Approximate Bayesian computation, stochastic algorithms and non-local means for complex noise models

Measurement Noise ◽

Supplementary Information ◽

Parameter Estimates ◽

Bayesian Computation ◽

Implicit Assumption ◽

Exact Inference ◽

Link Type ◽

Approximate Bayesian ◽

Noise Models

AbstractMotivationApproximate Bayesian Computation (ABC) is an increasingly popular method for likelihood-free parameter inference in systems biology and other fields of research, since it allows analysing complex stochastic models. However, the introduced approximation error is often not clear. It has been shown that ABC actually gives exact inference under the implicit assumption of a measurement noise model. Noise being common in biological systems, it is intriguing to exploit this insight. But this is difficult in practice, since ABC is in general highly computationally demanding. Thus, the question we want to answer here is how to efficiently account for measurement noise in ABC.ResultsWe illustrate exemplarily how ABC yields erroneous parameter estimates when neglecting measurement noise. Then, we discuss practical ways of correctly including the measurement noise in the analysis. We present an efficient adaptive sequential importance sampling based algorithm applicable to various model types and noise models. We test and compare it on several models, including ordinary and stochastic differential equations, Markov jump processes, and stochastically interacting agents, and noise models including normal, Laplace, and Poisson noise. We conclude that the proposed algorithm could improve the accuracy of parameter estimates for a broad spectrum of applications.AvailabilityThe developed algorithms are made publicly available as part of the open-source python toolbox pyABC (https://github.com/icb-dcm/pyabc)[email protected] informationSupplementary information is available at bioRxiv online. Supplementary code and data are available online at http://doi.org/10.5281/zenodo.3631120.

Efficient exact inference for dynamical systems with noisy measurements using sequential approximate Bayesian computation

Bioinformatics ◽

10.1093/bioinformatics/btaa397 ◽

2020 ◽

Vol 36 (Supplement_1) ◽

pp. i551-i559

Author(s):

Yannik Schälte ◽

Jan Hasenauer

Keyword(s):

Approximation Error ◽

Measurement Noise ◽

Supplementary Information ◽

Parameter Estimates ◽

Bayesian Computation ◽

Implicit Assumption ◽

Exact Inference ◽

Approximate Bayesian ◽

Noise Models

Abstract Motivation Approximate Bayesian computation (ABC) is an increasingly popular method for likelihood-free parameter inference in systems biology and other fields of research, as it allows analyzing complex stochastic models. However, the introduced approximation error is often not clear. It has been shown that ABC actually gives exact inference under the implicit assumption of a measurement noise model. Noise being common in biological systems, it is intriguing to exploit this insight. But this is difficult in practice, as ABC is in general highly computationally demanding. Thus, the question we want to answer here is how to efficiently account for measurement noise in ABC. Results We illustrate exemplarily how ABC yields erroneous parameter estimates when neglecting measurement noise. Then, we discuss practical ways of correctly including the measurement noise in the analysis. We present an efficient adaptive sequential importance sampling-based algorithm applicable to various model types and noise models. We test and compare it on several models, including ordinary and stochastic differential equations, Markov jump processes and stochastically interacting agents, and noise models including normal, Laplace and Poisson noise. We conclude that the proposed algorithm could improve the accuracy of parameter estimates for a broad spectrum of applications. Availability and implementation The developed algorithms are made publicly available as part of the open-source python toolbox pyABC (https://github.com/icb-dcm/pyabc). Supplementary information Supplementary data are available at Bioinformatics online.

Gaussian process enhanced semi-automatic approximate Bayesian computation: parameter inference in a stochastic differential equation system for chemotaxis

Journal of Computational Physics ◽

10.1016/j.jcp.2020.109999 ◽

2020 ◽

pp. 109999

Author(s):

Agnieszka Borowska ◽

Diana Giurghita ◽

Dirk Husmeier

Keyword(s):

Differential Equation ◽

Stochastic Differential Equation ◽

Gaussian Process ◽

Equation System ◽

Bayesian Computation ◽

Differential Equation System ◽

Parameter Inference ◽

Weighted approximate Bayesian computation via Sanov’s theorem

Computational Statistics ◽

10.1007/s00180-021-01093-4 ◽

2021 ◽

Author(s):

Cecilia Viscardi ◽

Michele Boreale ◽

Fabio Corradi

Keyword(s):

Large Deviations ◽

Posterior Distribution ◽

Bayesian Computation ◽

Information Theoretic ◽

Discrete Random Variables ◽

Positive Weights ◽

Approximate Bayesian ◽

Information Theoretic Method ◽

Computational Resources

AbstractWe consider the problem of sample degeneracy in Approximate Bayesian Computation. It arises when proposed values of the parameters, once given as input to the generative model, rarely lead to simulations resembling the observed data and are hence discarded. Such “poor” parameter proposals do not contribute at all to the representation of the parameter’s posterior distribution. This leads to a very large number of required simulations and/or a waste of computational resources, as well as to distortions in the computed posterior distribution. To mitigate this problem, we propose an algorithm, referred to as the Large Deviations Weighted Approximate Bayesian Computation algorithm, where, via Sanov’s Theorem, strictly positive weights are computed for all proposed parameters, thus avoiding the rejection step altogether. In order to derive a computable asymptotic approximation from Sanov’s result, we adopt the information theoretic “method of types” formulation of the method of Large Deviations, thus restricting our attention to models for i.i.d. discrete random variables. Finally, we experimentally evaluate our method through a proof-of-concept implementation.

Inference of Brain Networks with Approximate Bayesian Computation – assessing face validity with an example application in Parkinsonism

NeuroImage ◽

10.1016/j.neuroimage.2021.118020 ◽

2021 ◽

pp. 118020

Author(s):

Timothy O. West ◽

Luc Berthouze ◽

Simon F. Farmer ◽

Hayriye Cagnan ◽

Vladimir Litvak

Keyword(s):

Brain Networks ◽

Face Validity ◽

Bayesian Computation ◽

Flow parameter estimation using laser absorption spectroscopy and approximate Bayesian computation

Experiments in Fluids ◽

10.1007/s00348-020-03122-2 ◽

2021 ◽

Vol 62 (2) ◽

Author(s):

Jason D. Christopher ◽

Olga A. Doronina ◽

Dan Petrykowski ◽

Torrey R. S. Hayden ◽

Caelan Lapointe ◽

...

Keyword(s):

Parameter Estimation ◽

Absorption Spectroscopy ◽

Flow Parameter ◽

Bayesian Computation ◽

Laser Absorption Spectroscopy ◽

Laser Absorption ◽

Approximate Bayesian Computation for Discrete Spaces

Entropy ◽

10.3390/e23030312 ◽

2021 ◽

Vol 23 (3) ◽

pp. 312

Author(s):

Ilze A. Auzina ◽

Jakub M. Tomczak

Keyword(s):

Likelihood Function ◽

Real Life ◽

Random Variables ◽

Bayesian Computation ◽

Inference Problem ◽

Markov Kernel ◽

Inference Problems ◽

Binary Neural Network ◽

Many real-life processes are black-box problems, i.e., the internal workings are inaccessible or a closed-form mathematical expression of the likelihood function cannot be defined. For continuous random variables, likelihood-free inference problems can be solved via Approximate Bayesian Computation (ABC). However, an optimal alternative for discrete random variables is yet to be formulated. Here, we aim to fill this research gap. We propose an adjusted population-based MCMC ABC method by re-defining the standard ABC parameters to discrete ones and by introducing a novel Markov kernel that is inspired by differential evolution. We first assess the proposed Markov kernel on a likelihood-based inference problem, namely discovering the underlying diseases based on a QMR-DTnetwork and, subsequently, the entire method on three likelihood-free inference problems: (i) the QMR-DT network with the unknown likelihood function, (ii) the learning binary neural network, and (iii) neural architecture search. The obtained results indicate the high potential of the proposed framework and the superiority of the new Markov kernel.