Biological data, including gene expression data, are generally high-dimensional and require efficient, generalizable, and scalable machine-learning methods to discover complex nonlinear patterns. Recent advances in machine learning can be attributed to deep neural networks (DNNs), which perform various tasks in terms of computer vision and natural language processing. However, standard DNNs are inappropriate for high-dimensional datasets generated in biology because they consider numerous parameters, which in turn require numerous samples. In this paper, we propose a DNN-based, nonlinear feature selection method, called the feature selection network (FsNet), for high-dimensional and small sample data. Specifically, FsNet comprises a selection layer that selects features and a reconstruction layer that stabilizes the training. Because a large number of parameters in the selection and reconstruction layers can easily result in overfitting under a limited number of samples, we utilized two tiny networks to predict the large virtual weight matrices of the selection and reconstruction layers. Experimental results on several real-world high-dimensional biological datasets demonstrate the efficacy of the proposed method.

This article analyses three feature screening procedures: Kendall’s Tau and Spearman Rho (TR), Hilbert-Schmidt Independence Criterion (HSIC) and conditional Maximum Mean Discrepancy (cMMD), where the latter is a modified version of the standard MMD for categorical classification. These association measures are not based on any specific underlying model, such as the linear regression. We provide the conditions for which the sure independence screening (SIS) property is satisfied under a lower bound assumption on the minimum signal strength of the association measure. The SIS property for the HSIC and cMMD is established for given bounded and symmetric kernels. Within the high-dimensional setting, we propose a two-step approach to control the false discovery rate (FDR) using the knockoff filtering. The performances of the association measures are assessed through simulated and real data experiments and compared with existing competing screening methods.

Detecting influential features in non-linear and/or high-dimensional data is a challenging and increasingly important task in machine learning. Variable selection methods have thus been gaining much attention as well as post-selection inference. Indeed, the selected features can be significantly flawed when the selection procedure is not accounted for. We propose a selective inference procedure using the so-called model-free "HSIC-Lasso" based on the framework of truncated Gaussians combined with the polyhedral lemma. We then develop an algorithm, which allows for low computational costs and provides a selection of the regularisation parameter. The performance of our method is illustrated by both artificial and real-world data based experiments, which emphasise a tight control of the type-I error, even for small sample sizes.

Genome-wide association studies (GWAS) explore the genetic causes of complex diseases. However, classical approaches ignore the biological context of the genetic variants and genes under study. To address this shortcoming, one can use biological networks, which model functional relationships, to search for functionally related susceptibility loci. Many such network methods exist, each arising from different mathematical frameworks, pre-processing steps, and assumptions about the network properties of the susceptibility mechanism. Unsurprisingly, this results in disparate solutions. To explore how to exploit these heterogeneous approaches, we selected six network methods and applied them to GENESIS, a nationwide French study on familial breast cancer. First, we verified that network methods recovered more interpretable results than a standard GWAS. We addressed the heterogeneity of their solutions by studying their overlap, computing what we called the consensus. The key gene in this consensus solution was COPS5, a gene related to multiple cancer hallmarks. Another issue we observed was that network methods were unstable, selecting very different genes on different subsamples of GENESIS. Therefore, we proposed a stable consensus solution formed by the 68 genes most consistently selected across multiple subsamples. This solution was also enriched in genes known to be associated with breast cancer susceptibility (BLM, CASP8, CASP10, DNAJC1, FGFR2, MRPS30, and SLC4A7, P-value = 3 × 10-4). The most connected gene was CUL3, a regulator of several genes linked to cancer progression. Lastly, we evaluated the biases of each method and the impact of their parameters on the outcome. In general, network methods preferred highly connected genes, even after random rewirings that stripped the connections of any biological meaning. In conclusion, we present the advantages of network-guided GWAS, characterize their shortcomings, and provide strategies to address them. To compute the consensus networks, implementations of all six methods are available at https://github.com/hclimente/gwas-tools.

MOTIVATION: Finding non-linear relationships between biomolecules and a biological outcome is computationally expensive and statistically challenging. Existing methods have important drawbacks, including among others lack of parsimony, non-convexity and computational overhead. Here we propose block HSIC Lasso, a non-linear feature selector that does not present the previous drawbacks. RESULTS: We compare block HSIC Lasso to other state-of-the-art feature selection techniques in both synthetic and real data, including experiments over three common types of genomic data: gene-expression microarrays, single-cell RNA sequencing and genome-wide association studies. In all cases, we observe that features selected by block HSIC Lasso retain more information about the underlying biology than those selected by other techniques. As a proof of concept, we applied block HSIC Lasso to a single-cell RNA sequencing experiment on mouse hippocampus. We discovered that many genes linked in the past to brain development and function are involved in the biological differences between the types of neurons. AVAILABILITY AND IMPLEMENTATION: Block HSIC Lasso is implemented in the Python 2/3 package pyHSICLasso, available on PyPI. Source code is available on GitHub (https://github.com/riken-aip/pyHSICLasso). SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.