Obtaining the desired effect of drugs is highly dependent on their molecular geometries. Thus, the current prevailing paradigm focuses on 3D point-cloud atom representations, utilizing graph neural network (GNN) parametrizations, with rotational symmetries baked in via E(3) invariant layers. We prove that such models must necessarily disregard chirality, a geometric property of the molecules that cannot be superimposed on their mirror image by rotation and translation. Chirality plays a key role in determining drug safety and potency. To address this glaring issue, we introduce a novel field-based representation, proposing reference rotations that replace rotational symmetry constraints. The proposed model captures all molecular geometries including chirality, while still achieving highly competitive performance with E(3)-based methods across standard benchmarking metrics.

Spatiotemporal dynamics models are fundamental for various domains, from heat propagation in materials to oceanic and atmospheric flows. However, currently available neural network-based spatiotemporal modeling approaches fall short when faced with data that is collected randomly over time and space, as is often the case with sensor networks in real-world applications like crowdsourced earthquake detection or pollution monitoring. In response, we developed a new method that can effectively learn spatiotemporal dynamics from such point process observations. Our model integrates techniques from neural differential equations, neural point processes, implicit neural representations and amortized variational inference to model both the dynamics of the system and the probabilistic locations and timings of observations. It outperforms existing methods on challenging spatiotemporal datasets by offering substantial improvements in predictive accuracy and computational efficiency, making it a useful tool for modeling and understanding complex dynamical systems observed under realistic, unconstrained conditions.

Bayesian optimisation (BO) using a Gaussian process (GP)-based surrogate model is a powerful tool for solving black-box optimisation problems but does not scale well to high-dimensional data. Previous works have proposed to use variational autoencoders (VAEs) to project high-dimensional data onto a low-dimensional latent space and to implement BO in the inferred latent space. In this work, we propose a conditional generative model for efficient high-dimensional BO that uses a GP surrogate model together with GP prior VAEs. A GP prior VAE extends the standard VAE by conditioning the generative and inference model on auxiliary covariates, capturing complex correlations across samples with a GP. Our model incorporates the observed target quantity values as auxiliary covariates learning a structured latent space that is better suited for the GP-based BO surrogate model. It handles partially observed auxiliary covariates using a unifying probabilistic framework and can also incorporate additional auxiliary covariates that may be available in real-world applications. We demonstrate that our method improves upon existing latent space BO methods on simulated datasets as well as on commonly used benchmarks.

High-dimensional time-series datasets are common in domains such as healthcare and economics. Variational autoencoder (VAE) models, where latent variables are modeled with a Gaussian process (GP) prior, have become a prominent model class to analyze such correlated datasets. However, their applications are challenged by the inherent cubic time complexity that requires specific GP approximation techniques, as well as the general challenge of modeling both shared and individual-specific correlations across time. Though inducing points enhance GP prior VAE scalability, optimizing them remains challenging, especially since discrete covariates resist gradient‑based methods. In this work, we propose a scalable basis function approximation technique for GP prior VAEs that mitigates these challenges and results in linear time complexity, with a global parametrization that eliminates the need for amortized variational inference and the associated amortization gap, making it well-suited for conditional generation tasks where accuracy and efficiency are crucial. Empirical evaluations on synthetic and real-world benchmark datasets demonstrate that our approach not only improves scalability and interpretability but also drastically enhances predictive performance.

MOTIVATION: Multiple instance learning (MIL) provides a structured approach to patient phenotype prediction with single-cell RNA-sequencing (scRNA-seq) data. However, existing MIL methods tend to overlook the hierarchical structure inherent in scRNA-seq data, especially the biological groupings of cells or cell types. This limitation may lead to suboptimal performance and poor interpretability at higher levels of cellular division. RESULTS: To address this gap, we present a novel approach to incorporate hierarchical information into the attention-based MIL framework. Specifically, our model applies the attention-based aggregation mechanism over both cells and cell types, thus enforcing a hierarchical structure on the flow of information throughout the model. Across extensive experiments, our proposed approach demonstrates highly competitive performance and shows robustness against limited sample sizes. Moreover, ablation test results show that simply applying the attention mechanism on cell types instead of cells leads to improved performance, underscoring the benefits of incorporating the hierarchical groupings. By identifying the critical cell types that are most relevant for prediction, we show that our model is capable of capturing biologically meaningful associations, suggesting its potential to facilitate biological discoveries. AVAILABILITY AND IMPLEMENTATION: Our source code is available at https://github.com/minhchaudo/hier-mil. All datasets used in this study are publicly available online.

Randomized controlled trials (RCTs) are the accepted standard for treatment effect estimation but they can be infeasible due to ethical reasons and prohibitive costs. Single-arm trials, where all patients belong to the treatment group, can be a viable alternative but require access to an external control group. We propose an identifiable deep latent-variable model for this scenario that can also account for missing covariate observations by modeling their structured missingness patterns. Our method uses amortized variational inference to learn both group-specific and identifiable shared latent representations, which can subsequently be used for {\em (i)} patient matching if treatment outcomes are not available for the treatment group, or for {\em (ii)} direct treatment effect estimation assuming outcomes are available for both groups. We evaluate the model on a public benchmark as well as on a data set consisting of a published RCT study and real-world electronic health records. Compared to previous methods, our results show improved performance both for direct treatment effect estimation as well as for effect estimation via patient matching.

Longitudinal data are important in numerous fields, such as healthcare, sociology and seismology, but real-world datasets present notable challenges for practitioners because they can be high-dimensional, contain structured missingness patterns, and measurement time points can be governed by an unknown stochastic process. While various solutions have been suggested, the majority of them have been designed to account for only one of these challenges. In this work, we propose a flexible and efficient latent-variable model that is capable of addressing all these limitations. Our approach utilizes Gaussian processes to capture correlations between samples and their associated missingness masks as well as to model the underlying point process. We construct our model as a variational autoencoder together with deep neural network parameterised decoder and encoder models, and develop a scalable amortised variational inference approach for efficient model training. We demonstrate competitive performance using both simulated and real datasets.

Conditional variational autoencoders (CVAEs) are versatile deep latent variable models that extend the standard VAE framework by conditioning the generative model with auxiliary covariates. The original CVAE model assumes that the data samples are independent, whereas more recent conditional VAE models, such as the Gaussian process (GP) prior VAEs, can account for complex correlation structures across all data samples. While several methods have been proposed to learn standard VAEs from partially observed datasets, these methods fall short for conditional VAEs. In this work, we propose a method to learn conditional VAEs from datasets in which auxiliary covariates can contain missing values as well. The proposed method augments the conditional VAEs with a prior distribution for the missing covariates and estimates their posterior using amortised variational inference. At training time, our method accounts for the uncertainty associated with the missing covariates while simultaneously maximising the evidence lower bound. We develop computationally efficient methods to learn CVAEs and GP prior VAEs that are compatible with mini-batching. Our experiments on simulated datasets as well as on real-world biomedical datasets show that the proposed method outperforms previous methods in learning conditional VAEs from non-temporal, temporal, and longitudinal datasets.

We introduce a novel grid-independent model for learning partial differential equations (PDEs) from noisy and partial observations on irregular spatiotemporal grids. We propose a space-time continuous latent neural PDE model with an efficient probabilistic framework and a novel encoder design for improved data efficiency and grid independence. The latent state dynamics are governed by a PDE model that combines the collocation method and the method of lines. We employ amortized variational inference for approximate posterior estimation and utilize a multiple shooting technique for enhanced training speed and stability. Our model demonstrates state-of-the-art performance on complex synthetic and real-world datasets, overcoming limitations of previous approaches and effectively handling partially-observed data. The proposed model outperforms recent methods, showing its potential to advance data-driven PDE modeling and enabling robust, grid-independent modeling of complex partially-observed dynamic processes across various domains.

MOTIVATION: Signal peptides (SPs) are short amino acid segments present at the N-terminus of newly synthesized proteins that facilitate protein translocation into the lumen of the endoplasmic reticulum, after which they are cleaved off. Specific regions of SPs influence the efficiency of protein translocation, and small changes in their primary structure can abolish protein secretion altogether. The lack of conserved motifs across SPs, sensitivity to mutations, and variability in the length of the peptides make SP prediction a challenging task that has been extensively pursued over the years. RESULTS: We introduce TSignal, a deep transformer-based neural network architecture that utilizes BERT language models and dot-product attention techniques. TSignal predicts the presence of SPs and the cleavage site between the SP and the translocated mature protein. We use common benchmark datasets and show competitive accuracy in terms of SP presence prediction and state-of-the-art accuracy in terms of cleavage site prediction for most of the SP types and organism groups. We further illustrate that our fully data-driven trained model identifies useful biological information on heterogeneous test sequences. AVAILABILITY AND IMPLEMENTATION: TSignal is available at: https://github.com/Dumitrescu-Alexandru/TSignal.

MOTIVATION: T cells use T cell receptors (TCRs) to recognize small parts of antigens, called epitopes, presented by major histocompatibility complexes. Once an epitope is recognized, an immune response is initiated and T cell activation and proliferation by clonal expansion begin. Clonal populations of T cells with identical TCRs can remain in the body for years, thus forming immunological memory and potentially mappable immunological signatures, which could have implications in clinical applications including infectious diseases, autoimmunity and tumor immunology. RESULTS: We introduce TCRconv, a deep learning model for predicting recognition between TCRs and epitopes. TCRconv uses a deep protein language model and convolutions to extract contextualized motifs and provides state-of-the-art TCR-epitope prediction accuracy. Using TCR repertoires from COVID-19 patients, we demonstrate that TCRconv can provide insight into T cell dynamics and phenotypes during the disease. AVAILABILITY AND IMPLEMENTATION: TCRconv is available at https://github.com/emmijokinen/tcrconv. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: T cells play an essential role in adaptive immune system to fight pathogens and cancer but may also give rise to autoimmune diseases. The recognition of a peptide-MHC (pMHC) complex by a T cell receptor (TCR) is required to elicit an immune response. Many machine learning models have been developed to predict the binding, but generalizing predictions to pMHCs outside the training data remains challenging. RESULTS: We have developed a new machine learning model that utilizes information about the TCR from both α and β chains, epitope sequence, and MHC. Our method uses ProtBERT embeddings for the amino acid sequences of both chains and the epitope, as well as convolution and multi-head attention architectures. We show the importance of each input feature as well as the benefit of including epitopes with only a few TCRs to the training data. We evaluate our model on existing databases and show that it compares favorably against other state-of-the-art models. AVAILABILITY AND IMPLEMENTATION: https://github.com/DaniTheOrange/EPIC-TRACE.

BACKGROUND: DNA methylation plays an important role in studying the epigenetics of various biological processes including many diseases. Although differential methylation of individual cytosines can be informative, given that methylation of neighboring CpGs are typically correlated, analysis of differentially methylated regions is often of more interest. RESULTS: We have developed a probabilistic method and software, LuxHMM, that uses hidden Markov model (HMM) to segment the genome into regions and a Bayesian regression model, which allows handling of multiple covariates, to infer differential methylation of regions. Moreover, our model includes experimental parameters that describe the underlying biochemistry in bisulfite sequencing and model inference is done using either variational inference for efficient genome-scale analysis or Hamiltonian Monte Carlo (HMC). CONCLUSIONS: Analyses of real and simulated bisulfite sequencing data demonstrate the competitive performance of LuxHMM compared with other published differential methylation analysis methods.

The variational autoencoder (VAE) is a popular deep latent variable model used to analyse high-dimensional datasets by learning a low-dimensional latent representation of the data. It simultaneously learns a generative model and an inference network to perform approximate posterior inference. Recently proposed extensions to VAEs that can handle temporal and longitudinal data have applications in healthcare, behavioural modelling, and predictive maintenance. However, these extensions do not account for heterogeneous data, i.e., data comprising of continuous and discrete attributes, which is common in many real-life applications. In this work, we propose the heterogeneous longitudinal VAE (HL-VAE) that extends the existing temporal and longitudinal VAEs to heterogeneous data for imputing missing values and unseen time point prediction. HL-VAE provides efficient inference for high-dimensional datasets and includes likelihood models for continuous, count, categorical, and ordinal data while accounting for missing observations. We demonstrate our model’s efficacy through simulated as well as clinical datasets, and show that our proposed model achieves competitive performance in missing value imputation and predictive accuracy.

Recent machine learning advances have proposed black-box estimation of \textit{unknown continuous-time system dynamics} directly from data. However, earlier works are based on approximative solutions or point estimates. We propose a novel Bayesian nonparametric model that uses Gaussian processes to infer posteriors of unknown ODE systems directly from data. We derive sparse variational inference with decoupled functional sampling to represent vector field posteriors. We also introduce a probabilistic shooting augmentation to enable efficient inference from arbitrarily long trajectories. The method demonstrates the benefit of computing vector field posteriors, with predictive uncertainty scores outperforming alternative methods on multiple ODE learning tasks.

MOTIVATION: Research on epigenetic modifications and other chromatin features at genomic regulatory elements elucidates essential biological mechanisms including the regulation of gene expression. Despite the growing number of epigenetic datasets, new tools are still needed to discover novel distinctive patterns of heterogeneous epigenetic signals at regulatory elements. RESULTS: We introduce ChromDMM, a product Dirichlet-multinomial mixture model for clustering genomic regions that are characterized by multiple chromatin features. ChromDMM extends the mixture model framework by profile shifting and flipping that can probabilistically account for inaccuracies in the position and strand-orientation of the genomic regions. Owing to hyper-parameter optimization, ChromDMM can also regularize the smoothness of the epigenetic profiles across the consecutive genomic regions. With simulated data, we demonstrate that ChromDMM clusters, shifts and strand-orients the profiles more accurately than previous methods. With ENCODE data, we show that the clustering of enhancer regions in the human genome reveals distinct patterns in several chromatin features. We further validate the enhancer clusters by their enrichment for transcriptional regulatory factor binding sites. AVAILABILITY AND IMPLEMENTATION: ChromDMM is implemented as an R package and is available at https://github.com/MariaOsmala/ChromDMM. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

BACKGROUND: Transcription factors (TFs) bind regulatory DNA regions with sequence specificity, form complexes and regulate gene expression. In cooperative TF-TF binding, two transcription factors bind onto a shared DNA binding site as a pair. Previous work has demonstrated pairwise TF-TF-DNA interactions with position weight matrices (PWMs), which may however not sufficiently take into account the complexity and flexibility of pairwise binding. RESULTS: We propose two random forest (RF) methods for joint TF-TF binding site prediction: ComBind and JointRF. We train models with previously published large-scale CAP-SELEX DNA libraries, which comprise DNA sequences enriched for binding of a selected TF pair. JointRF builds a random forest with sub-sequences selected from CAP-SELEX DNA reads with previously proposed pairwise PWM. JointRF outperforms (area under receiver operating characteristics curve, AUROC, 0.75) the current state-of-the-art method i.e. orientation and spacing specific pairwise PWMs (AUROC 0.59). Thus, JointRF may be utilized to improve prediction accuracy for pre-determined binding preferences. However, pairwise TF binding is currently considered flexible; a pair may bind DNA with different orientations and amounts of dinucleotide gaps or overlap between the two motifs. Thus, we developed ComBind, which utilizes random forests by considering simultaneously multiple orientations and spacings of the two factors. Our approach outperforms (AUROC 0.78) PWMs, as well as JointRF (p<0.00195). ComBind provides an approach for predicting TF-TF binding sites without prior knowledge on pairwise binding preferences. However, more research is needed to assess ComBind eligibility for practical applications. CONCLUSIONS: Random forest is well suited for modeling pairwise TF-TF-DNA binding specificities, and ComBind provides an improvement to pairwise binding site prediction accuracy.

BACKGROUND: cfMeDIP-seq is a low-cost method for determining the DNA methylation status of cell-free DNA and it has been successfully combined with statistical methods for accurate cancer diagnostics. We investigate the diagnostic classification aspect by applying statistical tests and dimension reduction techniques for feature selection and probabilistic modeling for the cancer type classification, and we also study the effect of sequencing depth. METHODS: We experiment with a variety of statistical methods that use different feature selection and feature extraction methods as well as probabilistic classifiers for diagnostic decision making. We test the (moderated) t-tests and the Fisher's exact test for feature selection, principal component analysis (PCA) as well as iterative supervised PCA (ISPCA) for feature generation, and GLMnet and logistic regression methods with sparsity promoting priors for classification. Probabilistic programming language Stan is used to implement Bayesian inference for the probabilistic models. RESULTS AND CONCLUSIONS: We compare overlaps of differentially methylated genomic regions as chosen by different feature selection methods, and evaluate probabilistic classifiers by evaluating the area under the receiver operating characteristic scores on discovery and validation cohorts. While we observe that many methods perform equally well as, and occasionally considerably better than, GLMnet that was originally proposed for cfMeDIP-seq based cancer classification, we also observed that performance of different methods vary across sequencing depths, cancer types and study cohorts. Overall, methods that seem robust and promising include Fisher's exact test and ISPCA for feature selection as well as a simple logistic regression model with the number of hyper and hypo-methylated regions as features.

BACKGROUND: DNA methylation is commonly measured using bisulfite sequencing (BS-seq). The quality of a BS-seq library is measured by its bisulfite conversion efficiency. Libraries with low conversion rates are typically excluded from analysis resulting in reduced coverage and increased costs. RESULTS: We have developed a probabilistic method and software, LuxRep, that implements a general linear model and simultaneously accounts for technical replicates (libraries from the same biological sample) from different bisulfite-converted DNA libraries. Using simulations and actual DNA methylation data, we show that including technical replicates with low bisulfite conversion rates generates more accurate estimates of methylation levels and differentially methylated sites. Moreover, using variational inference speeds up computation time necessary for whole genome analysis. CONCLUSIONS: In this work we show that taking into account technical replicates (i.e. libraries) of BS-seq data of varying bisulfite conversion rates, with their corresponding experimental parameters, improves methylation level estimation and differential methylation detection.

Clinical patient records are an example of high-dimensional data that is typically collected from disparate sources and comprises of multiple likelihoods with noisy as well as missing values. In this work, we propose an unsupervised generative model that can learn a low-dimensional representation among the observations in a latent space, while making use of all available data in a heterogeneous data setting with missing values. We improve upon the existing Gaussian process latent variable model (GPLVM) by incorporating multiple likelihoods and deep neural network parameterised back-constraints to create a non-linear dimensionality reduction technique for heterogeneous data. In addition, we develop a variational inference method for our model that uses numerical quadrature. We establish the effectiveness of our model and compare against existing GPLVM methods on a standard benchmark dataset as well as on clinical data of Parkinson’s disease patients treated at the HUS Helsinki University Hospital.

Longitudinal datasets measured repeatedly over time from individual subjects, arise in many biomedical, psychological, social, and other studies. A common approach to analyse high-dimensional data that contains missing values is to learn a low-dimensional representation using variational autoencoders (VAEs). However, standard VAEs assume that the learnt representations are i.i.d., and fail to capture the correlations between the data samples. We propose the Longitudinal VAE (L-VAE), that uses a multi-output additive Gaussian process (GP) prior to extend the VAE’s capability to learn structured low-dimensional representations imposed by auxiliary covariate information, and derive a new KL divergence upper bound for such GPs. Our approach can simultaneously accommodate both time-varying shared and random effects, produce structured low-dimensional representations, disentangle effects of individual covariates or their interactions, and achieve highly accurate predictive performance. We compare our model against previous methods on synthetic as well as clinical datasets, and demonstrate the state-of-the-art performance in data imputation, reconstruction, and long-term prediction tasks.

Model-based reinforcement learning (MBRL) approaches rely on discrete-time state transition models whereas physical systems and the vast majority of control tasks operate in continuous-time. To avoid time-discretization approximation of the underlying process, we propose a continuous-time MBRL framework based on a novel actor-critic method. Our approach also infers the unknown state evolution differentials with Bayesian neural ordinary differential equations (ODE) to account for epistemic uncertainty. We implement and test our method on a new ODE-RL suite that explicitly solves continuous-time control systems. Our experiments illustrate that the model is robust against irregular and noisy data, and can solve classic control problems in a sample-efficient manner.

Abstract Motivation Longitudinal study designs are indispensable for studying disease progression. Inferring covariate effects from longitudinal data, however, requires interpretable methods that can model complicated covariance structures and detect non-linear effects of both categorical and continuous covariates, as well as their interactions. Detecting disease effects is hindered by the fact that they often occur rapidly near the disease initiation time, and this time point cannot be exactly observed. An additional challenge is that the effect magnitude can be heterogeneous over the subjects. Results We present lgpr, a widely applicable and interpretable method for non-parametric analysis of longitudinal data using additive Gaussian processes. We demonstrate that it outperforms previous approaches in identifying the relevant categorical and continuous covariates in various settings. Furthermore, it implements important novel features, including the ability to account for the heterogeneity of covariate effects, their temporal uncertainty, and appropriate observation models for different types of biomedical data. The lgpr tool is implemented as a comprehensive and user-friendly R-package. Availability and implementation lgpr is available at jtimonen.github.io/lgpr-usage with documentation, tutorials, test data and code for reproducing the experiments of this article. Supplementary information Supplementary data are available at Bioinformatics online.

Adaptive immune system uses T cell receptors (TCRs) to recognize pathogens and to consequently initiate immune responses. TCRs can be sequenced from individuals and methods analyzing the specificity of the TCRs can help us better understand individuals' immune status in different disorders. For this task, we have developed TCRGP, a novel Gaussian process method that predicts if TCRs recognize specified epitopes. TCRGP can utilize the amino acid sequences of the complementarity determining regions (CDRs) from TCRα and TCRβ chains and learn which CDRs are important in recognizing different epitopes. Our comprehensive evaluation with epitope-specific TCR sequencing data shows that TCRGP achieves on average higher prediction accuracy in terms of AUROC score than existing state-of-the-art methods in epitope-specificity predictions. We also propose a novel analysis approach for combined single-cell RNA and TCRαβ (scRNA+TCRαβ) sequencing data by quantifying epitope-specific TCRs with TCRGP and identify HBV-epitope specific T cells and their transcriptomic states in hepatocellular carcinoma patients.

MOTIVATION: DNA methylation is an important epigenetic modification, which has multiple functions. DNA methylation and its connections to diseases have been extensively studied in recent years. It is known that DNA methylation levels of neighboring cytosines are correlated and that differential DNA methylation typically occurs rather as regions instead of individual cytosine level. RESULTS: We have developed a generalized linear mixed model, LuxUS, that makes use of the correlation between neighboring cytosines to facilitate analysis of differential methylation. LuxUS implements a likelihood model for bisulfite sequencing data that accounts for experimental variation in underlying biochemistry. LuxUS can model both binary and continuous covariates, and mixed model formulation enables including replicate and cytosine random effects. Spatial correlation is included to the model through a cytosine random effect correlation structure. We show with simulation experiments that using the spatial correlation, we gain more power to the statistical testing of differential DNA methylation. Results with real bisulfite sequencing dataset show that LuxUS is able to detect biologically significant differentially methylated cytosines. AVAILABILITY AND IMPLEMENTATION: The tool is available at https://github.com/hallav/LuxUS. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

BACKGROUND: The binding sites of transcription factors (TFs) and the localisation of histone modifications in the human genome can be quantified by the chromatin immunoprecipitation assay coupled with next-generation sequencing (ChIP-seq). The resulting chromatin feature data has been successfully adopted for genome-wide enhancer identification by several unsupervised and supervised machine learning methods. However, the current methods predict different numbers and different sets of enhancers for the same cell type and do not utilise the pattern of the ChIP-seq coverage profiles efficiently. RESULTS: In this work, we propose a PRobabilistic Enhancer PRedictIoN Tool (PREPRINT) that assumes characteristic coverage patterns of chromatin features at enhancers and employs a statistical model to account for their variability. PREPRINT defines probabilistic distance measures to quantify the similarity of the genomic query regions and the characteristic coverage patterns. The probabilistic scores of the enhancer and non-enhancer samples are utilised to train a kernel-based classifier. The performance of the method is demonstrated on ENCODE data for two cell lines. The predicted enhancers are computationally validated based on the transcriptional regulatory protein binding sites and compared to the predictions obtained by state-of-the-art methods. CONCLUSION: PREPRINT performs favorably to the state-of-the-art methods, especially when requiring the methods to predict a larger set of enhancers. PREPRINT generalises successfully to data from cell type not utilised for training, and often the PREPRINT performs better than the previous methods. The PREPRINT enhancers are less sensitive to the choice of prediction threshold. PREPRINT identifies biologically validated enhancers not predicted by the competing methods. The enhancers predicted by PREPRINT can aid the genome interpretation in functional genomics and clinical studies.

We propose a novel deep learning paradigm of differential flows that learn a stochastic differential equation transformations of inputs prior to a standard classification or regression function. The key property of differential Gaussian processes is the warping of inputs through infinitely deep, but infinitesimal, differential fields, that generalise discrete layers into a dynamical system. We demonstrate excellent results as compared to deep Gaussian processes and Bayesian neural networks.

We present Ordinary Differential Equation Variational Auto-Encoder (ODE2VAE), a latent second order ODE model for high-dimensional sequential data. Leveraging the advances in deep generative models, ODE2VAE can simultaneously learn the embedding of high dimensional trajectories and infer arbitrarily complex continuous-time latent dynamics. Our model explicitly decomposes the latent space into momentum and position components and solves a second order ODE system, which is in contrast to recurrent neural network (RNN) based time series models and recently proposed black-box ODE techniques. In order to account for uncertainty, we propose probabilistic latent ODE dynamics parameterized by deep Bayesian neural networks. We demonstrate our approach on motion capture, image rotation, and bouncing balls datasets. We achieve state-of-the-art performance in long term motion prediction and imputation tasks.

MOTIVATION: Metabolic flux balance analysis (FBA) is a standard tool in analyzing metabolic reaction rates compatible with measurements, steady-state and the metabolic reaction network stoichiometry. Flux analysis methods commonly place model assumptions on fluxes due to the convenience of formulating the problem as a linear programing model, while many methods do not consider the inherent uncertainty in flux estimates. RESULTS: We introduce a novel paradigm of Bayesian metabolic flux analysis that models the reactions of the whole genome-scale cellular system in probabilistic terms, and can infer the full flux vector distribution of genome-scale metabolic systems based on exchange and intracellular (e.g. 13C) flux measurements, steady-state assumptions, and objective function assumptions. The Bayesian model couples all fluxes jointly together in a simple truncated multivariate posterior distribution, which reveals informative flux couplings. Our model is a plug-in replacement to conventional metabolic balance methods, such as FBA. Our experiments indicate that we can characterize the genome-scale flux covariances, reveal flux couplings, and determine more intracellular unobserved fluxes in Clostridium acetobutylicum from 13C data than flux variability analysis. AVAILABILITY AND IMPLEMENTATION: The COBRA compatible software is available at github.com/markusheinonen/bamfa. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Ordinary differential equations (ODEs) provide a powerful formalism to model molecular networks mechanistically. However, inferring the model structure, given a set of time course measurements and a large number of alternative molecular mechanisms, is a challenging and open research question. Existing search heuristics are designed only for finding a single best model configuration and cannot account for the uncertainty in selecting the network components. In this study, we present a novel Markov chain Monte Carlo approach for performing Bayesian model structure inference over ODE models. We formulate a Metropolis algorithm that explores the model space efficiently and is suitable for obtaining probabilistic inferences about the network structure. The method and its special parallelization possibilities are demonstrated using simulated data. Furthermore, we apply the method to a time course RNA sequencing data set to infer the structure of the transiently evolving core regulatory network that steers the T helper 17 (Th17) cell differentiation. Our results are in agreement with the earlier finding that the Th17 lineage-specific differentiation program evolves in three sequential phases. Further, the analysis provides us with probabilistic predictions on the molecular interactions that are active in different phases of Th17 cell differentiation.

In conventional ODE modelling coefficients of an equation driving the system state forward in time are estimated. However, for many complex systems it is practically impossible to determine the equations or interactions governing the underlying dynamics. In these settings, parametric ODE model cannot be formulated. Here, we overcome this issue by introducing a novel paradigm of nonparametric ODE modelling that can learn the underlying dynamics of arbitrary continuous-time systems without prior knowledge. We propose to learn non-linear, unknown differential functions from state observations using Gaussian process vector fields within the exact ODE formalism. We demonstrate the model’s capabilities to infer dynamics from sparse data and to simulate the system forward into future.

Motivation: Proteins are commonly used by biochemical industry for numerous processes. Refining these proteins' properties via mutations causes stability effects as well. Accurate computational method to predict how mutations affect protein stability is necessary to facilitate efficient protein design. However, accuracy of predictive models is ultimately constrained by the limited availability of experimental data. Results: We have developed mGPfusion, a novel Gaussian process (GP) method for predicting protein's stability changes upon single and multiple mutations. This method complements the limited experimental data with large amounts of molecular simulation data. We introduce a Bayesian data fusion model that re-calibrates the experimental and in silico data sources and then learns a predictive GP model from the combined data. Our protein-specific model requires experimental data only regarding the protein of interest and performs well even with few experimental measurements. The mGPfusion models proteins by contact maps and infers the stability effects caused by mutations with a mixture of graph kernels. Our results show that mGPfusion outperforms state-of-the-art methods in predicting protein stability on a dataset of 15 different proteins and that incorporating molecular simulation data improves the model learning and prediction accuracy. Availability and implementation: Software implementation and datasets are available at github.com/emmijokinen/mgpfusion. Supplementary information: Supplementary data are available at Bioinformatics online.

Motivation: Co-localization of trait associated SNPs for specific transcription-factor binding sites or regulatory regions in the genome can yield profound insight into underlying causal mechanisms. Analysis is complicated because the truly causal SNPs are generally unknown and can be either SNPs reported in GWAS studies or other proxy SNPs in their linkage disequilibrium. Hence, a comprehensive pipeline for SNP co-localization analysis that utilizes all relevant information about both the genotyped SNPs and their proxies is needed. Results: We developed an R package snpEnrichR for SNP co-localization analysis. The software integrates different tools for random SNP generation and genome co-localization analysis to automatize and help users to create custom SNP co-localization analysis. We show via an example that including proxy SNPs in SNP co-localization analysis enhances the sensitivity of co-localization detection. Availability and implementation: The software is available at https://github.com/kartiek/snpEnrichR.

We present a novel approach for non-stationary Gaussian process regression (GPR), where the three key parameters – noise variance, signal variance and lengthscale – can be simultaneously input-dependent. We develop gradient-based inference methods to learn the unknown function and the non-stationary model parameters, without requiring any model approximations. For inferring the full posterior distribution we use Hamiltonian Monte Carlo (HMC), which conveniently extends the analytical gradient-based GPR learning by guiding the sampling with the gradients. The MAP solution can also be learned with gradient ascent. In experiments on several synthetic datasets and in modelling of temporal gene expression, the non-stationary GPR is shown to give major improvement when modeling realistic input-dependent dynamics.

MOTIVATION: 5-methylcytosine (5mC) is a widely studied epigenetic modification of DNA. The ten-eleven translocation (TET) dioxygenases oxidize 5mC into oxidized methylcytosines (oxi-mCs): 5-hydroxymethylcytosine (5hmC), 5-formylcytosine (5fC) and 5-carboxylcytosine (5caC). DNA methylation modifications have multiple functions. For example, 5mC is shown to be associated with diseases and oxi-mC species are reported to have a role in active DNA demethylation through 5mC oxidation and DNA repair, among others, but the detailed mechanisms are poorly understood. Bisulphite sequencing and its various derivatives can be used to gain information about all methylation modifications at single nucleotide resolution. Analysis of bisulphite based sequencing data is complicated due to the convoluted read-outs and experiment-specific variation in biochemistry. Moreover, statistical analysis is often complicated by various confounding effects. How to analyse 5mC and oxi-mC data sets with arbitrary and complex experimental designs is an open and important problem. RESULTS: We propose the first method to quantify oxi-mC species with arbitrary covariate structures from bisulphite based sequencing data. Our probabilistic modeling framework combines a previously proposed hierarchical generative model for oxi-mC-seq data and a general linear model component to account for confounding effects. We show that our method provides accurate methylation level estimates and accurate detection of differential methylation when compared with existing methods. Analysis of novel and published data gave insights into to the demethylation of the forkhead box P3 (Foxp3) locus during the induced T regulatory cell differentiation. We also demonstrate how our covariate model accurately predicts methylation levels of the Foxp3 locus. Collectively, LuxGLM method improves the analysis of DNA methylation modifications, particularly for oxi-mC species. AVAILABILITY AND IMPLEMENTATION: An implementation of the proposed method is available under MIT license at https://github.org/tare/LuxGLM/ CONTACT: [email protected] or [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: Cell differentiation is steered by extracellular signals that activate a cell type specific transcriptional program. Molecular mechanisms that drive the differentiation can be analyzed by combining mathematical modeling with population average data. For standard mathematical models, the population average data is informative only if the measurements come from a homogeneous cell culture. In practice, however, the differentiation efficiencies are always imperfect. Consequently, cell cultures are inherently mixtures of several cell types, which have different molecular mechanisms and exhibit quantitatively different dynamics. There is an urgent need for data-driven mathematical modeling approaches that can detect possible heterogeneity and, further, recover the molecular mechanisms from heterogeneous data. RESULTS: We develop a novel method that models a heterogeneous population using homogeneous subpopulations that evolve in parallel. Different subpopulations can represent different cell types and each subpopulation can have cell type specific molecular mechanisms. We present statistical methodology that can be used to quantify the effect of heterogeneity and to infer the subpopulation specific molecular interactions. After a proof of principle study with simulated data, we apply our methodology to analyze the differentiation of human Th17 cells using time-course RNA sequencing data. We construct putative molecular networks driving the T cell activation and Th17 differentiation and allow the cell populations to be split into two subpopulations in the case of heterogeneous samples. Our analysis shows that the heterogeneity indeed has a statistically significant effect on observed dynamics and, furthermore, our statistical methodology can infer both the subpopulation specific molecular mechanisms and the effect of heterogeneity. AVAILABILITY AND IMPLEMENTATION: An implementation of the method is available at http://research.ics.aalto.fi/csb/software/subpop/ CONTACT: [email protected] or [email protected] information: Supplementary data are available at Bioinformatics online.

MOTIVATION: Mechanistic models based on ordinary differential equations provide powerful and accurate means to describe the dynamics of molecular machinery which orchestrates gene regulation. When combined with appropriate statistical techniques, mechanistic models can be calibrated using experimental data and, in many cases, also the model structure can be inferred from time-course measurements. However, existing mechanistic models are limited in the sense that they rely on the assumption of static network structure and cannot be applied when transient phenomena affect, or rewire, the network structure. In the context of gene regulatory network inference, network rewiring results from the net impact of possible unobserved transient phenomena such as changes in signaling pathway activities or epigenome, which are generally difficult, but important, to account for. RESULTS: We introduce a novel method that can be used to infer dynamically evolving regulatory networks from time-course data. Our method is based on the notion that all mechanistic ordinary differential equation models can be coupled with a latent process that approximates the network structure rewiring process. We illustrate the performance of the method using simulated data and, further, we apply the method to study the regulatory interactions during T helper 17 (Th17) cell differentiation using time-course RNA sequencing data. The computational experiments with the real data show that our method is capable of capturing the experimentally verified rewiring effects of the core Th17 regulatory network. We predict Th17 lineage specific subnetworks that are activated sequentially and control the differentiation process in an overlapping manner. AVAILABILITY AND IMPLEMENTATION: An implementation of the method is available at http://research.ics.aalto.fi/csb/software/lem/ CONTACTS: [email protected] or [email protected].

Biology is rapidly turning into an information science, thanks to enormous advances in the ability to observe the molecular properties of cells, organs and individuals. This wealth of data allows us to model molecular systems at an unprecedented level of detail and to start to understand the underlying biological mechanisms. The burgeoning field of systems biology creates a huge need for methods from machine learning, which find statistical dependencies and patterns in these large-scale datasets and use these to establish models of complex molecular systems. MLSB is a successful series of workshops that aims to provide a scientific forum for the exchange between researchers from Systems Biology and Machine Learning, to promote the exchange of ideas, interactions and collaborations between these communities.

MOTIVATION: Transcription factors (TFs) are a class of DNA-binding proteins that have a central role in regulating gene expression. To reveal mechanisms of transcriptional regulation, a number of computational tools have been proposed for predicting TF-DNA interaction sites. Recent studies have shown that genome-wide sequencing data on open chromatin sites from a DNase I hypersensitivity experiments (DNase-seq) has a great potential to map putative binding sites of all transcription factors in a single experiment. Thus, computational methods for analysing DNase-seq to accurately map TF-DNA interaction sites are highly needed. RESULTS: Here, we introduce a novel discriminative algorithm, BinDNase, for predicting TF-DNA interaction sites using DNase-seq data. BinDNase implements an efficient method for selecting and extracting informative features from DNase I signal for each TF, either at single nucleotide resolution or for larger regions. The method is applied to 57 transcription factors in cell line K562 and 31 transcription factors in cell line HepG2 using data from the ENCODE project. First, we show that BinDNase compares favourably to other supervised and unsupervised methods developed for TF-DNA interaction prediction using DNase-seq data. We demonstrate the importance to model each TF with a separate prediction model, reflecting TF-specific DNA accessibility around the TF-DNA interaction site. We also show that a highly standardised DNase-seq data (pre)processing is a requisite for accurate TF binding predictions and that sequencing depth has on average only a moderate effect on prediction accuracy. Finally, BinDNase's binding predictions generalise to other cell types, thus making BinDNase a versatile tool for accurate TF binding prediction. AVAILABILITY AND IMPLEMENTATION: R implementation of the algorithm is available in: http://research.ics.aalto.fi/csb/software/bindnase/. CONTACT: [email protected] SUPPLEMENTARY INFORMATION: Supplemental data are available at Bioinformatics online.

BACKGROUND: Transcription factors (TFs) are proteins that bind to DNA and regulate gene expression. To understand details of gene regulation, characterizing TF binding sites in different cell types, diseases and among individuals is essential. However, sometimes TF binding can only be measured from biological samples that contain multiple cell or tissue types. Sample heterogeneity can have a considerable effect on TF binding site detection. While manual separation techniques can be used to isolate a cell type of interest from heterogeneous samples, such techniques are challenging and can change intra-cellular interactions, including protein-DNA binding. Computational deconvolution methods have emerged as an alternative strategy to study heterogeneous samples and numerous methods have been proposed to analyze gene expression. However, no computational method exists to deconvolve cell type specific TF binding from heterogeneous samples. RESULTS: We present a probabilistic method, MixChIP, to identify cell type specific TF binding sites from heterogeneous chromatin immunoprecipitation sequencing (ChIP-seq) data. Our method simultaneously estimates the binding strength in different cell types as well as the proportions of different cell types in each sample when only partial prior information about cell type composition is available. We demonstrate the utility of MixChIP by analyzing ChIP-seq data from two cell lines which we artificially mix to generate (simulated) heterogeneous samples and by analyzing ChIP-seq data from breast cancer patients measuring oestrogen receptor (ER) binding in primary breast cancer tissues. We show that MixChIP is more accurate in detecting TF binding sites from multiple heterogeneous ChIP-seq samples than the standard methods which do not account for sample heterogeneity. CONCLUSIONS: Our results show that MixChIP can estimate cell-type proportions and identify cell type specific TF binding sites from heterogeneous ChIP-seq samples. Thus, MixChIP can be an invaluable tool in analyzing heterogeneous ChIP-seq samples, such as those originating from cancer studies. R implementation is available at http://research.ics.aalto.fi/csb/software/mixchip/ .

MOTIVATION: Gene expression profiling using RNA-seq is a powerful technique for screening RNA species' landscapes and their dynamics in an unbiased way. While several advanced methods exist for differential expression analysis of RNA-seq data, proper tools to anal.yze RNA-seq time-course have not been proposed. RESULTS: In this study, we use RNA-seq to measure gene expression during the early human T helper 17 (Th17) cell differentiation and T-: cell activation (Th0). To quantify Th17-: specific gene expression dynamics, we present a novel statistical methodology, DyNB, for analyzing time-course RNA-seq data. We use non-parametric Gaussian processes to model temporal correlation in gene expression and combine that with negative binomial likelihood for the count data. To account for experiment-: specific biases in gene expression dynamics, such as differences in cell differentiation efficiencies, we propose a method to rescale the dynamics between replicated measurements. We develop an MCMC sampling method to make inference of differential expression dynamics between conditions. DyNB identifies several known and novel genes involved in Th17 differentiation. Analysis of differentiation efficiencies revealed consistent patterns in gene expression dynamics between different cultures. We use qRT-PCR to validate differential expression and differentiation efficiencies for selected genes. Comparison of the results with those obtained via traditional timepoint-: wise analysis shows that time-course analysis together with time rescaling between cultures identifies differentially expressed genes which would not otherwise be detected. AVAILABILITY: An implementation of the proposed computational methods will be available at http://research.ics.aalto.fi/csb/software/

MOTIVATION: Signaling networks mediate responses to different stimuli using a multitude of feed-forward, feedback and cross-talk mechanisms, and malfunctions in these mechanisms have an important role in various diseases. To understand a disease and to help discover novel therapeutic approaches, we have to reveal the molecular mechanisms underlying signal transduction and use that information to design targeted perturbations. RESULTS: We have pursued this direction by developing an efficient computational approach, Sorad, which can estimate the structure of signal transduction networks and the associated continuous signaling dynamics from phosphoprotein time-course measurements. Further, Sorad can identify experimental conditions that modulate the signaling toward a desired response. We have analyzed comprehensive phosphoprotein time-course data from a human hepatocellular liver carcinoma cell line and demonstrate here that Sorad provides more accurate predictions of phosphoprotein responses to given stimuli than previously presented methods and, importantly, that Sorad can estimate experimental conditions to achieve a desired signaling response. Because Sorad is data driven, it has a high potential to generate novel hypotheses for further research. Our analysis of the hepatocellular liver carcinoma data predict a regulatory connection where AKT activity is dependent on IKK in TGFα stimulated cells, which is supported by the original data but not included in the original model. AVAILABILITY: An implementation of the proposed computational methods will be available at http://research.ics.aalto.fi/csb/software/. CONTACT: [email protected] or [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Transcription factor (TF) binding to DNA can be modeled in a number of different ways. It is highly debated which modeling methods are the best, how the models should be built and what can they be applied to. In this study a linear k-mer model proposed for predicting TF specificity in protein binding microarrays (PBM) is applied to a high-throughput SELEX data and the question of how to choose the most informative k-mers to the binding model is studied. We implemented the standard cross-validation scheme to reduce the number of k-mers in the model and observed that the number of k-mers can often be reduced significantly without a great negative effect on prediction accuracy. We also found that the later SELEX enrichment cycles provide a much better discrimination between bound and unbound sequences as model prediction accuracies increased for all proteins together with the cycle number. We compared prediction performance of k-mer and position specific weight matrix (PWM) models derived from the same SELEX data. Consistent with previous results on PBM data, performance of the k-mer model was on average 9%-units better. For the 15 proteins in the SELEX data set with medium enrichment cycles, classification accuracies were on average 71% and 62% for k-mer and PWMs, respectively. Finally, the k-mer model trained with SELEX data was evaluated on ChIP-seq data demonstrating substantial improvements for some proteins. For protein GATA1 the model can distinquish between true ChIP-seq peaks and negative peaks. For proteins RFX3 and NFATC1 the performance of the model was no better than chance.

MOTIVATION: Tissue heterogeneity, arising from multiple cell types, is a major confounding factor in experiments that focus on studying cell types, e.g. their expression profiles, in isolation. Although sample heterogeneity can be addressed by manual microdissection, prior to conducting experiments, computational treatment on heterogeneous measurements have become a reliable alternative to perform this microdissection in silico. Favoring computation over manual purification has its advantages, such as time consumption, measuring responses of multiple cell types simultaneously, keeping samples intact of external perturbations and unaltered yield of molecular content. RESULTS: We formalize a probabilistic model, DSection, and show with simulations as well as with real microarray data that DSection attains increased modeling accuracy in terms of (i) estimating cell-type proportions of heterogeneous tissue samples, (ii) estimating replication variance and (iii) identifying differential expression across cell types under various experimental conditions. As our reference we use the corresponding linear regression model, which mirrors the performance of the majority of current non-probabilistic modeling approaches. AVAILABILITY AND SOFTWARE: All codes are written in Matlab, and are freely available upon request as well as at the project web page http://www.cs.tut.fi/∼erkkila2/. Furthermore, a web-application for DSection exists at http://informatics.systemsbiology.net/DSection. CONTACT: [email protected]; [email protected]

MOTIVATION: Regulation of gene expression is fundamental to the operation of a cell. Revealing the structure and dynamics of a gene regulatory network (GRN) is of great interest and represents a considerably challenging computational problem. The GRN estimation problem is complicated by the fact that the number of gene expression measurements is typically extremely small when compared with the dimension of the biological system. Further, because the gene regulation process is intrinsically complex, commonly used parametric models can provide too simple description of the underlying phenomena and, thus, can be unreliable. In this article, we propose a novel methodology for the inference of GRNs from time-series and steady-state gene expression measurements. The presented framework is based on the use of Bayesian analysis with ordinary differential equations (ODEs) and non-parametric Gaussian process modeling for the transcriptional-level regulation. RESULTS: The performance of the proposed structure inference method is evaluated using a recently published in vivo dataset. By comparing the obtained results with those of existing ODE- and Bayesian-based inference methods we demonstrate that the proposed method provides more accurate network structure learning. The predictive capabilities of the method are examined by splitting the dataset into a training set and a test set and by predicting the test set based on the training set. AVAILABILITY: A MATLAB implementation of the method will be available from http://www.cs.tut.fi/~aijo2/gp upon publication.

BACKGROUND: Cluster analysis has become a standard computational method for gene function discovery as well as for more general explanatory data analysis. A number of different approaches have been proposed for that purpose, out of which different mixture models provide a principled probabilistic framework. Cluster analysis is increasingly often supplemented with multiple data sources nowadays, and these heterogeneous information sources should be made as efficient use of as possible. RESULTS: This paper presents a novel Beta-Gaussian mixture model (BGMM) for clustering genes based on Gaussian distributed and beta distributed data. The proposed BGMM can be viewed as a natural extension of the beta mixture model (BMM) and the Gaussian mixture model (GMM). The proposed BGMM method differs from other mixture model based methods in its integration of two different data types into a single and unified probabilistic modeling framework, which provides a more efficient use of multiple data sources than methods that analyze different data sources separately. Moreover, BGMM provides an exceedingly flexible modeling framework since many data sources can be modeled as Gaussian or beta distributed random variables, and it can also be extended to integrate data that have other parametric distributions as well, which adds even more flexibility to this model-based clustering framework. We developed three types of estimation algorithms for BGMM, the standard expectation maximization (EM) algorithm, an approximated EM and a hybrid EM, and propose to tackle the model selection problem by well-known model selection criteria, for which we test the Akaike information criterion (AIC), a modified AIC (AIC3), the Bayesian information criterion (BIC), and the integrated classification likelihood-BIC (ICL-BIC). CONCLUSION: Performance tests with simulated data show that combining two different data sources into a single mixture joint model greatly improves the clustering accuracy compared with either of its two extreme cases, GMM or BMM. Applications with real mouse gene expression data (modeled as Gaussian distribution) and protein-DNA binding probabilities (modeled as beta distribution) also demonstrate that BGMM can yield more biologically reasonable results compared with either of its two extreme cases. One of our applications has found three groups of genes that are likely to be involved in Myd88-dependent Toll-like receptor 3/4 (TLR-3/4) signaling cascades, which might be useful to better understand the TLR-3/4 signal transduction.

BACKGROUND: In practice many biological time series measurements, including gene microarrays, are conducted at time points that seem to be interesting in the biologist's opinion and not necessarily at fixed time intervals. In many circumstances we are interested in finding targets that are expressed periodically. To tackle the problems of uneven sampling and unknown type of noise in periodicity detection, we propose to use robust regression. METHODS: The aim of this paper is to develop a general framework for robust periodicity detection and review and rank different approaches by means of simulations. We also show the results for some real measurement data. RESULTS: The simulation results clearly show that when the sampling of time series gets more and more uneven, the methods that assume even sampling become unusable. We find that M-estimation provides a good compromise between robustness and computational efficiency. CONCLUSION: Since uneven sampling occurs often in biological measurements, the robust methods developed in this paper are expected to have many uses. The regression based formulation of the periodicity detection problem easily adapts to non-uniform sampling. Using robust regression helps to reject inconsistently behaving data points. AVAILABILITY: The implementations are currently available for Matlab and will be made available for the users of R as well. More information can be found in the web-supplement 1.

BACKGROUND: Periodic phenomena are widespread in biology. The problem of finding periodicity in biological time series can be viewed as a multiple hypothesis testing of the spectral content of a given time series. The exact noise characteristics are unknown in many bioinformatics applications. Furthermore, the observed time series can exhibit other non-idealities, such as outliers, short length and distortion from the original wave form. Hence, the computational methods should preferably be robust against such anomalies in the data. RESULTS: We propose a general-purpose robust testing procedure for finding periodic sequences in multiple time series data. The proposed method is based on a robust spectral estimator which is incorporated into the hypothesis testing framework using a so-called g-statistic together with correction for multiple testing. This results in a robust testing procedure which is insensitive to heavy contamination of outliers, missing-values, short time series, nonlinear distortions, and is completely insensitive to any monotone nonlinear distortions. The performance of the methods is evaluated by performing extensive simulations. In addition, we compare the proposed method with another recent statistical signal detection estimator that uses Fisher's test, based on the Gaussian noise assumption. The results demonstrate that the proposed robust method provides remarkably better robustness properties. Moreover, the performance of the proposed method is preferable also in the standard Gaussian case. We validate the performance of the proposed method on real data on which the method performs very favorably. CONCLUSION: As the time series measured from biological systems are usually short and prone to contain different kinds of non-idealities, we are very optimistic about the multitude of possible applications for our proposed robust statistical periodicity detection method.

BACKGROUND: Very few analytical approaches have been reported to resolve the variability in microarray measurements stemming from sample heterogeneity. For example, tissue samples used in cancer studies are usually contaminated with the surrounding or infiltrating cell types. This heterogeneity in the sample preparation hinders further statistical analysis, significantly so if different samples contain different proportions of these cell types. Thus, sample heterogeneity can result in the identification of differentially expressed genes that may be unrelated to the biological question being studied. Similarly, irrelevant gene combinations can be discovered in the case of gene expression based classification. RESULTS: We propose a computational framework for removing the effects of sample heterogeneity by "microdissecting" microarray data in silico. The computational method provides estimates of the expression values of the pure (non-heterogeneous) cell samples. The inversion of the sample heterogeneity can be facilitated by providing accurate estimates of the mixing percentages of different cell types in each measurement. For those cases where no such information is available, we develop an optimization-based method for joint estimation of the mixing percentages and the expression values of the pure cell samples. We also consider the problem of selecting the correct number of cell types. CONCLUSION: The efficiency of the proposed methods is illustrated by applying them to a carefully controlled cDNA microarray data obtained from heterogeneous samples. The results demonstrate that the methods are capable of reconstructing both the sample and cell type specific expression values from heterogeneous mixtures and that the mixing percentages of different cell types can also be estimated. Furthermore, a general purpose model selection method can be used to select the correct number of cell types.

Forcing functions represent an important class of Boolean functions that have been extensively studied in the analysis of the dynamics of random Boolean networks as models of genetic regulatory systems. Several other so-called Post classes of Boolean functions are closely related to forcing functions and have been used in learning theory as well as in control systems. We develop novel spectral algorithms to test membership of a Boolean function in these classes. These algorithms are highly efficient and are essential in learning problems, especially in the context of genetic regulatory networks, where the same learning procedures are applied repeatedly.

Many time-series encountered in data mining applications exhibit outliers, missing data, and small sample sizes (specifically, short time-series) that can cause standard methods to perform poorly. Motivated by requirements for the analysis of cDNA microarray time-series data, this paper describes a rank-based approach to periodic component detection for such time-series and examines its performance for several different simulation-based scenarios.