Bayesian inference using qualitative observations of underlying continuous variables

Mitra, Eshan D.; Hlavacek, William S.

doi:10.1093/bioinformatics/btaa084

Cited by 10 publications

(17 citation statements)

References 24 publications

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“…Instead of optimizing the surrogate data, the quantitative data could directly be used to calculate the objective function. A first Bayesian formulation has been proposed (Mitra and Hlavacek 2020 ), but it remains unclear, which statistical model is best suited for the use of qualitative data. A proper statistical formulation would also benefit the integration of qualitative and quantitative data (Mitra et al.…”

Section: Discussionmentioning

confidence: 99%

“…The parameters were estimated by minimizing this penalized objective function. This approach was implemented in the toolbox pyBioNetFit (Mitra et al 2019), making it generally applicable to other problems and recently extended using a probabilistic distance measure (Mitra and Hlavacek 2020).…”

Section: Introductionmentioning

confidence: 99%

“…This approach was implemented in the toolbox pyBioNetFit (Mitra et al. 2019 ), making it generally applicable to other problems and recently extended using a probabilistic distance measure (Mitra and Hlavacek 2020 ). (2) Pargett and Umulis ( 2013 ) and Pargett et al.…”

Section: Introductionmentioning

confidence: 99%

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Parameterization of mechanistic models from qualitative data using an efficient optimal scaling approach

2020

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Quantitative dynamical models facilitate the understanding of biological processes and the prediction of their dynamics. These models usually comprise unknown parameters, which have to be inferred from experimental data. For quantitative experimental data, there are several methods and software tools available. However, for qualitative data the available approaches are limited and computationally demanding. Here, we consider the optimal scaling method which has been developed in statistics for categorical data and has been applied to dynamical systems. This approach turns qualitative variables into quantitative ones, accounting for constraints on their relation. We derive a reduced formulation for the optimization problem defining the optimal scaling. The reduced formulation possesses the same optimal points as the established formulation but requires less degrees of freedom. Parameter estimation for dynamical models of cellular pathways revealed that the reduced formulation improves the robustness and convergence of optimizers. This resulted in substantially reduced computation times. We implemented the proposed approach in the open-source Python Parameter EStimation TOolbox (pyPESTO) to facilitate reuse and extension. The proposed approach enables efficient parameterization of quantitative dynamical models using qualitative data.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Parameterization of mechanistic models from qualitative data using an efficient optimal scaling approach

2020

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“…Therefore, several tailored parameter estimation approaches have been developed: (i) Oguz et al [2013] optimized the number of qualitative observations that were correctly captured by the model. (ii) Mitra et al used qualitative observations as static penalty functions [Mitra et al, 2018] and proposed a pseudo-likelihood function [Mitra and Hlavacek, 2020]. (iii) Pargett et al [2014] employed the concept of the optimal scaling approach (introduced by Shepard [1962]), which is based on finding the best possible quantitative representation (so-called surrogate data) of the qualitative observations.…”

Section: Introductionmentioning

confidence: 99%

Efficient gradient-based parameter estimation for dynamic models using qualitative data

Schmiester

Weindl

Hasenauer

2021

Preprint

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Motivation: Unknown parameters of dynamical models are commonly estimated from experimental data. However, while various efficient optimization and uncertainty analysis methods have been proposed for quantitative data, methods for qualitative data are rare and suffer from bad scaling and convergence. Results: Here, we propose an efficient and reliable framework for estimating the parameters of ordinary differential equation models from qualitative data. In this framework, we derive a semi-analytical algorithm for gradient calculation of the optimal scaling method developed for qualitative data. This enables the use of efficient gradient-based optimization algorithms. We demonstrate that the use of gradient information improves performance of optimization and uncertainty quantification on several application examples. On average, we achieve a speedup of more than one order of magnitude compared to gradient-free optimization. Additionally, in some examples, the gradient-based approach yields substantially improved objective function values and quality of the fits. Accordingly, the proposed framework substantially improves the parameterization of models from qualitative data. Availability: The proposed approach is implemented in the open-source Python Parameter EStimation TOolbox (pyPESTO). All application examples and code to reproduce this study are available at https://doi.org/10.5281/zenodo.4507613.

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“…More recently, Mitra et al applied predefined constraint-based models of categorical data and modified their approach to allow definition of a likelihood function within a Bayesian formalism. 12, 13 However, the ad hoc nature of their constraint models leaves room for biasing assumptions. Given the limited application of Bayesian methods and biases introduced by ad hoc assumptions, the field still has a limited understanding of the contribution of nonquantitative and quantitative data to mechanistic knowledge in biological systems.…”

Section: Introductionmentioning

confidence: 99%

Predictive uncertainty in mechanistic models of cellular processes calibrated to experimental data

Ramanathan

López

2021

Preprint

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Mathematical models are often used to study the structure and dynamics of network-driven cellular processes. In cell biology, models representing biochemical reaction networks have provided significant insights but are often plagued by a dearth of available quantitative data necessary for simulation and analysis. This has in turn led to questions about the usefulness of biochemical network models with unidentifiable parameters and high-degree of parameter sloppiness. In response, approaches to incorporate highly-available non-quantitative data and use this data to improve model certainty have been undertaken with various degrees of success. Here we employ a Bayesian inference and Machine Learning approach to first explore how quantitative and non-quantitative data can constrain a mechanistic model of apoptosis execution, in which all models can be identified. We find that two orders of magnitude more ordinal data measurements than those typically collected are necessary to achieve the same accuracy as that obtained from a quantitative dataset. We also find that ordinal and nominal non-quantitative data on their own can be combined to reduce model uncertainty and thus improve model accuracy. Further analysis demonstrates that the accuracy and certainty of model predictions strongly depends on accurate formulations of the measurement as well as the size and make-up of the nonquantitative datasets. Finally, we demonstrate the potential of a data-driven Machine Learning measurement model to identify informative mechanistic features that predict or define nonquantitative cellular phenotypes, from a systems perspective.

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Bayesian inference using qualitative observations of underlying continuous variables

Cited by 10 publications

References 24 publications

Parameterization of mechanistic models from qualitative data using an efficient optimal scaling approach

Parameterization of mechanistic models from qualitative data using an efficient optimal scaling approach

Efficient gradient-based parameter estimation for dynamic models using qualitative data

Predictive uncertainty in mechanistic models of cellular processes calibrated to experimental data

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