Depth normalization of small RNA sequencing: using data and biology to select a suitable method.

Deep sequencing has become one of the most popular tools for transcriptome profiling in biomedical studies. While an abundance of computational methods exists for 'normalizing' sequencing data to remove unwanted between-sample variations due to experimental handling, there is no consensus on which normalization is the most suitable for a given data set. To address this problem, we developed 'DANA'-an approach for assessing the performance of normalization methods for microRNA sequencing data based on biology-motivated and data-driven metrics. Our approach takes advantage of well-known biological features of microRNAs for their expression pattern and chromosomal clustering to simultaneously assess (i) how effectively normalization removes handling artifacts and (ii) how aptly normalization preserves biological signals. With DANA, we confirm that the performance of eight commonly used normalization methods vary widely across different data sets and provide guidance for selecting a suitable method for the data at hand. Hence, it should be adopted as a routine preprocessing step (preceding normalization) for microRNA sequencing data analysis. DANA is implemented in R and publicly available at https://github.com/LXQin/DANA.

Statistical guarantees for regularized neural networks.

Neural networks have become standard tools in the analysis of data, but they lack comprehensive mathematical theories. For example, there are very few statistical guarantees for learning neural networks from data, especially for classes of estimators that are used in practice or at least similar to such. In this paper, we develop a general statistical guarantee for estimators that consist of a least-squares term and a regularizer. We then exemplify this guarantee with ℓ1-regularization, showing that the corresponding prediction error increases at most logarithmically in the total number of parameters and can even decrease in the number of layers. Our results establish a mathematical basis for regularized estimation of neural networks, and they deepen our mathematical understanding of neural networks and deep learning more generally.

Integrating additional knowledge into the estimation of graphical models.

Graphical models such as brain connectomes derived from functional magnetic resonance imaging (fMRI) data are considered a prime gateway to understanding network-type processes. We show, however, that standard methods for graphical modeling can fail to provide accurate graph recovery even with optimal tuning and large sample sizes. We attempt to solve this problem by leveraging information that is often readily available in practice but neglected, such as the spatial positions of the measurements. This information is incorporated into the tuning parameter of neighborhood selection, for example, in the form of pairwise distances. Our approach is computationally convenient and efficient, carries a clear Bayesian interpretation, and improves standard methods in terms of statistical stability. Applied to data about Alzheimer's disease, our approach allows us to highlight the central role of lobes in the connectivity structure of the brain and to identify an increased connectivity within the cerebellum for Alzheimer's patients compared to other subjects.

Aggregating Knockoffs for False Discovery Rate Control with an Application to Gut Microbiome Data.

Recent discoveries suggest that our gut microbiome plays an important role in our health and wellbeing. However, the gut microbiome data are intricate; for example, the microbial diversity in the gut makes the data high-dimensional. While there are dedicated high-dimensional methods, such as the lasso estimator, they always come with the risk of false discoveries. Knockoffs are a recent approach to control the number of false discoveries. In this paper, we show that knockoffs can be aggregated to increase power while retaining sharp control over the false discoveries. We support our method both in theory and simulations, and we show that it can lead to new discoveries on microbiome data from the American Gut Project. In particular, our results indicate that several phyla that have been overlooked so far are associated with obesity.