Moment-Based Variational Inference for Markov Jump Processes

We propose moment-based variational inference as a flexible framework for approximate smoothing of latent Markov jump processes. The main ingredient of our approach is to partition the set of all transitions of the latent process into classes. This allows to express the Kullback-Leibler divergence between the approximate and the exact posterior process in terms of a set of moment functions that arise naturally from the chosen partition. To illustrate possible choices of the partition, we consider special classes of jump processes that frequently occur in applications. We then extend the results to parameter inference and demonstrate the method on several examples.Comment: Accepted by the 36th International Conference on Machine Learning (ICML 2019

Automatic Prediction Of Small Group Performance In Information Sharing Tasks

In this paper, we describe a novel approach, based on Markov jump processes, to model small group conversational dynamics and to predict small group performance. More precisely, we estimate conversational events such as turn taking, backchannels, turn-transitions at the micro-level (1 minute windows) and then we bridge the micro-level behavior and the macro-level performance. We tested our approach with a cooperative task, the Information Sharing task, and we verified the relevance of micro- level interaction dynamics in determining a good group performance (e.g. higher speaking turns rate and more balanced participation among group members).Comment: Presented at Collective Intelligence conference, 2012 (arXiv:1204.2991

Modeling Infection with Multi-agent Dynamics

Developing the ability to comprehensively study infections in small populations enables us to improve epidemic models and better advise individuals about potential risks to their health. We currently have a limited understanding of how infections spread within a small population because it has been difficult to closely track an infection within a complete community. The paper presents data closely tracking the spread of an infection centered on a student dormitory, collected by leveraging the residents' use of cellular phones. The data are based on daily symptom surveys taken over a period of four months and proximity tracking through cellular phones. We demonstrate that using a Bayesian, discrete-time multi-agent model of infection to model real-world symptom reports and proximity tracking records gives us important insights about infec-tions in small populations

Parameter estimation and inference for stochastic reaction-diffusion systems: application to morphogenesis in D. melanogaster

Background: Reaction-diffusion systems are frequently used in systems biology to model developmental and signalling processes. In many applications, count numbers of the diffusing molecular species are very low, leading to the need to explicitly model the inherent variability using stochastic methods. Despite their importance and frequent use, parameter estimation for both deterministic and stochastic reaction-diffusion systems is still a challenging problem. Results: We present a Bayesian inference approach to solve both the parameter and state estimation problem for stochastic reaction-diffusion systems. This allows a determination of the full posterior distribution of the parameters (expected values and uncertainty). We benchmark the method by illustrating it on a simple synthetic experiment. We then test the method on real data about the diffusion of the morphogen Bicoid in Drosophila melanogaster. The results show how the precision with which parameters can be inferred varies dramatically, indicating that the ability to infer full posterior distributions on the parameters can have important experimental design consequences. Conclusions: The results obtained demonstrate the feasibility and potential advantages of applying a Bayesian approach to parameter estimation in stochastic reaction-diffusion systems. In particular, the ability to estimate credibility intervals associated with parameter estimates can be precious for experimental design. Further work, however, will be needed to ensure the method can scale up to larger problems

Model Reduction for the Chemical Master Equation: an Information-Theoretic Approach

The complexity of mathematical models in biology has rendered model reduction an essential tool in the quantitative biologist's toolkit. For stochastic reaction networks described using the Chemical Master Equation, commonly used methods include time-scale separation, the Linear Mapping Approximation and state-space lumping. Despite the success of these techniques, they appear to be rather disparate and at present no general-purpose approach to model reduction for stochastic reaction networks is known. In this paper we show that most common model reduction approaches for the Chemical Master Equation can be seen as minimising a well-known information-theoretic quantity between the full model and its reduction, the Kullback-Leibler divergence defined on the space of trajectories. This allows us to recast the task of model reduction as a variational problem that can be tackled using standard numerical optimisation approaches. In addition we derive general expressions for the propensities of a reduced system that generalise those found using classical methods. We show that the Kullback-Leibler divergence is a useful metric to assess model discrepancy and to compare different model reduction techniques using three examples from the literature: an autoregulatory feedback loop, the Michaelis-Menten enzyme system and a genetic oscillator

A variational approach to moment-closure approximations for the kinetics of biomolecular reaction networks

Approximate solutions of the chemical master equation and the chemical Fokker-Planck equation are an important tool in the analysis of biomolecular reaction networks. Previous studies have highlighted a number of problems with the moment-closure approach used to obtain such approximations, calling it an ad-hoc method. In this article, we give a new variational derivation of moment-closure equations which provides us with an intuitive understanding of their properties and failure modes and allows us to correct some of these problems. We use mixtures of product-Poisson distributions to obtain a flexible parametric family which solves the commonly observed problem of divergences at low system sizes. We also extend the recently introduced entropic matching approach to arbitrary ansatz distributions and Markov processes, demonstrating that it is a special case of variational moment closure. This provides us with a particularly principled approximation method. Finally, we extend the above approaches to cover the approximation of multi-time joint distributions, resulting in a viable alternative to process-level approximations which are often intractable.Comment: Minor changes and clarifications; corrected some typo