A probabilistic approach to explore human miRNA targetome by integrating miRNA-overexpression data and sequence information
通过整合 miRNA 表达数据和序列信息探索人类 miRNA 靶标组的概率方法

Associate Editor: Ivo Hofacker
副主编：Ivo Hofacker

Received on July 18, 2013; revised on October 6, 2013; accepted on October 15, 2013
2013年7月18日收到；2013年10月6日修订；2013年10月15日接受

MicroRNAs (miRNAs) repress protein production in animal species by forming Watson-Crick base pairing to the 3’-untranslated regions of the target messenger RNAs (mRNAs) (Friedman et al., 2009). The binding primarily occurs at the $2-7\mathrm{nt}$$2-7\mathrm{nt}$2-7nt2-7 \mathrm{nt} positions from the $5^{\prime }$$5^{\prime }$5^(')5^{\prime} end of the miRNA, which is termed as the ‘seed’ and the binding as the ‘seed match’ (Lewis et al., 2003). MiRNA regulations have been implicated in numerous developmental and pathogenic processes (Bartel, 2009). Functional characterization of miRNAs depends on precise identification of their targets. However, it has proved difficult to experimentally identify miRNA-mRNA interactions.
微小RNA（miRNA）通过与目标信使RNA（mRNA）的3'-非翻译区形成Watson-Crick碱基配对，抑制动物体内蛋白质的产生（Friedman等人，2009年）。这种结合主要发生在 miRNA 的 $5^{\prime }$$5^{\prime }$5^(')5^{\prime} 端 $2-7\mathrm{nt}$$2-7\mathrm{nt}$2-7nt2-7 \mathrm{nt} 位置，称为 "种子"，而这种结合称为 "种子配对"（Lewis 等，2003 年）。miRNA 的调控与许多发育和致病过程有关（Bartel，2009 年）。miRNA 的功能表征取决于对其靶标的精确鉴定。然而，实验证明很难确定 miRNA 与 mRNA 之间的相互作用。

To date, according to mirTarBase, only 3565 interactions between 432 miRNAs and 1959 target genes in human have
迄今为止，根据 mirTarBase，人类 432 个 miRNA 与 1959 个靶基因之间只有 3565 次相互作用

been confirmed using high-confidence low-throughput assays such as Western blot (Hsu et al., 2011). On the other hand, computational prediction provides a rapid alternative method to identify putative miRNA targets that can be subsequently validated. However, accurate prediction of miRNA targets remains a challenge with the current state-of-the-art algorithms achieving $<50\mathrm{\%}$$<50\mathrm{\%}$< 50%<50 \% specificity and having poor agreement among them (Alexiou et al., 2009). Most of these prediction programs are based on sequence complementarity, evolutionary conservation (Friedman et al., 2009; Lewis et al., 2003), free energy (Enright et al., 2004; Krek et al., 2005; Lewis et al., 2003) and/ or target site accessibility (Kertesz et al., 2007). Although it is shown that evolutionary conservation can improve signal-to-noise ratios, the conservation approach is limited, as not all of the functional target sites are conserved (e.g. lineage- and species-specific target sites) and vice versa. In particular, the performance of conservation-based methods drops drastically when restricted to only mammalian genomes because of short evolutionary time (Friedman et al., 2009). Similarly, the energy- or accessibility-based methods rely on secondary structure prediction tools such as RNAfold (Lorenz et al., 2011), which itself has room for improvements. These limitations also underscore the historical lack of genome-wide functional data that measure the in vivo impact of miRNA regulation, which was alleviated by the recent developments of transcriptomic and proteomic profiling methods (Baek et al., 2008; Lim et al., 2005; Selbach et al., 2008).
通过高置信度的低通量检测方法，如 Western 印迹法（Hsu et al.）另一方面，计算预测为确定推定的 miRNA 靶点提供了一种快速的替代方法，这些靶点可随后进行验证。然而，精确预测 miRNA 靶标仍然是一个挑战，目前最先进的算法都能达到 $<50\mathrm{\%}$$<50\mathrm{\%}$< 50%<50 \% 特异性，但它们之间的一致性很差（Alexiou 等，2009 年）。这些预测程序大多基于序列互补性、进化保护（Friedman 等人，2009 年；Lewis 等人，2003 年）、自由能（Enright 等人，2004 年；Krek 等人，2005 年；Lewis 等人，2003 年）和/或靶位点可及性（Kertesz 等人，2007 年）。尽管研究表明进化保护能提高信噪比，但保护方法也有局限性，因为并非所有功能性靶位点（如品系和物种特异性靶位点）都得到保护，反之亦然。特别是，由于进化时间较短，当局限于哺乳动物基因组时，基于保守性的方法性能急剧下降（Friedman 等，2009 年）。同样，基于能量或可及性的方法依赖于二级结构预测工具，如 RNAfold（Lorenz 等人，2011 年），而该工具本身还有改进的余地。这些局限性也凸显了过去缺乏测量 miRNA 调控对体内影响的全基因组功能数据，而最近转录组和蛋白质组分析方法的发展缓解了这一问题（Baek 等人，2008 年；Lim 等人，2005 年；Selbach 等人，2008 年）。

Particularly, overexpression of miRNA coupled with expression profiling of mRNA by either microarray or RNA-seq has proved to be a promising approach (Arvey et al., 2010; Lim et al., 2005). Consequently, genome-wide comparison of differential gene expression holds a new promise to elucidate the global impact of a specific miRNA regulation without solely relying on evolutionary conservation. To improve the prediction of relative repression of mRNA, several studies have proposed a series of additional determinants including seed match type (6mer seed, 7 mer-tA1, 7 mer-m8 and 8mer), number of target sites, site relative location on the $3^{\prime }$$3^{\prime }$3^(')3^{\prime}-untranslated region, local AU content, 3 '-supplementary paring, seed-pairing stability and target-site abundance (Arvey et al., 2010; Garcia et al., 2011; Grimson et al., 2007), which are combined together in a single value termed as the ‘context score’ made available from targetScan Web site (Garcia et al., 2011). Accordingly, we hypothesize that target prediction can be improved by integrating expression change and sequence information such as context score and
特别是，miRNA 的过表达与微阵列或 RNA-seq 的 mRNA 表达谱分析相结合，已被证明是一种很有前景的方法（Arvey 等人，2010 年；Lim 等人，2005 年）。因此，全基因组的差异基因表达比较为阐明特定 miRNA 调控的全球影响带来了新的希望，而无需完全依赖进化保护。为了改进对 mRNA 相对抑制的预测，一些研究提出了一系列额外的决定因素，包括种子匹配类型（6mer seed、7 mer-tA1、7 mer-m8 和 8mer）、靶位点数量、位点在 $3^{\prime }$$3^{\prime }$3^(')3^{\prime} 非翻译区的相对位置、局部 AU 含量、3'-补充配对、种子配对稳定性和靶位点丰度（Arvey et al、2010；Garcia 等人，2011；Grimson 等人，2007），它们被合并为一个单一值，称为 "上下文得分"，可从 targetScan 网站获取（Garcia 等人，2011）。因此，我们假设，通过整合表达变化和序列信息（如上下文得分和 "目标预测"），可以改进目标预测。
other orthogonal sequence-based features such as conservation (Friedman et al., 2009) into a probabilistic score.
其他基于序列的正交特征（如保持性）（Friedman 等人，2009 年）转化为概率得分。

The proposed model differs from most of the previous expres-sion-based target prediction methods in three important aspects. First, our model is specifically designed for miRNAoverexpression experiments to interrogate targets of a particular miRNA in a specific cell condition. To our knowledge, only a few methods are suitable for such task (Liu et al., 2010a). Most existing methods such as GenMiR++ (Huang et al., 2007) and GroupMiR (Le and Bar-Joseph, 2011) are based on global miRNA-target expression correlation, which requires a large set of expression profiles of both mRNA and miRNA measured across various distinct conditions and may miss targets that are specific to only a subset of the input samples. Second, the proposed model is unsupervised such that it infers miRNA-targets solely based on their distinct high-dimensional patterns of expression fold-changes and sequence features. However, the existing methods are mostly regression-based frameworks by treating gene expression as response and miRNA expression as input variables (Huang et al., 2007; Le and Bar-Joseph, 2011) or supervised learning by explicitly operating on a training dataset of confidence positive and negative targets (Liu et al., 2010b; Sumazin et al., 2011), which are incomplete and difficult to obtain. Third, our method operates on the entire gene set to more closely model the overall likelihood rather than only on a subset of genes prefiltered by targetScan score (Huang et al., 2007) or sample variance (Le and Bar-Joseph, 2011).
所提出的模型在三个重要方面有别于以往大多数基于表达的靶标预测方法。首先，我们的模型是专门为 miRNA 表达实验设计的，目的是检测特定细胞条件下特定 miRNA 的靶标。据我们所知，只有少数方法适用于此类任务（Liu 等，2010a）。现有的大多数方法，如 GenMiR++（Huang 等人，2007 年）和 GroupMiR（Le 和 Bar-Joseph，2011 年），都是基于全局 miRNA-靶点表达相关性的，这需要在各种不同条件下测量大量 mRNA 和 miRNA 的表达谱，可能会漏掉只对输入样本的一部分具有特异性的靶点。其次，所提出的模型是无监督的，它仅根据表达折叠变化和序列特征的不同高维模式来推断 miRNA 目标。然而，现有的方法大多是基于回归的框架，将基因表达作为响应变量，miRNA 表达作为输入变量（Huang 等人，2007 年；Le 和 Bar-Joseph，2011 年），或者是监督学习，明确地在置信阳性和阴性目标的训练数据集上操作（Liu 等人，2010 年 b；Sumazin 等人，2011 年），而这些数据集是不完整的，也很难获得。第三，我们的方法对整个基因集进行操作，从而更接近于对整体可能性建模，而不是只对通过 targetScan 分数（Huang 等人，2007 年）或样本方差（Le 和 Bar-Joseph，2011 年）预过滤的基因子集进行操作。

We describe a novel probabilistic method for miRNA target prediction problem by integrating miRNA-overexpression data and sequence-based scores from other prediction methods. Briefly, each score feature is considered an independent observed variable as input to a variational Bayesian-Gaussian mixture model (VB-GMM). We chose a Bayesian over a maximum likelihood approach to avoid overfitting. Specifically, given expression fold-change (due to miRNA transfection), we use a three-component VB-GMM to infer downregulated targets accounting for genes with little or positive fold-change [due to off-target effects (Khan et al., 2009)]. Otherwise, two-component VB-GMM is applied to unsigned sequence scores. The parameters for the VB-GMM are optimized using variational Bayesian expectation maximization algorithm. The mixture component with the largest absolute means of observed negative fold-change or sequence score is associated with miRNA targets and denoted as ‘target component’. The other components correspond to the ‘background component’. It follows that inferring miRNA-mRNA interactions is equivalent to inferring the posterior distribution of the target component given the observed variables. The targetScore is computed as the sigmoid-transformed fold-change weighted by the averaged posteriors of target components over all of the features (3).
我们介绍了一种新的概率方法，该方法通过整合 miRNA 表达数据和其他预测方法中基于序列的分数来解决 miRNA 目标预测问题。简而言之，每个得分特征都被视为一个独立的观察变量，作为变异贝叶斯-高斯混合模型（VB-GMM）的输入。我们选择贝叶斯方法而不是最大似然方法，以避免过度拟合。具体来说，在给定表达折叠变化（由于 miRNA 转染）的情况下，我们使用一个三分量 VB-GMM 来推断下调靶标，其中包括折叠变化很小或为正的基因（由于脱靶效应（Khan 等人，2009 年））。否则，两分量 VB-GMM 将应用于无符号序列得分。VB-GMM 的参数采用变异贝叶斯期望最大化算法进行优化。观测到的负折叠变化或序列得分绝对均值最大的混合物成分与 miRNA 靶标相关，称为 "靶标成分"。其他成分对应于 "背景成分"。由此可见，推断 miRNA 与 mRNA 之间的相互作用等同于推断目标成分在观测到的变量中的后验分布。targetScore 是根据所有特征的目标成分的平均后验分布加权计算出来的 sigmoid 变形折叠变化（3）。

Assuming there are $N$$N$NN genes, we denote $\mathbf{x}={(x_1,\dots ,x_N)}^T$$\mathbf{x}={\left(x_1,\dots ,x_N\right)}^T$x=(x_(1),dots,x_(N))^(T)\mathbf{x}=\left(x_{1}, \ldots, x_{N}\right)^{T} as the $\log$$\log$log\log expression fold-change $\left({\mathbf{x}}_f\right)$$\left({\mathbf{x}}_f\right)$(x_(f))\left(\mathbf{x}_{f}\right) or sequence scores $\left({\mathbf{x}}_l\right)$$\left({\mathbf{x}}_l\right)$(x_(l))\left(\mathbf{x}_{l}\right). Thus, for $L$$L$LL sets of sequence scores, $\mathbf{x}\in \{{\mathbf{x}}_f,{\mathbf{x}}_1,\dots ,{\mathbf{x}}_L\}$$\mathbf{x}\in \left\{{\mathbf{x}}_f,{\mathbf{x}}_1,\dots ,{\mathbf{x}}_L\right\}$xin{x_(f),x_(1),dots,x_(L)}\mathbf{x} \in\left\{\mathbf{x}_{f}, \mathbf{x}_{1}, \ldots, \mathbf{x}_{L}\right\}. To simplify the following equations, we use $\mathbf{x}$$\mathbf{x}$x\mathbf{x} to represent one of the independent variables without loss of generality. To infer target genes for a miRNA given $\mathbf{x}$$\mathbf{x}$x\mathbf{x}, we need to obtain the posterior distribution $p(\mathbf{z}\mid \mathbf{x})$$p(\mathbf{z}\mid \mathbf{x})$p(z∣x)p(\mathbf{z} \mid \mathbf{x}) of the latent variable $\mathbf{z}\in \{z_1,\dots ,z_K\}$$\mathbf{z}\in \left\{z_1,\dots ,z_K\right\}$zin{z_(1),dots,z_(K)}\mathbf{z} \in\left\{z_{1}, \ldots, z_{K}\right\}, where $K=3(K=2)$$K=3(K=2)$K=3(K=2)K=3(K=2) for modeling signed (unsigned) scores such as logarithmic fold-changes (sequence scores).
假设有 $N$$N$NN 个基因，我们将 $\mathbf{x}={(x_1,\dots ,x_N)}^T$$\mathbf{x}={\left(x_1,\dots ,x_N\right)}^T$x=(x_(1),dots,x_(N))^(T)\mathbf{x}=\left(x_{1}, \ldots, x_{N}\right)^{T} 表示为 $\log$$\log$log\log 表达折叠变化 $\left({\mathbf{x}}_f\right)$$\left({\mathbf{x}}_f\right)$(x_(f))\left(\mathbf{x}_{f}\right) 或序列得分 $\left({\mathbf{x}}_l\right)$$\left({\mathbf{x}}_l\right)$(x_(l))\left(\mathbf{x}_{l}\right) 。因此，对于 $L$$L$LL 组序列得分， $\mathbf{x}\in \{{\mathbf{x}}_f,{\mathbf{x}}_1,\dots ,{\mathbf{x}}_L\}$$\mathbf{x}\in \left\{{\mathbf{x}}_f,{\mathbf{x}}_1,\dots ,{\mathbf{x}}_L\right\}$xin{x_(f),x_(1),dots,x_(L)}\mathbf{x} \in\left\{\mathbf{x}_{f}, \mathbf{x}_{1}, \ldots, \mathbf{x}_{L}\right\} 。为了简化下面的等式，我们使用 $\mathbf{x}$$\mathbf{x}$x\mathbf{x} 代表其中一个自变量，但不失一般性。要推断给定 $\mathbf{x}$$\mathbf{x}$x\mathbf{x} 的 miRNA 的靶基因，我们需要得到潜变量 $\mathbf{z}\in \{z_1,\dots ,z_K\}$$\mathbf{z}\in \left\{z_1,\dots ,z_K\right\}$zin{z_(1),dots,z_(K)}\mathbf{z} \in\left\{z_{1}, \ldots, z_{K}\right\} 的后验分布 $p(\mathbf{z}\mid \mathbf{x})$$p(\mathbf{z}\mid \mathbf{x})$p(z∣x)p(\mathbf{z} \mid \mathbf{x}) ，其中 $K=3(K=2)$$K=3(K=2)$K=3(K=2)K=3(K=2) 用于建模有符号（无符号）分数，如对数折叠变化（序列分数）。

We follow the standard Bayesian GMM based on Bishop (2006, pp. $474-482$$474-482$474-482474-482 ) with only minor modifications. Although univariate GMM ( $D=1$$D=1$D=1D=1 ) is applied to each variable separately, we implemented and describe the following formalism as a more general multivariate GMM, allowing modeling the covariance matrices. Briefly, the latent variables $\mathbf{z}$$\mathbf{z}$z\mathbf{z} are sampled at probabilities $\pi$$\pi$pi\pi (mixing coefficient), that follow a Dirichlet prior $\mathrm{Dir}(\pi \mid {\alpha }_0)$$\mathrm{Dir}\left(\pi \mid {\alpha }_0\right)$Dir(pi∣alpha_(0))\operatorname{Dir}\left(\pi \mid \alpha_{0}\right) with hyperparameters ${\alpha }_0=({\alpha }_{0,1},\dots ,{\alpha }_{0,K})$${\alpha }_0=\left({\alpha }_{0,1},\dots ,{\alpha }_{0,K}\right)$alpha_(0)=(alpha_(0,1),dots,alpha_(0,K))\alpha_{0}=\left(\alpha_{0,1}, \ldots, \alpha_{0, K}\right). To account for the relative frequency of targets and non-targets for any miRNA, we set the ${\alpha }_{0,1}$${\alpha }_{0,1}$alpha_(0,1)\alpha_{0,1} (associated with the target component) to $aN$$aN$aNa N and other ${\alpha }_{0,k}=(1-a)\times N/(K-1)$${\alpha }_{0,k}=(1-a)\times N/(K-1)$alpha_(0,k)=(1-a)xx N//(K-1)\alpha_{0, k}=(1-a) \times N /(K-1), where $a=0.01$$a=0.01$a=0.01a=0.01 (by default). Assuming $\mathbf{x}$$\mathbf{x}$x\mathbf{x} follows a Gaussian distribution $\mathcal{N}(\mathbf{x}\mid \mu ,{\mathrm{\Lambda }}^{-1})$$\mathcal{N}\left(\mathbf{x}\mid \mu ,{\mathrm{\Lambda }}^{-1}\right)$N(x∣mu,Lambda^(-1))\mathcal{N}\left(\mathbf{x} \mid \mu, \Lambda^{-1}\right), where $\mathbf{\Lambda }$$\mathbf{\Lambda }$Lambda\boldsymbol{\Lambda} (precision matrix) is the inverse covariance matrix, $p(\mu ,\mathbf{\Lambda })$$p(\mu ,\mathbf{\Lambda })$p(mu,Lambda)p(\mu, \boldsymbol{\Lambda}) together follow a Gaussian-Wishart prior $\prod _k^K\mathcal{N}({\mu }_k\mid {\mathbf{m}}_0,{\left({\beta }_0\mathbf{\Lambda }\right)}^{-1})\mathcal{W}({\mathrm{\Lambda }}_k\mid {\mathbf{W}}_0,{\nu }_0)$$\prod _k^K \mathcal{N}\left({\mu }_k\mid {\mathbf{m}}_0,{\left({\beta }_0\mathbf{\Lambda }\right)}^{-1}\right)\mathcal{W}\left({\mathrm{\Lambda }}_k\mid {\mathbf{W}}_0,{\nu }_0\right)$prod_(k)^(K)N(mu_(k)∣m_(0),(beta_(0)Lambda)^(-1))W(Lambda_(k)∣W_(0),nu_(0))\prod_{k}^{K} \mathcal{N}\left(\mu_{k} \mid \mathbf{m}_{0},\left(\beta_{0} \boldsymbol{\Lambda}\right)^{-1}\right) \mathcal{W}\left(\Lambda_{k} \mid \mathbf{W}_{0}, \nu_{0}\right), where the hyperparameters $\{{\mathbf{m}}_0,{\beta }_0,{\mathbf{W}}_0,v_0\}=\{\hat{\mu },1,{\mathbf{I}}_{D\times D},D+1\}$$\left\{{\mathbf{m}}_0,{\beta }_0,{\mathbf{W}}_0,v_0\right\}=\left\{\widehat{\mu },1,{\mathbf{I}}_{D\times D},D+1\right\}${m_(0),beta_(0),W_(0),v_(0)}={( hat(mu)),1,I_(D xx D),D+1}\left\{\mathbf{m}_{0}, \beta_{0}, \mathbf{W}_{0}, v_{0}\right\}=\left\{\hat{\mu}, 1, \mathbf{I}_{D \times D}, D+1\right\}.
我们沿用基于 Bishop（2006 年，第 $474-482$$474-482$474-482474-482 页）的标准贝叶斯 GMM，只做了细微修改。虽然单变量 GMM ( $D=1$$D=1$D=1D=1 ) 是分别应用于每个变量的，但我们将下面的形式主义作为更一般的多变量 GMM 来实施和描述，允许对协方差矩阵建模。简而言之，潜变量 $\mathbf{z}$$\mathbf{z}$z\mathbf{z} 是以概率 $\pi$$\pi$pi\pi （混合系数）采样的，该概率遵循超参数 ${\alpha }_0=({\alpha }_{0,1},\dots ,{\alpha }_{0,K})$${\alpha }_0=\left({\alpha }_{0,1},\dots ,{\alpha }_{0,K}\right)$alpha_(0)=(alpha_(0,1),dots,alpha_(0,K))\alpha_{0}=\left(\alpha_{0,1}, \ldots, \alpha_{0, K}\right) 的 Dirichlet 先验 $\mathrm{Dir}(\pi \mid {\alpha }_0)$$\mathrm{Dir}\left(\pi \mid {\alpha }_0\right)$Dir(pi∣alpha_(0))\operatorname{Dir}\left(\pi \mid \alpha_{0}\right) 。为了考虑任何 miRNA 目标和非目标的相对频率，我们将 ${\alpha }_{0,1}$${\alpha }_{0,1}$alpha_(0,1)\alpha_{0,1} （与目标成分相关）设为 $aN$$aN$aNa N ，将其他 ${\alpha }_{0,k}=(1-a)\times N/(K-1)$${\alpha }_{0,k}=(1-a)\times N/(K-1)$alpha_(0,k)=(1-a)xx N//(K-1)\alpha_{0, k}=(1-a) \times N /(K-1) 设为 $a=0.01$$a=0.01$a=0.01a=0.01 （默认）。假设 $\mathbf{x}$$\mathbf{x}$x\mathbf{x} 遵循高斯分布 $\mathcal{N}(\mathbf{x}\mid \mu ,{\mathrm{\Lambda }}^{-1})$$\mathcal{N}\left(\mathbf{x}\mid \mu ,{\mathrm{\Lambda }}^{-1}\right)$N(x∣mu,Lambda^(-1))\mathcal{N}\left(\mathbf{x} \mid \mu, \Lambda^{-1}\right) ，其中 $\mathbf{\Lambda }$$\mathbf{\Lambda }$Lambda\boldsymbol{\Lambda} （精度矩阵）是逆协方差矩阵， $p(\mu ,\mathbf{\Lambda })$$p(\mu ,\mathbf{\Lambda })$p(mu,Lambda)p(\mu, \boldsymbol{\Lambda}) 一起遵循高斯-Wishart 先验 $\prod _k^K\mathcal{N}({\mu }_k\mid {\mathbf{m}}_0,{\left({\beta }_0\mathbf{\Lambda }\right)}^{-1})\mathcal{W}({\mathrm{\Lambda }}_k\mid {\mathbf{W}}_0,{\nu }_0)$$\prod _k^K \mathcal{N}\left({\mu }_k\mid {\mathbf{m}}_0,{\left({\beta }_0\mathbf{\Lambda }\right)}^{-1}\right)\mathcal{W}\left({\mathrm{\Lambda }}_k\mid {\mathbf{W}}_0,{\nu }_0\right)$prod_(k)^(K)N(mu_(k)∣m_(0),(beta_(0)Lambda)^(-1))W(Lambda_(k)∣W_(0),nu_(0))\prod_{k}^{K} \mathcal{N}\left(\mu_{k} \mid \mathbf{m}_{0},\left(\beta_{0} \boldsymbol{\Lambda}\right)^{-1}\right) \mathcal{W}\left(\Lambda_{k} \mid \mathbf{W}_{0}, \nu_{0}\right) ，其中超参数 $\{{\mathbf{m}}_0,{\beta }_0,{\mathbf{W}}_0,v_0\}=\{\hat{\mu },1,{\mathbf{I}}_{D\times D},D+1\}$$\left\{{\mathbf{m}}_0,{\beta }_0,{\mathbf{W}}_0,v_0\right\}=\left\{\widehat{\mu },1,{\mathbf{I}}_{D\times D},D+1\right\}${m_(0),beta_(0),W_(0),v_(0)}={( hat(mu)),1,I_(D xx D),D+1}\left\{\mathbf{m}_{0}, \beta_{0}, \mathbf{W}_{0}, v_{0}\right\}=\left\{\hat{\mu}, 1, \mathbf{I}_{D \times D}, D+1\right\} 。

Let $\theta =\{\mathbf{z},\pi ,\mu ,\mathbf{\Lambda }\}$$\theta =\{\mathbf{z},\pi ,\mu ,\mathbf{\Lambda }\}$theta={z,pi,mu,Lambda}\theta=\{\mathbf{z}, \pi, \mu, \boldsymbol{\Lambda}\}. The marginal log likelihood can be written in terms of lower bound $\mathcal{L}(q)$$\mathcal{L}(q)$L(q)\mathcal{L}(q) (first term) and Kullback-Leibler divergence $\mathcal{K}\mathcal{L}(q\Vert p)$$\mathcal{K}\mathcal{L}(q\Vert p)$KL(q||p)\mathcal{K} \mathcal{L}(q \| p) (second term):
设 $\theta =\{\mathbf{z},\pi ,\mu ,\mathbf{\Lambda }\}$$\theta =\{\mathbf{z},\pi ,\mu ,\mathbf{\Lambda }\}$theta={z,pi,mu,Lambda}\theta=\{\mathbf{z}, \pi, \mu, \boldsymbol{\Lambda}\} 。边际对数似然可以用下界 $\mathcal{L}(q)$$\mathcal{L}(q)$L(q)\mathcal{L}(q) （第一项）和库尔贝-莱布勒发散 $\mathcal{K}\mathcal{L}(q\Vert p)$$\mathcal{K}\mathcal{L}(q\Vert p)$KL(q||p)\mathcal{K} \mathcal{L}(q \| p) （第二项）来表示：

where $q(\theta )$$q(\theta )$q(theta)q(\theta) is a proposed distribution for $p(\theta \mid \mathbf{x})$$p(\theta \mid \mathbf{x})$p(theta∣x)p(\theta \mid \mathbf{x}), which does not have a closed form distribution. Because $\ln p(\mathbf{x})$$\ln p(\mathbf{x})$ln p(x)\ln p(\mathbf{x}) is a constant, maximizing $\mathcal{L}(q)$$\mathcal{L}(q)$L(q)\mathcal{L}(q) implies minimizing $\mathcal{K}\mathcal{L}(q\Vert p)$$\mathcal{K}\mathcal{L}(q\Vert p)$KL(q||p)\mathcal{K} \mathcal{L}(q \| p). The general optimal solution $\ln q_j^{\ast }\left({\theta }_j\right)$$\ln q_j^{\ast }\left({\theta }_j\right)$ln q_(j)^(**)(theta_(j))\ln q_{j}^{*}\left(\theta_{j}\right) is the expectation of variable $j$$j$jj with respect to other variables, ${\mathbb{E}}_{i\ne j}[\ln p(\mathbf{x},\theta )]$${\mathbb{E}}_{i\ne j}[\ln p(\mathbf{x},\theta )]$E_(i!=j)[ln p(x,theta)]\mathbb{E}_{i \neq j}[\ln p(\mathbf{x}, \theta)]. In particular, we define $q(\mathbf{z},\pi ,\mu ,\mathbf{\Lambda })=q(\mathbf{z})q(\pi )q(\mu ,\mathbf{\Lambda })$$q(\mathbf{z},\pi ,\mu ,\mathbf{\Lambda })=q(\mathbf{z})q(\pi )q(\mu ,\mathbf{\Lambda })$q(z,pi,mu,Lambda)=q(z)q(pi)q(mu,Lambda)q(\mathbf{z}, \pi, \mu, \boldsymbol{\Lambda})=q(\mathbf{z}) q(\pi) q(\mu, \boldsymbol{\Lambda}). The expectations for the three terms (at $\log$$\log$log\log scale), namely, $\ln q^{\ast }(\mathbf{z}),\ln q^{\ast }(\pi ),\ln q^{\ast }(\mu )$$\ln q^{\ast }(\mathbf{z}),\ln q^{\ast }(\pi ),\ln q^{\ast }(\mu )$ln q^(**)(z),ln q^(**)(pi),ln q^(**)(mu)\ln q^{*}(\mathbf{z}), \ln q^{*}(\pi), \ln q^{*}(\mu), have the same forms as the initial distributions due to the conjugacy of the priors. However, they require evaluation of the parameters $\{\mathbf{z},\pi ,\mu ,\mathbf{\Lambda }\}$$\{\mathbf{z},\pi ,\mu ,\mathbf{\Lambda }\}${z,pi,mu,Lambda}\{\mathbf{z}, \pi, \mu, \boldsymbol{\Lambda}\}, which in turn all depend on the expectations of $\mathbf{z}$$\mathbf{z}$z\mathbf{z} or the posterior of interest:
其中， $q(\theta )$$q(\theta )$q(theta)q(\theta) 是 $p(\theta \mid \mathbf{x})$$p(\theta \mid \mathbf{x})$p(theta∣x)p(\theta \mid \mathbf{x}) 的拟议分布，而 $p(\theta \mid \mathbf{x})$$p(\theta \mid \mathbf{x})$p(theta∣x)p(\theta \mid \mathbf{x}) 并没有封闭形式的分布。因为 $\ln p(\mathbf{x})$$\ln p(\mathbf{x})$ln p(x)\ln p(\mathbf{x}) 是一个常数，所以最大化 $\mathcal{L}(q)$$\mathcal{L}(q)$L(q)\mathcal{L}(q) 意味着最小化 $\mathcal{K}\mathcal{L}(q\Vert p)$$\mathcal{K}\mathcal{L}(q\Vert p)$KL(q||p)\mathcal{K} \mathcal{L}(q \| p) 。一般最优解 $\ln q_j^{\ast }\left({\theta }_j\right)$$\ln q_j^{\ast }\left({\theta }_j\right)$ln q_(j)^(**)(theta_(j))\ln q_{j}^{*}\left(\theta_{j}\right) 是变量 $j$$j$jj 相对于其他变量 ${\mathbb{E}}_{i\ne j}[\ln p(\mathbf{x},\theta )]$${\mathbb{E}}_{i\ne j}[\ln p(\mathbf{x},\theta )]$E_(i!=j)[ln p(x,theta)]\mathbb{E}_{i \neq j}[\ln p(\mathbf{x}, \theta)] 的期望值。我们特别定义了 $q(\mathbf{z},\pi ,\mu ,\mathbf{\Lambda })=q(\mathbf{z})q(\pi )q(\mu ,\mathbf{\Lambda })$$q(\mathbf{z},\pi ,\mu ,\mathbf{\Lambda })=q(\mathbf{z})q(\pi )q(\mu ,\mathbf{\Lambda })$q(z,pi,mu,Lambda)=q(z)q(pi)q(mu,Lambda)q(\mathbf{z}, \pi, \mu, \boldsymbol{\Lambda})=q(\mathbf{z}) q(\pi) q(\mu, \boldsymbol{\Lambda}) 。由于先验的共轭性，三项的期望（在 $\log$$\log$log\log 尺度上），即 $\ln q^{\ast }(\mathbf{z}),\ln q^{\ast }(\pi ),\ln q^{\ast }(\mu )$$\ln q^{\ast }(\mathbf{z}),\ln q^{\ast }(\pi ),\ln q^{\ast }(\mu )$ln q^(**)(z),ln q^(**)(pi),ln q^(**)(mu)\ln q^{*}(\mathbf{z}), \ln q^{*}(\pi), \ln q^{*}(\mu) ，与初始分布具有相同的形式。但是，它们需要对参数 $\{\mathbf{z},\pi ,\mu ,\mathbf{\Lambda }\}$$\{\mathbf{z},\pi ,\mu ,\mathbf{\Lambda }\}${z,pi,mu,Lambda}\{\mathbf{z}, \pi, \mu, \boldsymbol{\Lambda}\} 进行评估，而这些参数又都取决于 $\mathbf{z}$$\mathbf{z}$z\mathbf{z} 或相关后验的期望：

where  其中
$\ln {\rho }_{nk}=\mathbb{E}[\ln {\pi }_k]+\frac{1}{2}\mathbb{E}[\ln \left|{\mathbf{\Lambda }}_k\right|]-\frac{D}{2}\ln (2\pi )-\frac{1}{2}{\mathbb{E}}_{{\mu }_k,{\mathit{A}}_k}[{({\mathbf{x}}_n-{\mu }_k)}^T{\mathbf{\Lambda }}_k({\mathbf{x}}_n-$$\ln {\rho }_{nk}=\mathbb{E}\left[\ln {\pi }_k\right]+\frac{1}{2}\mathbb{E}\left[\ln \left|{\mathbf{\Lambda }}_k\right|\right]-\frac{D}{2}\ln (2\pi )-\frac{1}{2}{\mathbb{E}}_{{\mu }_k,{\mathit{A}}_k}\left[{\left({\mathbf{x}}_n-{\mu }_k\right)}^T{\mathbf{\Lambda }}_k\left({\mathbf{x}}_n-\right.\right.$ln rho_(nk)=E[ln pi_(k)]+(1)/(2)E[ln|Lambda_(k)|]-(D)/(2)ln(2pi)-(1)/(2)E_(mu_(k),A_(k))[(x_(n)-mu_(k))^(T)Lambda_(k)(x_(n)-:}\ln \rho_{n k}=\mathbb{E}\left[\ln \pi_{k}\right]+\frac{1}{2} \mathbb{E}\left[\ln \left|\boldsymbol{\Lambda}_{k}\right|\right]-\frac{D}{2} \ln (2 \pi)-\frac{1}{2} \mathbb{E}_{\mu_{k}, \boldsymbol{A}_{k}}\left[\left(\mathbf{x}_{n}-\mu_{k}\right)^{T} \boldsymbol{\Lambda}_{k}\left(\mathbf{x}_{n}-\right.\right. ${\mu }_k)]$$\left.\left.{\mu }_k\right)\right]${:mu_(k))]\left.\left.\mu_{k}\right)\right]. The inter-dependence between the expectations and model parameters falls naturally into an expectation-maximization (EM) framework, namely variational Bayesian expectation maximization. Briefly, we first initialize the model parameters based on priors and randomly sample $K$$K$KK data points $\mu$$\mu$mu\mu. At the $i^{t^{th}}$$i^{t^{th}}$i^(t^(th))i^{t^{t h}} iteration, we evaluate (2) using the model parameters (VB-E step) and update the model parameters using (2) (VB-M step). The EM iteration terminates when $\mathcal{L}(q)$$\mathcal{L}(q)$L(q)\mathcal{L}(q) improves by $<{10}^{-20}$$<{10}^{-20}$< 10^(-20)<10^{-20} (default). Please refer to Bishop (2006) for more details.
$\ln {\rho }_{nk}=\mathbb{E}[\ln {\pi }_k]+\frac{1}{2}\mathbb{E}[\ln \left|{\mathbf{\Lambda }}_k\right|]-\frac{D}{2}\ln (2\pi )-\frac{1}{2}{\mathbb{E}}_{{\mu }_k,{\mathit{A}}_k}[{({\mathbf{x}}_n-{\mu }_k)}^T{\mathbf{\Lambda }}_k({\mathbf{x}}_n-$$\ln {\rho }_{nk}=\mathbb{E}\left[\ln {\pi }_k\right]+\frac{1}{2}\mathbb{E}\left[\ln \left|{\mathbf{\Lambda }}_k\right|\right]-\frac{D}{2}\ln (2\pi )-\frac{1}{2}{\mathbb{E}}_{{\mu }_k,{\mathit{A}}_k}\left[{\left({\mathbf{x}}_n-{\mu }_k\right)}^T{\mathbf{\Lambda }}_k\left({\mathbf{x}}_n-\right.\right.$ln rho_(nk)=E[ln pi_(k)]+(1)/(2)E[ln|Lambda_(k)|]-(D)/(2)ln(2pi)-(1)/(2)E_(mu_(k),A_(k))[(x_(n)-mu_(k))^(T)Lambda_(k)(x_(n)-:}\ln \rho_{n k}=\mathbb{E}\left[\ln \pi_{k}\right]+\frac{1}{2} \mathbb{E}\left[\ln \left|\boldsymbol{\Lambda}_{k}\right|\right]-\frac{D}{2} \ln (2 \pi)-\frac{1}{2} \mathbb{E}_{\mu_{k}, \boldsymbol{A}_{k}}\left[\left(\mathbf{x}_{n}-\mu_{k}\right)^{T} \boldsymbol{\Lambda}_{k}\left(\mathbf{x}_{n}-\right.\right. ${\mu }_k)]$$\left.\left.{\mu }_k\right)\right]${:mu_(k))]\left.\left.\mu_{k}\right)\right] 。期望值和模型参数之间的相互依存关系很自然地归入期望最大化（EM）框架，即变异贝叶斯期望最大化。简而言之，我们首先根据前验初始化模型参数，然后随机采样 $K$$K$KK 数据点 $\mu$$\mu$mu\mu 。在 $i^{t^{th}}$$i^{t^{th}}$i^(t^(th))i^{t^{t h}} 迭代中，我们使用模型参数对 (2) 进行评估（VB-E 步骤），并使用 (2) 更新模型参数（VB-M 步骤）。当 $\mathcal{L}(q)$$\mathcal{L}(q)$L(q)\mathcal{L}(q) 改善 $<{10}^{-20}$$<{10}^{-20}$< 10^(-20)<10^{-20} （默认值）时，EM迭代结束。详情请参考 Bishop (2006)。

We define the targetScore as an integrative probabilistic score of a gene being the target $t$$t$tt of a miRNA:
我们将 targetScore 定义为基因成为 miRNA 靶标 $t$$t$tt 的综合概率得分：

We collected miRNA-overexpression data corresponding to 84 Gene Expression Omnibus (GEO) series, 6 platforms, 77 human cells or tissues and 113 distinct miRNAs (Supplementary Table S1). To our knowledge, this is by far the largest compendium of miRNA-overexpression data. To automate data downloading and processing, we developed a pipeline written in R, making use of the function getGEO from GEOquery R/Bioconductor package (Davis and Meltzer, 2007). For each dataset, the pipeline downloads and quantile normalizes (if necessary) the expression data and calculates (when necessary) the log fold-change (logFC) in
我们收集了 84 个基因表达总库（GEO）系列、6 个平台、77 个人类细胞或组织和 113 个不同 miRNA 的 miRNA 表达数据（补充表 S1）。据我们所知，这是迄今为止最大的 miRNA 表达数据汇编。为了实现数据下载和处理的自动化，我们利用 GEOquery R/Bioconductor 软件包（Davis 和 Meltzer，2007 年）中的 getGEO 函数，开发了一个用 R 语言编写的管道。对于每个数据集，该管道都会下载表达数据并进行量化归一化处理（如有必要），并计算（如有必要）其对折变化（logFC）。
treatment (miRNA transfected) versus (mock) control. For mRNAs interrogated by multiple probes in a single experiment, we took the average of the fold-changes. Each of the 286 data vectors contains $\mathrm{logFC}$$\mathrm{logFC}$logFC\operatorname{logFC} values for $N\le 18560$$N\le 18560$N <= 18560N \leq 18560 RefSeq mRNAs (i.e. with prefix NM for known protein coding mRNA obtained from University of California, Santa Cruz) due to transfection of one of the 113 miRNAs. For two $\mathrm{logFC}$$\mathrm{logFC}$logFC\operatorname{logFC} vectors associated with the same miRNA transfection (conducted in different studies), we removed mRNAs for which neither of the vectors contains a $\mathrm{logFC}$$\mathrm{logFC}$logFC\operatorname{logFC} value and filled the remaining missing values in one vector with the non-missing values in the other. For more than two $\mathrm{logFC}$$\mathrm{logFC}$logFC\operatorname{logFC} vectors for the same miRNA transfection, we removed mRNAs absent in all of those vectors and performed imputation for the remaining missing values using impute. knn from impute R package (Troyanskaya et al., 2001). Finally, we picked one representative $\mathrm{logFC}$$\mathrm{logFC}$logFC\operatorname{logFC} vector per miRNA, which has the highest Pearson correlation with the binary vector of the validated targets (Hsu et al., 2011) or averaged them if no validated target was available. As a result, we have $113\mathrm{logFC}$$113\mathrm{logFC}$113 logFC113 \operatorname{logFC} data vectors for 113 distinct miRNA transfections.
处理（转染 miRNA）与（模拟）对照。对于在一次实验中使用多个探针检测的 mRNA，我们取折叠变化的平均值。在 286 个数据载体中，每个载体都包含因转染 113 个 miRNA 中的一个而导致的 $\mathrm{logFC}$$\mathrm{logFC}$logFC\operatorname{logFC} $N\le 18560$$N\le 18560$N <= 18560N \leq 18560 RefSeq mRNA（即前缀为 NM 的已知蛋白质编码 mRNA，从加州大学圣克鲁兹分校获得）的 $\mathrm{logFC}$$\mathrm{logFC}$logFC\operatorname{logFC} 值。对于与同一 miRNA 转染相关的两个 $\mathrm{logFC}$$\mathrm{logFC}$logFC\operatorname{logFC} 载体（在不同研究中进行），我们剔除了两个载体都不包含 $\mathrm{logFC}$$\mathrm{logFC}$logFC\operatorname{logFC} 值的 mRNA，并用另一个载体中的非缺失值填补了一个载体中的剩余缺失值。对于同一 miRNA 转染的两个以上 $\mathrm{logFC}$$\mathrm{logFC}$logFC\operatorname{logFC} 向量，我们删除了所有这些向量中缺失的 mRNA，并使用 impute R 软件包（Troyanskaya 等人，2001 年）中的 impute.最后，我们为每个 miRNA 挑选了一个具有代表性的 $\mathrm{logFC}$$\mathrm{logFC}$logFC\operatorname{logFC} 向量，它与验证靶标的二元向量具有最高的皮尔逊相关性（Hsu 等，2011 年），如果没有验证靶标，则取平均值。因此，我们得到了 113 个不同 miRNA 转染的 $113\mathrm{logFC}$$113\mathrm{logFC}$113 logFC113 \operatorname{logFC} 数据载体。

We compared targetScore with seven published methods (Table 1). Among these methods, Expmicro is the only method that also uses miRNA-overexpression data. The other six methods are sequencebased, and their predictions are fine-tuned by the authors and the results provided on their Web site are the most accurate ones. Thus, we only ran Expmicro locally on the same test data and directly downloaded the target predictions by the other six programs from their corresponding Web sites. Specifically, predictions on all target sites (including conserved and non-conserved sites) from targetScan 6.1 were obtained for both context + scores (CS) and probability of conserved targeting (PCT). The latest PicTar2 target predictions were obtained from doRiNA database (database of RNA interactions in post-transcriptional regulation) (Anders et al., 2011). The miRanda predictions for sites with both good and non-good mirSVR scores were obtained at http://www.micro rna.org/. For Probability of Interaction by Target Accessibility (PITA) predictions, the accessibility energy $\mathrm{\Delta }\mathrm{\Delta }G$$\mathrm{\Delta }\mathrm{\Delta }G$Delta Delta G\Delta \Delta G on target sites flanked by $3/15$$3/15$3//153 / 15 nt upstream/downstream (’ $3/15$$3/15$3//153 / 15 flank’) was chosen as recommended by the authors (Kertesz et al., 2007). SVMicro predictions were obtained from http://compgenomics.utsa.edu/svmicro.html. Expmicro was run on the SVMicro scores and expression fold-changes (Liu et al., 2010a).
我们将 targetScore 与七种已发表的方法进行了比较（表 1）。在这些方法中，Expmicro 是唯一同时使用 miRNA 表达数据的方法。其他六种方法都是基于序列的，其预测结果由作者进行了微调，其网站上提供的结果是最准确的。因此，我们只在本地对相同的测试数据运行了 Expmicro，并直接从相应的网站上下载了其他六种程序的靶标预测结果。具体来说，我们从 targetScan 6.1 中获得了所有目标位点（包括保守位点和非保守位点）的上下文+分数（CS）和保守目标概率（PCT）预测结果。最新的 PicTar2 目标预测来自 doRiNA 数据库（转录后调控中的 RNA 相互作用数据库）（Anders 等人，2011 年）。具有良好和非良好 mirSVR 评分的位点的 miRanda 预测可从 http://www.micro rna.org/获得。对于目标可及性相互作用概率（PITA）预测，根据作者的建议（Kertesz 等，2007 年），选择了上游/下游侧翼为 $3/15$$3/15$3//153 / 15 nt 的目标位点的可及性能量 $\mathrm{\Delta }\mathrm{\Delta }G$$\mathrm{\Delta }\mathrm{\Delta }G$Delta Delta G\Delta \Delta G （" $3/15$$3/15$3//153 / 15 flank"）。SVMicro 预测结果来自 http://compgenomics.utsa.edu/svmicro.html。Expmicro 在 SVMicro 分数和表达折叠变化上运行（Liu 等人，2010a）。

2.7.1 Gold standard Experimentally validated targets were downloaded from mirTarBase (Hsu et al., 2011) (http://mirtarbase.mbc.nctu. edu.tw). MirTarBase is one of the most comprehensive databases that support bulk download and agree with other databases such as TarBase (Vergoulis et al., 2012) and miRecords (Xiao et al., 2009). MirTarBase 3.5 contains 3565 validated interactions between 432 human miRNAs and 1959 target genes. The average (median) number of targets per miRNA is 8.2 (3).
2.7.1 金标准 从 mirTarBase（Hsu 等，2011 年）（http://mirtarbase.mbc.nctu. edu.tw）下载实验验证的靶标。MirTarBase 是支持批量下载的最全面的数据库之一，与 TarBase (Vergoulis et al., 2012) 和 miRecords (Xiao et al., 2009) 等其他数据库一致。MirTarBase 3.5 包含 432 个人类 miRNA 与 1959 个靶基因之间的 3565 次有效相互作用。每个 miRNA 的靶基因平均数（中位数）为 8.2 (3)。
2.7.2 Methods of comparison We first compared the performances of using $\mathrm{logFC}$$\mathrm{logFC}$logFC\operatorname{logFC} and the six methods that use sequence information alone (Table 1) in discriminating validated targets from the rest. To have a reliable estimate, we selected the test data corresponding to miRNAs that have at least three validated targets from mirTarBase and at least 1 predicted target from each of the predictors. Based on the results, we then picked two overall best sequence-based methods. The scores from those two methods were then integrated along with $\mathrm{logFC}$$\mathrm{logFC}$logFC\operatorname{logFC} into the proposed targetScore Equation (3). Next, we modified our testing set by including miRNAs that have at least one target predicted from each of the two best-performing sequence-based methods and at least 10 validated targets from mirTarBase. Finally, we evaluated the performances of $\log \mathrm{FC}$$\log \mathrm{FC}$log FC\log \mathrm{FC} and sequence-based methods alone in comparison with Expmicro (Liu et al., 2010a) and the proposed targetScore.
2.7.2 比较方法 我们首先比较了使用 $\mathrm{logFC}$$\mathrm{logFC}$logFC\operatorname{logFC} 和仅使用序列信息的六种方法（表 1）在区分有效靶标和其他靶标方面的表现。为了得到可靠的估计结果，我们选择了与至少有三个来自 mirTarBase 的验证靶标和至少有一个来自每个预测因子的预测靶标的 miRNA 相对应的测试数据。根据结果，我们选出了两种基于序列的总体最佳方法。然后将这两种方法的得分与 $\mathrm{logFC}$$\mathrm{logFC}$logFC\operatorname{logFC} 整合到拟议的 targetScore 公式 (3) 中。接下来，我们对测试集进行了修改，纳入了至少有一种靶标是由两种表现最好的基于序列的方法预测的，并且至少有 10 个靶标是由 mirTarBase 验证的 miRNA。最后，我们将 $\log \mathrm{FC}$$\log \mathrm{FC}$log FC\log \mathrm{FC} 和基于序列的方法单独与 Expmicro（Liu 等人，2010a）和建议的 targetScore 进行了比较，评估了它们的性能。
2.7.3 Systematic evaluation For each comparison, the sensitivity and specificity of the methods were systematically assessed using receiver operating characteristic (ROC) curve and summarized by the area under the curve (AUC) (Fig. 2). For a given score cutoff, the true- and false-positive rates (TPR and FPR) are estimated as the respective ratios of TPR $=\mathrm{TP}/\mathrm{P}$$=\mathrm{TP}/\mathrm{P}$=TP//P=\mathrm{TP} / \mathrm{P} and $\mathrm{FPR}=\mathrm{FP}/\mathrm{N}$$\mathrm{FPR}=\mathrm{FP}/\mathrm{N}$FPR=FP//N\mathrm{FPR}=\mathrm{FP} / \mathrm{N}, where TP and FP are the numbers of true and false positives, and P and N are the total numbers of positive and negative miRNA targets within the test data. Predicted targets outside of the test data were not counted. ROC is plotted by iteratively evaluating TPR ( $y$$y$yy-axis) and FPR ( $x$$x$xx-axis) while relaxing the scoring cutoff. In addition, we constructed precision-recall (PR) curve (PRC) and assessed the precision $\mathrm{TP}/(\mathrm{TP}+\mathrm{FP})$$\mathrm{TP}/(\mathrm{TP}+\mathrm{FP})$TP//(TP+FP)\mathrm{TP} /(\mathrm{TP}+\mathrm{FP}) of each method at the same recall (or TPR ). Comparing to ROC, PR is more informative in evaluating the performance at the top predictions. Both ROC and PR statistics were obtained using ROCR package (Sing et al., 2005).
2.7.3 系统评估 对于每种比较方法，均使用接收器操作特征曲线（ROC）对其灵敏度和特异性进行系统评估，并以曲线下面积（AUC）进行总结（图 2）。对于给定的得分临界值，真阳性率和假阳性率（TPR 和 FPR）分别按 TPR $=\mathrm{TP}/\mathrm{P}$$=\mathrm{TP}/\mathrm{P}$=TP//P=\mathrm{TP} / \mathrm{P} 和 $\mathrm{FPR}=\mathrm{FP}/\mathrm{N}$$\mathrm{FPR}=\mathrm{FP}/\mathrm{N}$FPR=FP//N\mathrm{FPR}=\mathrm{FP} / \mathrm{N} 的比率估算，其中 TP 和 FP 是真阳性和假阳性的数量，P 和 N 是测试数据中阳性和阴性 miRNA 靶点的总数。测试数据之外的预测靶标不计算在内。ROC 是通过迭代评估 TPR（ $y$$y$yy 轴）和 FPR（ $x$$x$xx 轴）绘制的，同时放宽了评分临界值。此外，我们还构建了精确度-召回率（PR）曲线（PRC），并评估了每种方法在相同召回率（或 TPR）下的精确度 $\mathrm{TP}/(\mathrm{TP}+\mathrm{FP})$$\mathrm{TP}/(\mathrm{TP}+\mathrm{FP})$TP//(TP+FP)\mathrm{TP} /(\mathrm{TP}+\mathrm{FP}) 。与 ROC 相比，PR 在评估最高预测性能方面更有参考价值。ROC 和 PR 统计数据都是使用 ROCR 软件包（Sing 等人，2005 年）获得的。
2.7.4 Evaluation using proteomic data To further evaluate the performance of each method, we used the available protein output data
2.7.4 使用蛋白质组数据进行评估 为了进一步评估每种方法的性能，我们使用了现有的蛋白质输出数据