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.
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checkRd: (-1) simule.Rd:18: Lost braces
    18 | level of the matrices. The \\eqn{\\lambda_n} in the following section:
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checkRd: (-1) simule.Rd:23: Lost braces
    23 | of each graph. The \\eqn{\\epsilon} in the following section: Details. If
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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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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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    68 | \\eqn{\\lambda_n} is the hyperparameter controlling the sparsity level of the
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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
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    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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