Variational Inference for sparse network reconstruction from count data
Variational Inference for sparse network reconstruction from count data
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发表时间：
2018-06
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通讯作者：
J. Chiquet;S. Robin;M. Mariadassou
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作者：
J. Chiquet;S. Robin;M. Mariadassou
在多元统计中，寻找直接交互的问题可以被表述为网络推理或网络重建的问题，高斯图形模型（GGM）为其提供了一个规范框架。不幸的是，高斯假设并不适用于在基因组学、社会科学或生态学等领域遇到的计数数据。为了规避这一限制，最先进的方法使用两步策略，首先将计数转换为伪高斯观测值，然后从大量的GGM推断文献中应用（部分）基于相关性的方法。我们采用了一种不同的立场，依靠潜在模型，我们直接通过泊松分布对潜在（隐藏）高斯相关变量有条件的泊松分布对计数进行建模。在多元泊松对数正态模型中，依赖结构完全由潜在层捕获。这个参数模型能够解释协变量对计数的影响。为了进行网络推理，我们在潜在高斯向量的逆协方差矩阵上添加了稀疏性诱导约束。与通常的高斯设置不同，惩罚似然通常是不可处理的，我们转而采用变分方法来实现近似似然最大化。通过对变分参数进行梯度上升和对协方差矩阵进行图形lasso步进交替求解相应的优化问题。我们表明，我们的方法与现有的微生物数据启发的模拟方法具有很强的竞争力。然后，我们在三个不同的数据集上说明了如何通过偏移量和整合外部协变量来计算采样努力（这在现有文献中几乎从未做过），从而极大地改变了推断网络的拓扑结构。
In multivariate statistics, the question of finding direct interactions can be formulated as a problem of network inference - or network reconstruction - for which the Gaussian graphical model (GGM) provides a canonical framework. Unfortunately, the Gaussian assumption does not apply to count data which are encountered in domains such as genomics, social sciences or ecology. To circumvent this limitation, state-of-the-art approaches use two-step strategies that first transform counts to pseudo Gaussian observations and then apply a (partial) correlation-based approach from the abundant literature of GGM inference. We adopt a different stance by relying on a latent model where we directly model counts by means of Poisson distributions that are conditional to latent (hidden) Gaussian correlated variables. In this multivariate Poisson lognormal-model, the dependency structure is completely captured by the latent layer. This parametric model enables to account for the effects of covariates on the counts. To perform network inference, we add a sparsity inducing constraint on the inverse covariance matrix of the latent Gaussian vector. Unlike the usual Gaussian setting, the penalized likelihood is generally not tractable, and we resort instead to a variational approach for approximate likelihood maximization. The corresponding optimization problem is solved by alternating a gradient ascent on the variational parameters and a graphical-Lasso step on the covariance matrix. We show that our approach is highly competitive with the existing methods on simulation inspired from microbiological data. We then illustrate on three various data sets how accounting for sampling efforts via offsets and integrating external covariates (which is mostly never done in the existing literature) drastically changes the topology of the inferred network.