Table 1.

Overview of methods for estimating regulatory activity from transcriptome data comparing input data, modelling, computational aspects and outcome variables

Method	Input	Model	Computation	Output
Approach by Schacht et al.	- mRNA expression data - TF binding information	Linear model $\widehat{g_{i,s}}=c+{\displaystyle \sum _t}{\beta }_t{b}_{t,i}\left({\theta }_{a,t}ac{t}_{t,s}+{\theta }_{g,t}{g}_{t,s}\right)$ with $ac{t}_{t,s}=\frac{{\displaystyle {\sum }_i}{b}_{t,i}{g}_{i,s}}{{\displaystyle {\sum }_i}{b}_{t,i}},{\theta }_{a,t}+{\theta }_{g,t}=1,{\theta }_{a,t},{\theta }_{g,t}\in \left\{0,1\right\}$	- Optimization criterion: minimize sum of absolute errors - Mixed-integer linear programming - Optimization via Gurobi 5.5	- parameter for each TF: β t - decision for each TF if θ a,tor θ g,t was chosen
RACER	- mRNA expression data - copy number variation - DNA methylation - miRNA expression signals - TF binding information - miRNA target site info (c)	Linear models: 1) $\widehat{g_{i,s}}=c+{\theta }_{CNV,s}CN{V}_{i,s}+{\theta }_{DM,s}D{M}_{i,s}+{\displaystyle \sum _t}{\beta }_{t,s}{b}_{t,i}+{\displaystyle \sum _{mi}}{\beta }_{mi,s}{c}_{i,mi}\mathit{miRN}{A}_{mi,s}$ 2) $\widehat{g_{i,s}}=\tilde{c}+{\tilde{\theta }}_{i,CNV}CN{V}_{i,s}+{\tilde{\theta }}_{i,DM}D{M}_{i,s}+{\displaystyle \sum _t}{\gamma }_{i,t}{\beta }_{t,s}+{\displaystyle \sum _{mi}}{\gamma }_{i,mi}{\beta }_{mi,\mathrm{s}}$	- Optimization criterion: minimize sum of squared errors with L1 norm penalty on linear coefficients - Elastic-net regularized generalized linear models and LASSO	1) sample-specific TF and miRNA activities β t,s and β mi,s 2) TF-gene γ i,t and miRNA-gene γ i,miinteractions across all samples
RABIT	- differential mRNA expression data - somatic mutations - DNA methylation - copy number variation - TF binding info - recognition motifs for RNA-binding protein (RBP)	Linear model: $\widehat{g_t}={\displaystyle \sum _f}{\theta }_f{B}_{f,i}+{\displaystyle \sum _t}{\beta }_t{b}_{t,i}$ With B: background factors (gene CNA, promoter DNA methylation, promoter degree promoter CpG content)	- Frisch-Waugh-Lovell method, select subset of significant TFs via model selection procedure and remove TFs with insignificant correlation across tumors	- regulatory activity score for each TF (t value of linear regression coefficient of t-test)
ISMARA	- gene expression or chromatin state measurements - annotation of promoters (number of predicted sites for motifs) - transcripts and associated promoters - miRNA target site predictions	Linear model $\widehat{g_{p,s}}=c_p+c_s+{\displaystyle \sum _m}{N}_{p,m}{\beta }_{m,s}$	- Optimization criterion: minimize sum of errors - Bayesian procedure, ridge regression - Gaussian prior for β m,s to avoid overfitting	- inferred motif activity profiles β m,swith set of TFs and miRNAs binding to sites of these motifs (= key regulators) - predicted target promoters, associated transcripts and genes - Network of known interactions between predicted targets and predicted regulatory interactions - enriched ontology categories
biRte	- mRNA differential expression - miRNA, TF measurements, CNV (optionally) - regulator (R) – target network	Likelihood model: $L_{D,\theta }\left(R\right)=p\left(D|R,\theta \right)={\displaystyle \prod _{\widehat{D}}p}\left(\widehat{D}|R,\theta \right)={\displaystyle \prod _{\widehat{D}}{\displaystyle \prod _c{\displaystyle \prod _{i}p\left({\widehat{D}}_{ic}|R_c,\theta \right)}}}$	- data specific marginal likelihoods using estimation of hidden state variables with via MCMC - Nested effects model structure Learning to reconstruct transcriptional network	- Estimation of active regulators - Estimation of associated transcriptional network
ARACNE	- microarray expression profiles	none	- local estimation of pairwise gene expression profile mutual information	- Reconstruction of gene regulatory network

Gene expression data is named “g” with index i, estimated parameters with “β”, TF binding information with “b”, TFs with “t”, samples with “s”, miRNAs with “mi” and model constants with “c”. Other variables are explained in the text