Model transparency is a prerequisite in many domains and an increasingly popular area in machine learning research. In the medical domain, for instance, unveiling the mechanisms behind a disease often has higher priority than the diagnostic itself since it might dictate or guide potential treatments and research directions. One of the most popular approaches to explain model global predictions is the permutation importance where the performance on permuted data is benchmarked against the baseline. However, this method and other related approaches will undervalue the importance of a feature in the presence of covariates since these cover part of its provided information. To address this issue, we propose Covered Information Disentanglement CID, a framework that considers all feature information overlap to correct the values provided by permutation importance. We further show how to compute CID efficiently when coupled with Markov random fields. We demonstrate its efficacy in adjusting permutation importance first on a controlled toy dataset and discuss its effect on real-world medical data.

BACKGROUND: Recent technological developments have enabled the measurement of a plethora of biomolecular data from various omics domains, and research is ongoing on statistical methods to leverage these omics data to better model and understand biological pathways and genetic architectures of complex phenotypes. Current reviews report that the simultaneous analysis of multiple (i.e. three or more) high dimensional omics data sources is still challenging and suitable statistical methods are unavailable. Often mentioned challenges are the lack of accounting for the hierarchical structure between omics domains and the difficulty of interpretation of genomewide results. This study is motivated to address these challenges. We propose multiset sparse Partial Least Squares path modeling (msPLS), a generalized penalized form of Partial Least Squares path modeling, for the simultaneous modeling of biological pathways across multiple omics domains. msPLS simultaneously models the effect of multiple molecular markers, from multiple omics domains, on the variation of multiple phenotypic variables, while accounting for the relationships between data sources, and provides sparse results. The sparsity in the model helps to provide interpretable results from analyses of hundreds of thousands of biomolecular variables. RESULTS: With simulation studies, we quantified the ability of msPLS to discover associated variables among high dimensional data sources. Furthermore, we analysed high dimensional omics datasets to explore biological pathways associated with Marfan syndrome and with Chronic Lymphocytic Leukaemia. Additionally, we compared the results of msPLS to the results of Multi-Omics Factor Analysis (MOFA), which is an alternative method to analyse this type of data. CONCLUSIONS: msPLS is an multiset multivariate method for the integrative analysis of multiple high dimensional omics data sources. It accounts for the relationship between multiple high dimensional data sources while it provides interpretable results through its sparse solutions. The biomarkers found by msPLS in the omics datasets can be interpreted in terms of biological pathways associated with the pathophysiology of Marfan syndrome and of Chronic Lymphocytic Leukaemia. Additionally, msPLS outperforms MOFA in terms of variation explained in the chronic lymphocytic leukaemia dataset while it identifies the two most important clinical markers for Chronic Lymphocytic Leukaemia AVAILABILITY: http://uva.csala.me/mspls.https://github.com/acsala/2018_msPLS.

The meaning of the term “Big Data” is still subject to debate, in spite of being widely used in biomedical publications. This confusion in definition leads to missed opportunities for peers to exchange knowledge and practices. A better understanding of Big Data may help researchers to identify themselves with the Big Data community. In this study, we investigate the most distinguishing features in “Big Data”-labelled publications by comparing them against publication without this label (nonBig Data), using text mining and machine learning methods. Furthermore, the usage of the term Big Data was analysed over time. Our models could successfully make a distinction between publications labelled with `Big Data' and those without. The most distinguishing features consisted of terms such as `omics', `computing', `storage', and `mining'. We observed that publications that do not use the term Big Data may also address topics that fall under well-accepted definitions of Big Data. Trends suggest that, while the use of the term Big Data increased, it is used less reliably now as compared to earlier years.

MOTIVATION: Recent technological developments have enabled the possibility of genetic and genomic integrated data analysis approaches, where multiple omics datasets from various biological levels are combined and used to describe (disease) phenotypic variations. The main goal is to explain and ultimately predict phenotypic variations by understanding their genetic basis and the interaction of the associated genetic factors. Therefore, understanding the underlying genetic mechanisms of phenotypic variations is an ever increasing research interest in biomedical sciences. In many situations, we have a set of variables that can be considered to be the outcome variables and a set that can be considered to be explanatory variables. Redundancy analysis (RDA) is an analytic method to deal with this type of directionality. Unfortunately, current implementations of RDA cannot deal optimally with the high dimensionality of omics data (p≫n). The existing theoretical framework, based on Ridge penalization, is suboptimal, since it includes all variables in the analysis. As a solution, we propose to use Elastic Net penalization in an iterative RDA framework to obtain a sparse solution. RESULTS: We proposed sparse redundancy analysis (sRDA) for high dimensional omics data analysis. We conducted simulation studies with our software implementation of sRDA to assess the reliability of sRDA. Both the analysis of simulated data, and the analysis of 485 512 methylation markers and 18,424 gene-expression values measured in a set of 55 patients with Marfan syndrome show that sRDA is able to deal with the usual high dimensionality of omics data. AVAILABILITY AND IMPLEMENTATION: http://uva.csala.me/rda. CONTACT: [email protected]. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: Canonical correlation analysis (CCA) can be used to capture the underlying genetic background of a complex disease, by associating two datasets containing information about a patient's phenotypical and genetic details. Often the genetic information is measured on a qualitative scale, consequently ordinary CCA cannot be applied to such data. Moreover, the size of the data in genetic studies can be enormous, thereby making the results difficult to interpret. RESULTS: We developed a penalized non-linear CCA approach that can deal with qualitative data by transforming each qualitative variable into a continuous variable through optimal scaling. Additionally, sparse results were obtained by adapting soft-thresholding to this non-linear version of the CCA. By means of simulation studies, we show that our method is capable of extracting relevant variables out of high-dimensional sets. We applied our method to a genetic dataset containing 144 patients with glial cancer. CONTACT: [email protected].

BACKGROUND: We generalized penalized canonical correlation analysis for analyzing microarray gene-expression measurements for checking completeness of known metabolic pathways and identifying candidate genes for incorporation in the pathway. We used Wold's method for calculation of the canonical variates, and we applied ridge penalization to the regression of pathway genes on canonical variates of the non-pathway genes, and the elastic net to the regression of non-pathway genes on the canonical variates of the pathway genes. RESULTS: We performed a small simulation to illustrate the model's capability to identify new candidate genes to incorporate in the pathway: in our simulations it appeared that a gene was correctly identified if the correlation with the pathway genes was 0.3 or more. We applied the methods to a gene-expression microarray data set of 12, 209 genes measured in 45 patients with glioblastoma, and we considered genes to incorporate in the glioma-pathway: we identified more than 25 genes that correlated > 0.9 with canonical variates of the pathway genes. CONCLUSION: We concluded that penalized canonical correlation analysis is a powerful tool to identify candidate genes in pathway analysis.

BACKGROUND: Serial Analysis of Gene Expressions (SAGE) produces gene expression measurements on a discrete scale, due to the finite number of molecules in the sample. This means that part of the variance in SAGE data should be understood as the sampling error in a binomial or Poisson distribution, whereas other variance sources, in particular biological variance, should be modeled using a continuous distribution function, i.e. a prior on the intensity of the Poisson distribution. One challenge is that such a model predicts a large number of genes with zero counts, which cannot be observed. RESULTS: We present a hierarchical Poisson model with a gamma prior and three different algorithms for estimating the parameters in the model. It turns out that the rate parameter in the gamma distribution can be estimated on the basis of a single SAGE library, whereas the estimate of the shape parameter becomes unstable. This means that the number of zero counts cannot be estimated reliably. When a bivariate model is applied to two SAGE libraries, however, the number of predicted zero counts becomes more stable and in approximate agreement with the number of transcripts observed across a large number of experiments. In all the libraries we analyzed there was a small population of very highly expressed tags, typically 1% of the tags, that could not be accounted for by the model. To handle those tags we chose to augment our model with a non-parametric component. We also show some results based on a log-normal distribution instead of the gamma distribution. CONCLUSION: By modeling SAGE data with a hierarchical Poisson model it is possible to separate the sampling variance from the variance in gene expression. If expression levels are reported at the gene level rather than at the tag level, genes mapped to multiple tags must be kept separate, since their expression levels show a different statistical behavior. A log-normal prior provided a better fit to our data than the gamma prior, but except for a small subpopulation of tags with very high counts, the two priors are similar.

BACKGROUND: Correlation between the expression levels of genes which are located close to each other on the genome has been found in various organisms, including yeast, drosophila and humans. Since such a correlation could be explained by several biochemical, evolutionary, genetic and technological factors, there is a need for statistical models that correspond to specific biological models for the correlation structure. RESULTS: We modelled the pairwise correlation between the expressions of the genes in a Drosophila microarray experiment as a normal mixture under Fisher's z-transform, and fitted the model to the correlations of expressions of adjacent as well as non-adjacent genes. We also analyzed simulated data for comparison. The model provided a good fit to the data. Further, correlation between the activities of two genes could, in most cases, be attributed to either of two factors: the two genes both being active in the same age group (adult or embryo), or the two genes being in proximity of each other on the chromosome. The interaction between these two factors was weak. CONCLUSIONS: Correlation between the activities of adjacent genes is higher than between non-adjacent genes. In the data we analyzed, this appeared, for the most part, to be a constant effect that applied to all pairs of adjacent genes.

BACKGROUND: When DNA microarray data are used for gene clustering, genotype/phenotype correlation studies, or tissue classification the signal intensities are usually transformed and normalized in several steps in order to improve comparability and signal/noise ratio. These steps may include subtraction of an estimated background signal, subtracting the reference signal, smoothing (to account for nonlinear measurement effects), and more. Different authors use different approaches, and it is generally not clear to users which method they should prefer. RESULTS: We used the ratio between biological variance and measurement variance (which is an F-like statistic) as a quality measure for transformation methods, and we demonstrate a method for maximizing that variance ratio on real data. We explore a number of transformations issues, including Box-Cox transformation, baseline shift, partial subtraction of the log-reference signal and smoothing. It appears that the optimal choice of parameters for the transformation methods depends on the data. Further, the behavior of the variance ratio, under the null hypothesis of zero biological variance, appears to depend on the choice of parameters. CONCLUSIONS: The use of replicates in microarray experiments is important. Adjustment for the null-hypothesis behavior of the variance ratio is critical to the selection of transformation method.