Uncertainty quantification is a primary challenge for reliable modeling and simulation of complex stochastic dynamics. Such problems are typically plagued with incomplete information that may enter as uncertainty in the model parameters, or even in the model itself. Furthermore, due to their dynamic nature, we need to assess the impact of these uncertainties on the transient and long-time behavior of the stochastic models and derive corresponding uncertainty bounds for observables of interest. A special class of such challenges is parametric uncertainties in the model and in particular sensitivity analysis along with the corresponding sensitivity bounds for stochastic dynamics. Moreover, sensitivity analysis can be further complicated in models with a high number of parameters that render straightforward approaches, such as gradient methods, impractical. In this paper, we derive uncertainty and sensitivity bounds for path-space observables of stochastic dynamics in terms of new goal-oriented divergences; the latter incorporate both observables and information theory objects such as the relative entropy rate. These bounds are tight, depend on the variance of the particular observable and are computable through Monte Carlo simulation. In the case of sensitivity analysis, the derived sensitivity bounds rely on the path Fisher Information Matrix, hence they depend only on local dynamics and are gradient-free. These features allow for computationally efficient implementation in systems with a high number of parameters, e.g., complex reaction networks and molecular simulations.Version: July 15, 2015 1 2. Uncertainty quantification information inequalities and sensitivity bounds.2.1. Distances and divergences of probability measures. Bounds of the type (1.1) are based on characterizing a distance or divergence between the measures, Q, P , under which the averages are evaluated. While our primary goal is to characterize the bounds based on relative entropy, other divergences can be c>0

We propose a new sensitivity analysis methodology for complex stochastic dynamics based on the Relative Entropy Rate. The method becomes computationally feasible at the stationary regime of the process and involves the calculation of suitable observables in path space for the Relative Entropy Rate and the corresponding Fisher Information Matrix. The stationary regime is crucial for stochastic dynamics and here allows us to address the sensitivity analysis of complex systems, including examples of processes with complex landscapes that exhibit metastability, non-reversible systems from a statistical mechanics perspective, and high-dimensional, spatially distributed models. All these systems exhibit, typically non-gaussian stationary probability distributions, while in the case of high-dimensionality, histograms are impossible to construct directly. Our proposed methods bypass these challenges relying on the direct Monte Carlo simulation of rigorously derived observables for the Relative Entropy Rate and Fisher Information in path space rather than on the stationary probability distribution itself. We demonstrate the capabilities of the proposed methodology by focusing here on two classes of problems: (a) Langevin particle systems with either reversible (gradient) or non-reversible (non-gradient) forcing, highlighting the ability of the method to carry out sensitivity analysis in non-equilibrium systems; and, (b) spatially extended Kinetic Monte Carlo models, showing that the method can handle high-dimensional problems.

BackgroundStochastic modeling and simulation provide powerful predictive methods for the intrinsic understanding of fundamental mechanisms in complex biochemical networks. Typically, such mathematical models involve networks of coupled jump stochastic processes with a large number of parameters that need to be suitably calibrated against experimental data. In this direction, the parameter sensitivity analysis of reaction networks is an essential mathematical and computational tool, yielding information regarding the robustness and the identifiability of model parameters. However, existing sensitivity analysis approaches such as variants of the finite difference method can have an overwhelming computational cost in models with a high-dimensional parameter space.ResultsWe develop a sensitivity analysis methodology suitable for complex stochastic reaction networks with a large number of parameters. The proposed approach is based on Information Theory methods and relies on the quantification of information loss due to parameter perturbations between time-series distributions. For this reason, we need to work on path-space, i.e., the set consisting of all stochastic trajectories, hence the proposed approach is referred to as “pathwise”. The pathwise sensitivity analysis method is realized by employing the rigorously-derived Relative Entropy Rate, which is directly computable from the propensity functions. A key aspect of the method is that an associated pathwise Fisher Information Matrix (FIM) is defined, which in turn constitutes a gradient-free approach to quantifying parameter sensitivities. The structure of the FIM turns out to be block-diagonal, revealing hidden parameter dependencies and sensitivities in reaction networks.ConclusionsAs a gradient-free method, the proposed sensitivity analysis provides a significant advantage when dealing with complex stochastic systems with a large number of parameters. In addition, the knowledge of the structure of the FIM can allow to efficiently address questions on parameter identifiability, estimation and robustness. The proposed method is tested and validated on three biochemical systems, namely: (a) a protein production/degradation model where explicit solutions are available, permitting a careful assessment of the method, (b) the p53 reaction network where quasi-steady stochastic oscillations of the concentrations are observed, and for which continuum approximations (e.g. mean field, stochastic Langevin, etc.) break down due to persistent oscillations between high and low populations, and (c) an Epidermal Growth Factor Receptor model which is an example of a high-dimensional stochastic reaction network with more than 200 reactions and a corresponding number of parameters.

No abstract

Background: Emerging pathogens such as Zika, chikungunya, Ebola, and dengue viruses are serious threats to national and global health security. Accurate forecasts of emerging epidemics and their severity are critical to minimizing subsequent mortality, morbidity, and economic loss. The recent introduction of chikungunya and Zika virus to the Americas underscores the need for better methods for disease surveillance and forecasting.Methods: To explore the suitability of current approaches to forecasting emerging diseases, the Defense Advanced Research Projects Agency (DARPA) launched the 2014–2015 DARPA Chikungunya Challenge to forecast the number of cases and spread of chikungunya disease in the Americas. Challenge participants (n=38 during final evaluation) provided predictions of chikungunya epidemics across the Americas for a six-month period, from September 1, 2014 to February 16, 2015, to be evaluated by comparison with incidence data reported to the Pan American Health Organization (PAHO). This manuscript presents an overview of the challenge and a summary of the approaches used by the winners.Results: Participant submissions were evaluated by a team of non-competing government subject matter experts based on numerical accuracy and methodology. Although this manuscript does not include in-depth analyses of the results, cursory analyses suggest that simpler models appear to outperform more complex approaches that included, for example, demographic information and transportation dynamics, due to the reporting biases, which can be implicitly captured in statistical models. Mosquito-dynamics, population specific information, and dengue-specific information correlated best with prediction accuracy.Conclusion: We conclude that with careful consideration and understanding of the relative advantages and disadvantages of particular methods, implementation of an effective prediction system is feasible. However, there is a need to improve the quality of the data in order to more accurately predict the course of epidemics.

Existing sensitivity analysis approaches are not able to handle efficiently stochastic reaction networks with a large number of parameters and species, which are typical in the modeling and simulation of complex biochemical phenomena. In this paper, a two-step strategy for parametric sensitivity analysis for such systems is proposed, exploiting advantages and synergies between two recently proposed sensitivity analysis methodologies for stochastic dynamics. The first method performs sensitivity analysis of the stochastic dynamics by means of the Fisher Information Matrix on the underlying distribution of the trajectories; the second method is a reduced-variance, finite-difference, gradient-type sensitivity approach relying on stochastic coupling techniques for variance reduction. Here we demonstrate that these two methods can be combined and deployed together by means of a new sensitivity bound which incorporates the variance of the quantity of interest as well as the Fisher Information Matrix estimated from the first method. The first step of the proposed strategy labels sensitivities using the bound and screens out the insensitive parameters in a controlled manner. In the second step of the proposed strategy, a finite-difference method is applied only for the sensitivity estimation of the (potentially) sensitive parameters that have not been screened out in the first step. Results on an epidermal growth factor network with fifty parameters and on a protein homeostasis with eighty parameters demonstrate that the proposed strategy is able to quickly discover and discard the insensitive parameters and in the remaining potentially sensitive parameters it accurately estimates the sensitivities. The new sensitivity strategy can be several times faster than current state-of-the-art approaches that test all parameters, especially in “sloppy” systems. In particular, the computational acceleration is quantified by the ratio between the total number of parameters over the number of the sensitive parameters.

Abstract-While the problem of estimating the amplitudes of sinusoidal components in signals, given an estimation of their frequencies, is linear and tractable, it is biased due to the unavoidable, in practice, errors in the estimation of frequencies. These errors are of great concern for processing signals with many sinusoidal like components as is the case of speech and audio. In this letter, we suggest using a time-varying sinusoidal representation which is able to iteratively correct frequency estimation errors. Then the corresponding amplitudes are computed through Least Squares. Experiments conducted on synthetic and speech signals show the suggested model's effectiveness in correcting frequency estimation errors and robustness in additive noise conditions.

Motivation Temporal variations in biological systems and more generally in natural sciences are typically modeled as a set of ordinary, partial or stochastic differential or difference equations. Algorithms for learning the structure and the parameters of a dynamical system are distinguished based on whether time is discrete or continuous, observations are time-series or time-course and whether the system is deterministic or stochastic, however, there is no approach able to handle the various types of dynamical systems simultaneously. Results In this paper, we present a unified approach to infer both the structure and the parameters of non-linear dynamical systems of any type under the restriction of being linear with respect to the unknown parameters. Our approach, which is named Unified Sparse Dynamics Learning (USDL), constitutes of two steps. First, an atemporal system of equations is derived through the application of the weak formulation. Then, assuming a sparse representation for the dynamical system, we show that the inference problem can be expressed as a sparse signal recovery problem, allowing the application of an extensive body of algorithms and theoretical results. Results on simulated data demonstrate the efficacy and superiority of the USDL algorithm under multiple interventions and/or stochasticity. Additionally, USDL’s accuracy significantly correlates with theoretical metrics such as the exact recovery coefficient. On real single-cell data, the proposed approach is able to induce high-confidence subgraphs of the signaling pathway. Availability and implementation Source code is available at Bioinformatics online. USDL algorithm has been also integrated in SCENERY (http://scenery.csd.uoc.gr/); an online tool for single-cell mass cytometry analytics. Supplementary information Supplementary data are available at Bioinformatics online.