An effective aggregation of node features into a graph-level representation via readout functions is an essential step in numerous learning tasks involving graph neural networks. Typically, readouts are simple and non-adaptive functions designed such that the resulting hypothesis space is permutation invariant. Prior work on deep sets indicates that such readouts might require complex node embeddings that can be difficult to learn via standard neighborhood aggregation schemes. Motivated by this, we investigate the potential of adaptive readouts given by neural networks that do not necessarily give rise to permutation invariant hypothesis spaces. We argue that in some problems such as binding affinity prediction where molecules are typically presented in a canonical form it might be possible to relax the constraints on permutation invariance of the hypothesis space and learn a more effective model of the affinity by employing an adaptive readout function. Our empirical results demonstrate the effectiveness of neural readouts on more than 40 datasets spanning different domains and graph characteristics. Moreover, we observe a consistent improvement over standard readouts (i.e., sum, max, and mean) relative to the number of neighborhood aggregation iterations and different convolutional operators.

MOTIVATION: Identification of modules of co-regulated genes is a crucial first step towards dissecting the regulatory circuitry underlying biological processes. Co-regulated genes are likely to reveal themselves by showing tight co-expression, e.g. high correlation of expression profiles across multiple time series datasets. However, numbers of up- or downregulated genes are often large, making it difficult to discriminate between dependent co-expression resulting from co-regulation and independent co-expression. Furthermore, modules of co-regulated genes may only show tight co-expression across a subset of the time series, i.e. show condition-dependent regulation. RESULTS: Wigwams is a simple and efficient method to identify gene modules showing evidence for co-regulation in multiple time series of gene expression data. Wigwams analyzes similarities of gene expression patterns within each time series (condition) and directly tests the dependence or independence of these across different conditions. The expression pattern of each gene in each subset of conditions is tested statistically as a potential signature of a condition-dependent regulatory mechanism regulating multiple genes. Wigwams does not require particular time points and can process datasets that are on different time scales. Differential expression relative to control conditions can be taken into account. The output is succinct and non-redundant, enabling gene network reconstruction to be focused on those gene modules and combinations of conditions that show evidence for shared regulatory mechanisms. Wigwams was run using six Arabidopsis time series expression datasets, producing a set of biologically significant modules spanning different combinations of conditions. AVAILABILITY AND IMPLEMENTATION: A Matlab implementation of Wigwams, complete with graphical user interfaces and documentation, is available at: warwick.ac.uk/wigwams. .

MOTIVATION: Identifying regulatory modules is an important task in the exploratory analysis of gene expression time series data. Clustering algorithms are often used for this purpose. However, gene regulatory events may induce complex temporal features in a gene expression profile, including time delays, inversions and transient correlations, which are not well accounted for by current clustering methods. As the cost of microarray experiments continues to fall, the temporal resolution of time course studies is increasing. This has led to a need to take account of detailed temporal features of this kind. Thus, while standard clustering methods are both widely used and much studied, their shared shortcomings with respect to such temporal features motivates the work presented here. RESULTS: Here, we introduce a temporal clustering approach for high-dimensional gene expression data which takes account of time delays, inversions and transient correlations. We do so by exploiting a recently introduced, message-passing-based algorithm called Affinity Propagation (AP). We take account of temporal features of interest following an approximate but efficient dynamic programming approach due to Qian et al. The resulting approach is demonstrably effective in its ability to discern non-obvious temporal features, yet efficient and robust enough for routine use as an exploratory tool. We show results on validated transcription factor-target pairs in yeast and on gene expression data from a study of Arabidopsis thaliana under pathogen infection. The latter reveals a number of biologically striking findings. AVAILABILITY: Matlab code for our method is available at http://www.wsbc.warwick.ac.uk/stevenkiddle/tcap.html.