Stochastic machine learning via sigma profiles to build a digital chemical space.

This work establishes a different paradigm on digital molecular spaces and their efficient navigation by exploiting sigma profiles. To do so, the remarkable capability of Gaussian processes (GPs), a type of stochastic machine learning model, to correlate and predict physicochemical properties from sigma profiles is demonstrated, outperforming state-of-the-art neural networks previously published. The amount of chemical information encoded in sigma profiles eases the learning burden of machine learning models, permitting the training of GPs on small datasets which, due to their negligible computational cost and ease of implementation, are ideal models to be combined with optimization tools such as gradient search or Bayesian optimization (BO). Gradient search is used to efficiently navigate the sigma profile digital space, quickly converging to local extrema of target physicochemical properties. While this requires the availability of pretrained GP models on existing datasets, such limitations are eliminated with the implementation of BO, which can find global extrema with a limited number of iterations. A remarkable example of this is that of BO toward boiling temperature optimization. Holding no knowledge of chemistry except for the sigma profile and boiling temperature of carbon monoxide (the worst possible initial guess), BO finds the global maximum of the available boiling temperature dataset (over 1,000 molecules encompassing more than 40 families of organic and inorganic compounds) in just 15 iterations (i.e., 15 property measurements), cementing sigma profiles as a powerful digital chemical space for molecular optimization and discovery, particularly when little to no experimental data is initially available.

Codiscovering graphical structure and functional relationships within data: A Gaussian Process framework for connecting the dots.

Most problems within and beyond the scientific domain can be framed into one of the following three levels of complexity of function approximation. Type 1: Approximate an unknown function given input/output data. Type 2: Consider a collection of variables and functions, some of which are unknown, indexed by the nodes and hyperedges of a hypergraph (a generalized graph where edges can connect more than two vertices). Given partial observations of the variables of the hypergraph (satisfying the functional dependencies imposed by its structure), approximate all the unobserved variables and unknown functions. Type 3: Expanding on Type 2, if the hypergraph structure itself is unknown, use partial observations of the variables of the hypergraph to discover its structure and approximate its unknown functions. These hypergraphs offer a natural platform for organizing, communicating, and processing computational knowledge. While most scientific problems can be framed as the data-driven discovery of unknown functions in a computational hypergraph whose structure is known (Type 2), many require the data-driven discovery of the structure (connectivity) of the hypergraph itself (Type 3). We introduce an interpretable Gaussian Process (GP) framework for such (Type 3) problems that does not require randomization of the data, access to or control over its sampling, or sparsity of the unknown functions in a known or learned basis. Its polynomial complexity, which contrasts sharply with the super-exponential complexity of causal inference methods, is enabled by the nonlinear ANOVA capabilities of GPs used as a sensing mechanism.

Multi-response Mendelian randomization: Identification of shared and distinct exposures for multimorbidity and multiple related disease outcomes.

The existing framework of Mendelian randomization (MR) infers the causal effect of one or multiple exposures on one single outcome. It is not designed to jointly model multiple outcomes, as would be necessary to detect causes of more than one outcome and would be relevant to model multimorbidity or other related disease outcomes. Here, we introduce multi-response Mendelian randomization (MR2), an MR method specifically designed for multiple outcomes to identify exposures that cause more than one outcome or, conversely, exposures that exert their effect on distinct responses. MR2 uses a sparse Bayesian Gaussian copula regression framework to detect causal effects while estimating the residual correlation between summary-level outcomes, i.e., the correlation that cannot be explained by the exposures, and vice versa. We show both theoretically and in a comprehensive simulation study how unmeasured shared pleiotropy induces residual correlation between outcomes irrespective of sample overlap. We also reveal how non-genetic factors that affect more than one outcome contribute to their correlation. We demonstrate that by accounting for residual correlation, MR2 has higher power to detect shared exposures causing more than one outcome. It also provides more accurate causal effect estimates than existing methods that ignore the dependence between related responses. Finally, we illustrate how MR2 detects shared and distinct causal exposures for five cardiovascular diseases in two applications considering cardiometabolic and lipidomic exposures and uncovers residual correlation between summary-level outcomes reflecting known relationships between cardiovascular diseases.

Enhancing RNA-seq analysis by addressing all co-existing biases using a self-benchmarking approach with 2D structural insights.

We introduce a groundbreaking approach: the minimum free energy-based Gaussian Self-Benchmarking (MFE-GSB) framework, designed to combat the myriad of biases inherent in RNA-seq data. Central to our methodology is the MFE concept, facilitating the adoption of a Gaussian distribution model tailored to effectively mitigate all co-existing biases within a k-mer counting scheme. The MFE-GSB framework operates on a sophisticated dual-model system, juxtaposing modeling data of uniform k-mer distribution against the real, observed sequencing data characterized by nonuniform k-mer distributions. The framework applies a Gaussian function, guided by the predetermined parameters-mean and SD-derived from modeling data, to fit unknown sequencing data. This dual comparison allows for the accurate prediction of k-mer abundances across MFE categories, enabling simultaneous correction of biases at the single k-mer level. Through validation with both engineered RNA constructs and human tissue RNA samples, its wide-ranging efficacy and applicability are demonstrated.

Exploring the Early Molecular Pathogenesis of Osteoarthritis Using Differential Network Analysis of Human Synovial Fluid.

The molecular mechanisms that drive the onset and development of osteoarthritis (OA) remain largely unknown. In this exploratory study, we used a proteomic platform (SOMAscan assay) to measure the relative abundance of more than 6000 proteins in synovial fluid (SF) from knees of human donors with healthy or mildly degenerated tissues, and knees with late-stage OA from patients undergoing knee replacement surgery. Using a linear mixed effects model, we estimated the differential abundance of 6251 proteins between the three groups. We found 583 proteins upregulated in the late-stage OA, including MMP1, collagenase 3 and interleukin-6. Further, we selected 760 proteins (800 aptamers) based on absolute fold changes between the healthy and mild degeneration groups. To those, we applied Gaussian Graphical Models (GGMs) to analyze the conditional dependence of proteins and to identify key proteins and subnetworks involved in early OA pathogenesis. After regularization and stability selection, we identified 102 proteins involved in GGM networks. Notably, network complexity was lost in the protein graph for mild degeneration when compared to controls, suggesting a disruption in the regular protein interplay. Furthermore, among our main findings were several downregulated (in mild degeneration versus healthy) proteins with unique interactions in the healthy group, one of which, SLCO5A1, has not previously been associated with OA. Our results suggest that this protein is important for healthy joint function. Further, our data suggests that SF proteomics, combined with GGMs, can reveal novel insights into the molecular pathogenesis and identification of biomarker candidates for early-stage OA.

Estimating human mobility in Holocene Western Eurasia with large-scale ancient genomic data.

The recent increase in openly available ancient human DNA samples allows for large-scale meta-analysis applications. Trans-generational past human mobility is one of the key aspects that ancient genomics can contribute to since changes in genetic ancestry-unlike cultural changes seen in the archaeological record-necessarily reflect movements of people. Here, we present an algorithm for spatiotemporal mapping of genetic profiles, which allow for direct estimates of past human mobility from large ancient genomic datasets. The key idea of the method is to derive a spatial probability surface of genetic similarity for each individual in its respective past. This is achieved by first creating an interpolated ancestry field through space and time based on multivariate statistics and Gaussian process regression and then using this field to map the ancient individuals into space according to their genetic profile. We apply this algorithm to a dataset of 3138 aDNA samples with genome-wide data from Western Eurasia in the last 10,000 y. Finally, we condense this sample-wise record with a simple summary statistic into a diachronic measure of mobility for subregions in Western, Central, and Southern Europe. For regions and periods with sufficient data coverage, our similarity surfaces and mobility estimates show general concordance with previous results and provide a meta-perspective of genetic changes and human mobility.

OSCAA: A two-dimensional Gaussian mixture model for copy number variation association analysis.

Copy number variants (CNVs) are prevalent in the human genome and are found to have a profound effect on genomic organization and human diseases. Discovering disease-associated CNVs is critical for understanding the pathogenesis of diseases and aiding their diagnosis and treatment. However, traditional methods for assessing the association between CNVs and disease risks adopt a two-stage strategy conducting quantitative CNV measurements first and then testing for association, which may lead to biased association estimation and low statistical power, serving as a major barrier in routine genome-wide assessment of such variation. In this article, we developed One-Stage CNV-disease Association Analysis (OSCAA), a flexible algorithm to discover disease-associated CNVs for both quantitative and qualitative traits. OSCAA employs a two-dimensional Gaussian mixture model that is built upon the PCs from copy number intensities, accounting for technical biases in CNV detection while simultaneously testing for their effect on outcome traits. In OSCAA, CNVs are identified and their associations with disease risk are evaluated simultaneously in a single step, taking into account the uncertainty of CNV identification in the statistical model. Our simulations demonstrated that OSCAA outperformed the existing one-stage method and traditional two-stage methods by yielding a more accurate estimate of the CNV-disease association, especially for short CNVs or CNVs with weak signals. In conclusion, OSCAA is a powerful and flexible approach for CNV association testing with high sensitivity and specificity, which can be easily applied to different traits and clinical risk predictions.

Enhancing genome-wide populus trait prediction through deep convolutional neural networks.

As a promising model, genome-based plant breeding has greatly promoted the improvement of agronomic traits. Traditional methods typically adopt linear regression models with clear assumptions, neither obtaining the linkage between phenotype and genotype nor providing good ideas for modification. Nonlinear models are well characterized in capturing complex nonadditive effects, filling this gap under traditional methods. Taking populus as the research object, this paper constructs a deep learning method, DCNGP, which can effectively predict the traits including 65 phenotypes. The method was trained on three datasets, and compared with other four classic models-Bayesian ridge regression (BRR), Elastic Net, support vector regression, and dualCNN. The results show that DCNGP has five typical advantages in performance: strong prediction ability on multiple experimental datasets; the incorporation of batch normalization layers and Early-Stopping technology enhancing the generalization capabilities and prediction stability on test data; learning potent features from the data and thus circumventing the tedious steps of manual production; the introduction of a Gaussian Noise layer enhancing predictive capabilities in the case of inherent uncertainties or perturbations; fewer hyperparameters aiding to reduce tuning time across datasets and improve auto-search efficiency. In this way, DCNGP shows powerful predictive ability from genotype to phenotype, which provide an important theoretical reference for building more robust populus breeding programs.

Inference of Locus-Specific Population Mixtures from Linked Genome-Wide Allele Frequencies.

Admixture between populations and species is common in nature. Since the influx of new genetic material might be either facilitated or hindered by selection, variation in mixture proportions along the genome is expected in organisms undergoing recombination. Various graph-based models have been developed to better understand these evolutionary dynamics of population splits and mixtures. However, current models assume a single mixture rate for the entire genome and do not explicitly account for linkage. Here, we introduce TreeSwirl, a novel method for inferring branch lengths and locus-specific mixture proportions by using genome-wide allele frequency data, assuming that the admixture graph is known or has been inferred. TreeSwirl builds upon TreeMix that uses Gaussian processes to estimate the presence of gene flow between diverged populations. However, in contrast to TreeMix, our model infers locus-specific mixture proportions employing a hidden Markov model that accounts for linkage. Through simulated data, we demonstrate that TreeSwirl can accurately estimate locus-specific mixture proportions and handle complex demographic scenarios. It also outperforms related D- and f-statistics in terms of accuracy and sensitivity to detect introgressed loci.

Fast matrix completion in epigenetic methylation studies with informative covariates.

DNA methylation is an important epigenetic mark that modulates gene expression through the inhibition of transcriptional proteins binding to DNA. As in many other omics experiments, the issue of missing values is an important one, and appropriate imputation techniques are important in avoiding an unnecessary sample size reduction as well as to optimally leverage the information collected. We consider the case where relatively few samples are processed via an expensive high-density whole genome bisulfite sequencing (WGBS) strategy and a larger number of samples is processed using more affordable low-density, array-based technologies. In such cases, one can impute the low-coverage (array-based) methylation data using the high-density information provided by the WGBS samples. In this paper, we propose an efficient Linear Model of Coregionalisation with informative Covariates (LMCC) to predict missing values based on observed values and covariates. Our model assumes that at each site, the methylation vector of all samples is linked to the set of fixed factors (covariates) and a set of latent factors. Furthermore, we exploit the functional nature of the data and the spatial correlation across sites by assuming some Gaussian processes on the fixed and latent coefficient vectors, respectively. Our simulations show that the use of covariates can significantly improve the accuracy of imputed values, especially in cases where missing data contain some relevant information about the explanatory variable. We also showed that our proposed model is particularly efficient when the number of columns is much greater than the number of rows-which is usually the case in methylation data analysis. Finally, we apply and compare our proposed method with alternative approaches on two real methylation datasets, showing how covariates such as cell type, tissue type or age can enhance the accuracy of imputed values.

Model-based multifacet clustering with high-dimensional omics applications.

High-dimensional omics data often contain intricate and multifaceted information, resulting in the coexistence of multiple plausible sample partitions based on different subsets of selected features. Conventional clustering methods typically yield only one clustering solution, limiting their capacity to fully capture all facets of cluster structures in high-dimensional data. To address this challenge, we propose a model-based multifacet clustering (MFClust) method based on a mixture of Gaussian mixture models, where the former mixture achieves facet assignment for gene features and the latter mixture determines cluster assignment of samples. We demonstrate superior facet and cluster assignment accuracy of MFClust through simulation studies. The proposed method is applied to three transcriptomic applications from postmortem brain and lung disease studies. The result captures multifacet clustering structures associated with critical clinical variables and provides intriguing biological insights for further hypothesis generation and discovery.

Bayesian joint modeling of multivariate longitudinal and survival outcomes using Gaussian copulas.

There is an increasing interest in the use of joint models for the analysis of longitudinal and survival data. While random effects models have been extensively studied, these models can be hard to implement and the fixed effect regression parameters must be interpreted conditional on the random effects. Copulas provide a useful alternative framework for joint modeling. One advantage of using copulas is that practitioners can directly specify marginal models for the outcomes of interest. We develop a joint model using a Gaussian copula to characterize the association between multivariate longitudinal and survival outcomes. Rather than using an unstructured correlation matrix in the copula model to characterize dependence structure as is common, we propose a novel decomposition that allows practitioners to impose structure (e.g., auto-regressive) which provides efficiency gains in small to moderate sample sizes and reduces computational complexity. We develop a Markov chain Monte Carlo model fitting procedure for estimation. We illustrate the method's value using a simulation study and present a real data analysis of longitudinal quality of life and disease-free survival data from an International Breast Cancer Study Group trial.

A semiparametric Gaussian mixture model for chest CT-based 3D blood vessel reconstruction.

Computed tomography (CT) has been a powerful diagnostic tool since its emergence in the 1970s. Using CT data, 3D structures of human internal organs and tissues, such as blood vessels, can be reconstructed using professional software. This 3D reconstruction is crucial for surgical operations and can serve as a vivid medical teaching example. However, traditional 3D reconstruction heavily relies on manual operations, which are time-consuming, subjective, and require substantial experience. To address this problem, we develop a novel semiparametric Gaussian mixture model tailored for the 3D reconstruction of blood vessels. This model extends the classical Gaussian mixture model by enabling nonparametric variations in the component-wise parameters of interest according to voxel positions. We develop a kernel-based expectation-maximization algorithm for estimating the model parameters, accompanied by a supporting asymptotic theory. Furthermore, we propose a novel regression method for optimal bandwidth selection. Compared to the conventional cross-validation-based (CV) method, the regression method outperforms the CV method in terms of computational and statistical efficiency. In application, this methodology facilitates the fully automated reconstruction of 3D blood vessel structures with remarkable accuracy.

Simultaneous clustering and estimation of networks in multiple graphical models.

Gaussian graphical models are widely used to study the dependence structure among variables. When samples are obtained from multiple conditions or populations, joint analysis of multiple graphical models are desired due to their capacity to borrow strength across populations. Nonetheless, existing methods often overlook the varying levels of similarity between populations, leading to unsatisfactory results. Moreover, in many applications, learning the population-level clustering structure itself is of particular interest. In this article, we develop a novel method, called Simultaneous Clustering and Estimation of Networks via Tensor decomposition (SCENT), that simultaneously clusters and estimates graphical models from multiple populations. Precision matrices from different populations are uniquely organized as a three-way tensor array, and a low-rank sparse model is proposed for joint population clustering and network estimation. We develop a penalized likelihood method and an augmented Lagrangian algorithm for model fitting. We also establish the clustering accuracy and norm consistency of the estimated precision matrices. We demonstrate the efficacy of the proposed method with comprehensive simulation studies. The application to the Genotype-Tissue Expression multi-tissue gene expression data provides important insights into tissue clustering and gene coexpression patterns in multiple brain tissues.

Adaptive Gaussian Markov random fields for child mortality estimation.

The under-5 mortality rate (U5MR), a critical health indicator, is typically estimated from household surveys in lower and middle income countries. Spatio-temporal disaggregation of household survey data can lead to highly variable estimates of U5MR, necessitating the usage of smoothing models which borrow information across space and time. The assumptions of common smoothing models may be unrealistic when certain time periods or regions are expected to have shocks in mortality relative to their neighbors, which can lead to oversmoothing of U5MR estimates. In this paper, we develop a spatial and temporal smoothing approach based on Gaussian Markov random field models which incorporate knowledge of these expected shocks in mortality. We demonstrate the potential for these models to improve upon alternatives not incorporating knowledge of expected shocks in a simulation study. We apply these models to estimate U5MR in Rwanda at the national level from 1985 to 2019, a time period which includes the Rwandan civil war and genocide.

A modeling framework for detecting and leveraging node-level information in Bayesian network inference.

Bayesian graphical models are powerful tools to infer complex relationships in high dimension, yet are often fraught with computational and statistical challenges. If exploited in a principled way, the increasing information collected alongside the data of primary interest constitutes an opportunity to mitigate these difficulties by guiding the detection of dependence structures. For instance, gene network inference may be informed by the use of publicly available summary statistics on the regulation of genes by genetic variants. Here we present a novel Gaussian graphical modeling framework to identify and leverage information on the centrality of nodes in conditional independence graphs. Specifically, we consider a fully joint hierarchical model to simultaneously infer (i) sparse precision matrices and (ii) the relevance of node-level information for uncovering the sought-after network structure. We encode such information as candidate auxiliary variables using a spike-and-slab submodel on the propensity of nodes to be hubs, which allows hypothesis-free selection and interpretation of a sparse subset of relevant variables. As efficient exploration of large posterior spaces is needed for real-world applications, we develop a variational expectation conditional maximization algorithm that scales inference to hundreds of samples, nodes and auxiliary variables. We illustrate and exploit the advantages of our approach in simulations and in a gene network study which identifies hub genes involved in biological pathways relevant to immune-mediated diseases.

DeepGpgs: a novel deep learning framework for predicting arginine methylation sites combined with Gaussian prior and gated self-attention mechanism.

Protein arginine methylation is an important posttranslational modification (PTM) associated with protein functional diversity and pathological conditions including cancer. Identification of methylation binding sites facilitates a better understanding of the molecular function of proteins. Recent developments in the field of deep neural networks have led to a proliferation of deep learning-based methylation identification studies because of their fast and accurate prediction. In this paper, we propose DeepGpgs, an advanced deep learning model incorporating Gaussian prior and gated attention mechanism. We introduce a residual network channel to extract the evolutionary information of proteins. Then we combine the adaptive embedding with bidirectional long short-term memory networks to form a context-shared encoder layer. A gated multi-head attention mechanism is followed to obtain the global information about the sequence. A Gaussian prior is injected into the sequence to assist in predicting PTMs. We also propose a weighted joint loss function to alleviate the false negative problem. We empirically show that DeepGpgs improves Matthews correlation coefficient by 6.3% on the arginine methylation independent test set compared with the existing state-of-the-art methylation site prediction methods. Furthermore, DeepGpgs has good robustness in phosphorylation site prediction of SARS-CoV-2, which indicates that DeepGpgs has good transferability and the potential to be extended to other modification sites prediction. The open-source code and data of the DeepGpgs can be obtained from https://github.com/saizhou1/DeepGpgs.

Context-dependent gene regulatory network reveals regulation dynamics and cell trajectories using unspliced transcripts.

Gene regulatory networks govern complex gene expression programs in various biological phenomena, including embryonic development, cell fate decisions and oncogenesis. Single-cell techniques are increasingly being used to study gene expression, providing higher resolution than traditional approaches. However, inferring a comprehensive gene regulatory network across different cell types remains a challenge. Here, we propose to construct context-dependent gene regulatory networks (CDGRNs) from single-cell RNA sequencing data utilizing both spliced and unspliced transcript expression levels. A gene regulatory network is decomposed into subnetworks corresponding to different transcriptomic contexts. Each subnetwork comprises the consensus active regulation pairs of transcription factors and their target genes shared by a group of cells, inferred by a Gaussian mixture model. We find that the union of gene regulation pairs in all contexts is sufficient to reconstruct differentiation trajectories. Functions specific to the cell cycle, cell differentiation or tissue-specific functions are enriched throughout the developmental process in each context. Surprisingly, we also observe that the network entropy of CDGRNs decreases along differentiation trajectories, indicating directionality in differentiation. Overall, CDGRN allows us to establish the connection between gene regulation at the molecular level and cell differentiation at the macroscopic level.

scGMAAE: Gaussian mixture adversarial autoencoders for diversification analysis of scRNA-seq data.

The progress of single-cell RNA sequencing (scRNA-seq) has led to a large number of scRNA-seq data, which are widely used in biomedical research. The noise in the raw data and tens of thousands of genes pose a challenge to capture the real structure and effective information of scRNA-seq data. Most of the existing single-cell analysis methods assume that the low-dimensional embedding of the raw data belongs to a Gaussian distribution or a low-dimensional nonlinear space without any prior information, which limits the flexibility and controllability of the model to a great extent. In addition, many existing methods need high computational cost, which makes them difficult to be used to deal with large-scale datasets. Here, we design and develop a depth generation model named Gaussian mixture adversarial autoencoders (scGMAAE), assuming that the low-dimensional embedding of different types of cells follows different Gaussian distributions, integrating Bayesian variational inference and adversarial training, as to give the interpretable latent representation of complex data and discover the statistical distribution of different types of cells. The scGMAAE is provided with good controllability, interpretability and scalability. Therefore, it can process large-scale datasets in a short time and give competitive results. scGMAAE outperforms existing methods in several ways, including dimensionality reduction visualization, cell clustering, differential expression analysis and batch effect removal. Importantly, compared with most deep learning methods, scGMAAE requires less iterations to generate the best results.

Graph deep learning enabled spatial domains identification for spatial transcriptomics.

Advancing spatially resolved transcriptomics (ST) technologies help biologists comprehensively understand organ function and tissue microenvironment. Accurate spatial domain identification is the foundation for delineating genome heterogeneity and cellular interaction. Motivated by this perspective, a graph deep learning (GDL) based spatial clustering approach is constructed in this paper. First, the deep graph infomax module embedded with residual gated graph convolutional neural network is leveraged to address the gene expression profiles and spatial positions in ST. Then, the Bayesian Gaussian mixture model is applied to handle the latent embeddings to generate spatial domains. Designed experiments certify that the presented method is superior to other state-of-the-art GDL-enabled techniques on multiple ST datasets. The codes and dataset used in this manuscript are summarized at https://github.com/narutoten520/SCGDL.