SUMMARY: Many biochemical processes in living organisms take place inside compartments that can interact with each other and remodel over time. In a recent work, we have shown how the stochastic dynamics of a compartmentalized biochemical system can be effectively studied using moment equations. With this technique, the time evolution of a compartment population is summarized using a finite number of ordinary differential equations, which can be analyzed very efficiently. However, the derivation of moment equations by hand can become time-consuming for systems comprising multiple reactants and interactions. Here we present Compartor, a toolbox that automatically generates the moment equations associated with a user-defined compartmentalized system. Through the moment equation method, Compartor renders the analysis of stochastic population models accessible to a broader scientific community. AVAILABILITY AND IMPLEMENTATION: Compartor is provided as a Python package and is available at https://pypi.org/project/compartor/. Source code and usage tutorials for Compartor are available at https://github.com/zechnerlab/Compartor.

Continuous Time Bayesian Networks (CTBNs) provide a powerful means to model complex network dynamics. How- ever, their inference is computationally demanding — especially if one considers incomplete and noisy time-series data. The latter gives rise to a joint state- and parameter estimation problem, which can only be solved numerically. Yet, finding the exact parameterization of the CTBN has often only secondary importance in practical scenarios. We therefore focus on the structure learning problem and present a way to analytically marginalize the Markov chain underlying the CTBN model with respect its parameters. Since the resulting stochastic process is parameter-free, its inference reduces to an optimal filtering problem. We solve the latter using an efficient parallel implementation of a sequential Monte Carlo scheme. Our framework enables CTBN inference to be applied to incomplete noisy time-series data frequently found in molecular biology and other disciplines.

The dynamics of stochastic reaction networks within cells are inevitably modulated by factors considered extrinsic to the network such as, for instance, the fluctuations in ribosome copy numbers for a gene regulatory network. While several recent studies demonstrate the importance of accounting for such extrinsic components, the resulting models are typically hard to analyze. In this work we develop a general mathematical framework that allows to uncouple the network from its dynamic environment by incorporating only the environment's effect onto the network into a new model. More technically, we show how such fluctuating extrinsic components (e.g., chemical species) can be marginalized in order to obtain this decoupled model. We derive its corresponding process- and master equations and show how stochastic simulations can be performed. Using several case studies, we demonstrate the significance of the approach.

MOTIVATION: After more than a decade since microarrays were used to predict phenotype of biological samples, real-life applications for disease screening and identification of patients who would best benefit from treatment are still emerging. The interest of the scientific community in identifying best approaches to develop such prediction models was reaffirmed in a competition style international collaboration called IMPROVER Diagnostic Signature Challenge whose results we describe herein. RESULTS: Fifty-four teams used public data to develop prediction models in four disease areas including multiple sclerosis, lung cancer, psoriasis and chronic obstructive pulmonary disease, and made predictions on blinded new data that we generated. Teams were scored using three metrics that captured various aspects of the quality of predictions, and best performers were awarded. This article presents the challenge results and introduces to the community the approaches of the best overall three performers, as well as an R package that implements the approach of the best overall team. The analyses of model performance data submitted in the challenge as well as additional simulations that we have performed revealed that (i) the quality of predictions depends more on the disease endpoint than on the particular approaches used in the challenge; (ii) the most important modeling factor (e.g. data preprocessing, feature selection and classifier type) is problem dependent; and (iii) for optimal results datasets and methods have to be carefully matched. Biomedical factors such as the disease severity and confidence in diagnostic were found to be associated with the misclassification rates across the different teams. AVAILABILITY: The lung cancer dataset is available from Gene Expression Omnibus (accession, GSE43580). The maPredictDSC R package implementing the approach of the best overall team is available at www.bioconductor.org or http://bioinformaticsprb.med.wayne.edu/.

In this work, a variational Bayesian framework for efficient training of echo state networks (ESNs) with automatic regularization and delay&sum (D&S) readout adaptation is proposed. The algorithm uses a classical batch learning of ESNs. By treating the network echo states as fixed basis functions parameterized with delay parameters, we propose a variational Bayesian ESN training scheme. The variational approach allows for a seamless combination of sparse Bayesian learning ideas and a variational Bayesian space-alternating generalized expectation-maximization (VB-SAGE) algorithm for estimating parameters of superimposed signals. While the former method realizes automatic regularization of ESNs, which also determines which echo states and input signals are relevant for "explaining" the desired signal, the latter method provides a basis for joint estimation of D&S readout parameters. The proposed training algorithm can naturally be extended to ESNs with fixed filter neurons. It also generalizes the recently proposed expectation-maximization-based D&S readout adaptation method. The proposed algorithm was tested on synthetic data prediction tasks as well as on dynamic handwritten character recognition.

In this paper we investigate the problem of learning Echo State Networks (ESN) with adaptable filter neurons and delay&sum readouts. A brute-force solution to this learning problem is often impractical due to nonlinearity and high dimensionality of the resulting optimization problem. In this work we propose an approximate solution to the ESN learning by appealing to the variational Bayesian EM-type of estimation algorithm. We show that such approach allows to significantly reduce the dimensionality of the resulting objective functions. Furthermore, it allows to implement ESN learning and adapt filter neurons and delays jointly within the variational framework. Simulations are performed for learning randomly generated target ESNs, as well as other synthetic nonlinear dynamic systems. The results demonstrate that the proposed learning algorithm can improve ESN learning for a wide class of problems.