TIGRESS: Trustful Inference of Gene REgulation using Stability Selection

Abstract

Background: Inferring the structure of gene regulatory networks (GRN) from a collection of gene expression data has many potential applications, from the elucidation of complex biological processes to the identification of potential drug targets. It is however a notoriously difficult problem, for which the many existing methods reach limited accuracy.

Results: In this paper, we formulate GRN inference as a sparse regression problem and investigate the performance of a popular feature selection method, least angle regression (LARS) combined with stability selection, for that purpose. We introduce a novel, robust and accurate scoring technique for stability selection, which improves the performance of feature selection with LARS. The resulting method, which we call TIGRESS (for Trustful Inference of Gene REgulation with Stability Selection), was ranked among the top GRN inference methods in the DREAM5 gene network inference challenge. In particular, TIGRESS was evaluated to be the best linear regression-based method in the challenge. We investigate in depth the influence of the various parameters of the method, and show that a fine parameter tuning can lead to significant improvements and state-of-the-art performance for GRN inference, in both directed and undirected settings.

Conclusions: TIGRESS reaches state-of-the-art performance on benchmark data, including both in silico and in vivo (E. coli and S. cerevisiae) networks. This study confirms the potential of feature selection techniques for GRN inference. Code and data are available on http://cbio.ensmp.fr/tigress. Moreover, TIGRESS can be run online through the GenePattern platform (GP-DREAM, http://dream.broadinstitute.org).

Figure 1

Stability selection. Illustration of the stability selection frequency F(g,t,L) for a fixed target gene g. Each curve represents a TF $t\in {\mathcal{T}}_g$, and the horizontal axis represents the number L of LARS steps. F(g,t,L) is the frequency with which t is selected in the first L LARS steps to predict g, when the expression matrix is randomly perturbed by selecting only a limited number of experiments and randomly weighting each expression array. For example, the TF corresponding to the highest curve was selected 57% of the time at the first LARS step, and 81% of the time in the first two LARS steps.

Figure 2

Score for network 1. Top plots show the score for R=4,000 and bottom plots depict the case R=10,000 for both the area (left) and the original (right) scoring settings, as a function of α and L.

Figure 3

Optimal values of the parameters. Optimal values of parameters L, α and N with respect to the number of resampling runs.

Figure 4

Impact of the number of resampling runs. Score as a function of R. In both scoring settings, α and L were set to 0.4 and 2, respectively.

Figure 5

Distribution of the number of TFs selected per gene for L=2. Histograms of the number of TFs selected per gene with respect to the total number of predictions when L=2.

Figure 6

Distribution of the number of TFs selected per gene for L=20. Histograms of the number of TFs selected per gene with respect to the total number of predictions when L=20.

Figure 7

Performance on network 1. ROC (left) and Precision/Recall (right) curves for several methods on Network 1.

Figure 8

Performance on DREAM5 network 3. ROC (Left) and Precision/Recall (Right) curves for several methods on DREAM5 network 3.

Figure 9

Performance on DREAM5 network 4. ROC (Left) and Precision/Recall (Right) curves for several methods on DREAM5 network 4.

Figure 10

In vivo networks results. Score with respect to L for DREAM5 networks 3 and 4 and E. coli network (α=0.4, R=10,000).

Figure 11

Performance on the E. coli network. ROC (Left) and Precision/Recall (Right) curves for several methods on the E. coli dataset.

Figure 12

Spurious edges shortest path distribution. Exact distribution of the shortest path between spuriously predicted TF-TG couples.

Figure 13

Distribution of the shortest path with respect to the number of predictions. Distribution of the shortest path length between nodes of spuriously detected edges and 95% confidence interval for the null distribution. These edges are ranked by order of discovery.

Figure 14

Distance-2 patterns. The three possible distance-2 patterns: siblings, couple and grandparent/grandchild relationships.

Figure 15

Distribution of distance-2 errors. Distribution of distance 2 errors with respect to the number of predictions. 95% error bars were computed using the quantiles of a hypergeometric distribution.

Figure 16

Results on DREAM4 networks. Overall score on the five multifactorial size 100 DREAM4 networks, as a function ofα and L.