparameter controlling the sparsity level of the
| ^
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69 | matrices and it is the \\code{lambda} in our function. The \\eqn{\\epsilon} is
| ^
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69 | matrices and it is the \\code{lambda} in our function. The \\eqn{\\epsilon} is
| ^
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72 | \\code{epsilon} parameter in our function and the default value is 1. For
| ^
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47 | \\item{Graphs}{A list of the estimated inverse
| ^
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47 | \\item{Graphs}{A list of the estimated inverse
| ^
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48 | covariance/correlation matrices.} \\item{share}{The share graph among
| ^
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48 | covariance/correlation matrices.} \\item{share}{The share graph among
| ^
Check History
NOTE 0 OK · 14 NOTE · 0 WARNING · 0 ERROR · 0 FAILURE Mar 9, 2026
NOTE
r-devel-linux-x86_64-debian-clang
CRAN incoming feasibility
Maintainer: ‘Beilun Wang <bw4mw@virginia.edu>’ The BugReports field in DESCRIPTION has https://github.com/QData/SIMULE which should likely be https://github.com/QData/SIMULE/issues instead.
NOTE
r-devel-linux-x86_64-debian-gcc
CRAN incoming feasibility
Maintainer: ‘Beilun Wang <bw4mw@virginia.edu>’ The BugReports field in DESCRIPTION has https://github.com/QData/SIMULE which should likely be https://github.com/QData/SIMULE/issues instead.
NOTE
r-devel-linux-x86_64-fedora-clang
Rd files
checkRd: (-1) simule-package.Rd:18: Lost braces; missing escapes or markup?
18 | Identifying context-specific entity networks from aggregated data is an important task, often arising in bioinformatics and neuroimaging. Computationally, this task can be formulated as jointly estimating multiple different, but related, sparse Undirected Graphical Models (UGM) from aggregated samples across several contexts. Previous joint-UGM studies have mostly focused on sparse Gaussian Graphical Models (sGG
NOTE
r-devel-linux-x86_64-fedora-gcc
Rd files
checkRd: (-1) simule-package.Rd:18: Lost braces; missing escapes or markup?
18 | Identifying context-specific entity networks from aggregated data is an important task, often arising in bioinformatics and neuroimaging. Computationally, this task can be formulated as jointly estimating multiple different, but related, sparse Undirected Graphical Models (UGM) from aggregated samples across several contexts. Previous joint-UGM studies have mostly focused on sparse Gaussian Graphical Models (sGG
NOTE
r-devel-macos-arm64
Rd files
checkRd: (-1) simule-package.Rd:18: Lost braces; missing escapes or markup?
18 | Identifying context-specific entity networks from aggregated data is an important task, often arising in bioinformatics and neuroimaging. Computationally, this task can be formulated as jointly estimating multiple different, but related, sparse Undirected Graphical Models (UGM) from aggregated samples across several contexts. Previous joint-UGM studies have mostly focused on sparse Gaussian Graphical Models (sGG
NOTE
r-devel-windows-x86_64
Rd files
checkRd: (-1) simule-package.Rd:18: Lost braces; missing escapes or markup?
18 | Identifying context-specific entity networks from aggregated data is an important task, often arising in bioinformatics and neuroimaging. Computationally, this task can be formulated as jointly estimating multiple different, but related, sparse Undirected Graphical Models (UGM) from aggregated samples across several contexts. Previous joint-UGM studies have mostly focused on sparse Gaussian Graphical Models (sGG
NOTE
r-patched-linux-x86_64
Rd files
checkRd: (-1) simule-package.Rd:18: Lost braces; missing escapes or markup?
18 | Identifying context-specific entity networks from aggregated data is an important task, often arising in bioinformatics and neuroimaging. Computationally, this task can be formulated as jointly estimating multiple different, but related, sparse Undirected Graphical Models (UGM) from aggregated samples across several contexts. Previous joint-UGM studies have mostly focused on sparse Gaussian Graphical Models (sGG
NOTE
r-release-linux-x86_64
Rd files
checkRd: (-1) simule-package.Rd:18: Lost braces; missing escapes or markup?
18 | Identifying context-specific entity networks from aggregated data is an important task, often arising in bioinformatics and neuroimaging. Computationally, this task can be formulated as jointly estimating multiple different, but related, sparse Undirected Graphical Models (UGM) from aggregated samples across several contexts. Previous joint-UGM studies have mostly focused on sparse Gaussian Graphical Models (sGG
NOTE
r-release-macos-arm64
Rd files
checkRd: (-1) simule-package.Rd:18: Lost braces; missing escapes or markup?
18 | Identifying context-specific entity networks from aggregated data is an important task, often arising in bioinformatics and neuroimaging. Computationally, this task can be formulated as jointly estimating multiple different, but related, sparse Undirected Graphical Models (UGM) from aggregated samples across several contexts. Previous joint-UGM studies have mostly focused on sparse Gaussian Graphical Models (sGG
NOTE
r-release-macos-x86_64
Rd files
checkRd: (-1) simule-package.Rd:18: Lost braces; missing escapes or markup?
18 | Identifying context-specific entity networks from aggregated data is an important task, often arising in bioinformatics and neuroimaging. Computationally, this task can be formulated as jointly estimating multiple different, but related, sparse Undirected Graphical Models (UGM) from aggregated samples across several contexts. Previous joint-UGM studies have mostly focused on sparse Gaussian Graphical Models (sGG
NOTE
r-release-windows-x86_64
Rd files
checkRd: (-1) simule-package.Rd:18: Lost braces; missing escapes or markup?
18 | Identifying context-specific entity networks from aggregated data is an important task, often arising in bioinformatics and neuroimaging. Computationally, this task can be formulated as jointly estimating multiple different, but related, sparse Undirected Graphical Models (UGM) from aggregated samples across several contexts. Previous joint-UGM studies have mostly focused on sparse Gaussian Graphical Models (sGG
NOTE
r-oldrel-macos-arm64
Rd files
checkRd: (-1) simule-package.Rd:18: Lost braces; missing escapes or markup?
18 | Identifying context-specific entity networks from aggregated data is an important task, often arising in bioinformatics and neuroimaging. Computationally, this task can be formulated as jointly estimating multiple different, but related, sparse Undirected Graphical Models (UGM) from aggregated samples across several contexts. Previous joint-UGM studies have mostly focused on sparse Gaussian Graphical Models (sGG
NOTE
r-oldrel-macos-x86_64
Rd files
checkRd: (-1) simule-package.Rd:18: Lost braces; missing escapes or markup?
18 | Identifying context-specific entity networks from aggregated data is an important task, often arising in bioinformatics and neuroimaging. Computationally, this task can be formulated as jointly estimating multiple different, but related, sparse Undirected Graphical Models (UGM) from aggregated samples across several contexts. Previous joint-UGM studies have mostly focused on sparse Gaussian Graphical Models (sGG
NOTE
r-oldrel-windows-x86_64
Rd files
checkRd: (-1) simule-package.Rd:18: Lost braces; missing escapes or markup?
18 | Identifying context-specific entity networks from aggregated data is an important task, often arising in bioinformatics and neuroimaging. Computationally, this task can be formulated as jointly estimating multiple different, but related, sparse Undirected Graphical Models (UGM) from aggregated samples across several contexts. Previous joint-UGM studies have mostly focused on sparse Gaussian Graphical Models (sGG
Dependency Network
Version History
new
1.3.0
Mar 9, 2026