Sparse inverse covariance estimation in Gaussian graphical models

One of the fundamental tasks in science is to find explainable relationships between observed phenomena. Recent work has addressed this problem by attempting to learn the structure of graphical models - especially Gaussian models - by the imposition of sparsity constraints. The graphical lasso is a popular method for learning the structure of a Gaussian model. It uses regularisation to impose sparsity. In real-world problems, there may be latent variables that confound the relationships between the observed variables. Ignoring these latents, and imposing sparsity in the space of the visibles, may lead to the pruning of important structural relationships. We address this problem by introducing an expectation maximisation (EM) method for learning a Gaussian model that is sparse in the joint space of visible and latent variables. By extending this to a conditional mixture, we introduce multiple structures, and allow side information to be used to predict which structure is most appropriate for each data point. Finally, we handle non-Gaussian data by extending each sparse latent Gaussian to a Gaussian copula. We train these models on a financial data set; we find the structures to be interpretable, and the new models to perform better than their existing competitors. A potential problem with the mixture model is that it does not require the structure to persist in time, whereas this may be expected in practice. So we construct an input-output HMM with sparse Gaussian emissions. But the main result is that, provided the side information is rich enough, the temporal component of the model provides little benefit, and reduces efficiency considerably. The GWishart distribution may be used as the basis for a Bayesian approach to learning a sparse Gaussian. However, sampling from this distribution often limits the efficiency of inference in these models. We make a small change to the state-of-the-art block Gibbs sampler to improve its efficiency. We then introduce a Hamiltonian Monte Carlo sampler that is much more efficient than block Gibbs, especially in high dimensions. We use these samplers to compare a Bayesian approach to learning a sparse Gaussian with the (non-Bayesian) graphical lasso. We find that, even when limited to the same time budget, the Bayesian method can perform better. In summary, this thesis introduces practically useful advances in structure learning for Gaussian graphical models and their extensions. The contributions include the addition of latent variables, a non-Gaussian extension, (temporal) conditional mixtures, and methods for efficient inference in a Bayesian formulation

On the Relation between a Nonlinear Elliptic Equation and Its Uniform Approximation

AbstractThe qualitative behavior of the solution set of nonlinear elliptic boundary value problems has in some instances been studied by reducing the partial differential equation to a related algebraic equation. Although this procedure often gives a good picture of the bifurcation diagram, it can be quite wrong. In this paper some relationships between the solutions of the two problems are investigated

The Gene Ontology knowledgebase in 2023

The Gene Ontology (GO) knowledgebase (http://geneontology.org) is a comprehensive resource concerning the functions of genes and gene products (proteins and noncoding RNAs). GO annotations cover genes from organisms across the tree of life as well as viruses, though most gene function knowledge currently derives from experiments carried out in a relatively small number of model organisms. Here, we provide an updated overview of the GO knowledgebase, as well as the efforts of the broad, international consortium of scientists that develops, maintains, and updates the GO knowledgebase. The GO knowledgebase consists of three components: (1) the GO-a computational knowledge structure describing the functional characteristics of genes; (2) GO annotations-evidence-supported statements asserting that a specific gene product has a particular functional characteristic; and (3) GO Causal Activity Models (GO-CAMs)-mechanistic models of molecular "pathways" (GO biological processes) created by linking multiple GO annotations using defined relations. Each of these components is continually expanded, revised, and updated in response to newly published discoveries and receives extensive QA checks, reviews, and user feedback. For each of these components, we provide a description of the current contents, recent developments to keep the knowledgebase up to date with new discoveries, and guidance on how users can best make use of the data that we provide. We conclude with future directions for the project

Comprehensive enhancer-target gene assignments improve gene set level interpretation of genome-wide regulatory data

Abstract Background Revealing the gene targets of distal regulatory elements is challenging yet critical for interpreting regulome data. Experiment-derived enhancer-gene links are restricted to a small set of enhancers and/or cell types, while the accuracy of genome-wide approaches remains elusive due to the lack of a systematic evaluation. We combined multiple spatial and in silico approaches for defining enhancer locations and linking them to their target genes aggregated across >500 cell types, generating 1860 human genome-wide distal enhancer-to-target gene definitions (EnTDefs). To evaluate performance, we used gene set enrichment (GSE) testing on 87 independent ENCODE ChIP-seq datasets of 34 transcription factors (TFs) and assessed concordance of results with known TF Gene Ontology annotations, and other benchmarks. Results The top ranked 741 (40%) EnTDefs significantly outperform the common, naïve approach of linking distal regions to the nearest genes, and the top 10 EnTDefs perform well when applied to ChIP-seq data of other cell types. The GSE-based ranking of EnTDefs is highly concordant with ranking based on overlap with curated benchmarks of enhancer-gene interactions. Both our top general EnTDef and cell-type-specific EnTDefs significantly outperform seven independent computational and experiment-based enhancer-gene pair datasets. We show that using our top EnTDefs for GSE with either genome-wide DNA methylation or ATAC-seq data is able to better recapitulate the biological processes changed in gene expression data performed in parallel for the same experiment than our lower-ranked EnTDefs. Conclusions Our findings illustrate the power of our approach to provide genome-wide interpretation regardless of cell type.http://deepblue.lib.umich.edu/bitstream/2027.42/173874/1/13059_2022_Article_2668.pd

The Gene Ontology knowledgebase in 2023.

The Gene Ontology (GO) knowledgebase (http://geneontology.org) is a comprehensive resource concerning the functions of genes and gene products (proteins and noncoding RNAs). GO annotations cover genes from organisms across the tree of life as well as viruses, though most gene function knowledge currently derives from experiments carried out in a relatively small number of model organisms. Here, we provide an updated overview of the GO knowledgebase, as well as the efforts of the broad, international consortium of scientists that develops, maintains, and updates the GO knowledgebase. The GO knowledgebase consists of three components: (1) the GO-a computational knowledge structure describing the functional characteristics of genes; (2) GO annotations-evidence-supported statements asserting that a specific gene product has a particular functional characteristic; and (3) GO Causal Activity Models (GO-CAMs)-mechanistic models of molecular "pathways" (GO biological processes) created by linking multiple GO annotations using defined relations. Each of these components is continually expanded, revised, and updated in response to newly published discoveries and receives extensive QA checks, reviews, and user feedback. For each of these components, we provide a description of the current contents, recent developments to keep the knowledgebase up to date with new discoveries, and guidance on how users can best make use of the data that we provide. We conclude with future directions for the project

The Gene Ontology Knowledgebase in 2023

: The Gene Ontology (GO) knowledgebase (http://geneontology.org) is a comprehensive resource concerning the functions of genes and gene products (proteins and non-coding RNAs). GO annotations cover genes from organisms across the tree of life as well as viruses, though most gene function knowledge currently derives from experiments carried out in a relatively small number of model organisms. Here, we provide an updated overview of the GO knowledgebase, as well as the efforts of the broad, international consortium of scientists that develops, maintains and updates the GO knowledgebase. The GO knowledgebase consists of three components: 1) the Gene Ontology - a computational knowledge structure describing functional characteristics of genes; 2) GO annotations - evidence-supported statements asserting that a specific gene product has a particular functional characteristic; and 3) GO Causal Activity Models (GO-CAMs) - mechanistic models of molecular "pathways" (GO biological processes) created by linking multiple GO annotations using defined relations. Each of these components is continually expanded, revised and updated in response to newly published discoveries, and receives extensive QA checks, reviews and user feedback. For each of these components, we provide a description of the current contents, recent developments to keep the knowledgebase up to date with new discoveries, as well as guidance on how users can best make use of the data we provide. We conclude with future directions for the project