36,764 research outputs found
Parameter Inference in Differential Equation Models of Biopathways using Time Warped Gradient Matching
Parameter inference in mechanistic models of biopathways based on systems
of coupled differential equations is a topical yet computationally challenging problem,
due to the fact that each parameter adaptation involves a numerical integration of the
differential equations. Techniques based on gradient matching, which aim to minimize
the discrepancy between the slope of a data interpolant and the derivatives predicted
from the differential equations, offer a computationally appealing shortcut to the inference
problem. However, gradient matching critically hinges on the smoothing scheme
for function interpolation, with spurious wiggles in the interpolant having a dramatic
effect on the subsequent inference. The present article demonstrates that a time warping
approach aiming to homogenize intrinsic functional length scales can lead to a signifi-
cant improvement in parameter estimation accuracy. We demonstrate the effectiveness
of this scheme on noisy data from a dynamical system with periodic limit cycle and a
biopathway
ODE parameter inference using adaptive gradient matching with Gaussian processes
Parameter inference in mechanistic models based on systems of coupled differential equa- tions is a topical yet computationally chal- lenging problem, due to the need to fol- low each parameter adaptation with a nu- merical integration of the differential equa- tions. Techniques based on gradient match- ing, which aim to minimize the discrepancy between the slope of a data interpolant and the derivatives predicted from the differen- tial equations, offer a computationally ap- pealing shortcut to the inference problem. The present paper discusses a method based on nonparametric Bayesian statistics with Gaussian processes due to Calderhead et al. (2008), and shows how inference in this model can be substantially improved by consistently inferring all parameters from the joint dis- tribution. We demonstrate the efficiency of our adaptive gradient matching technique on three benchmark systems, and perform a de- tailed comparison with the method in Calder- head et al. (2008) and the explicit ODE inte- gration approach, both in terms of parameter inference accuracy and in terms of computa- tional efficiency
Gradient matching methods for computational inference in mechanistic models for systems biology: a review and comparative analysis
Parameter inference in mathematical models of biological pathways, expressed as coupled ordinary differential equations (ODEs), is a challenging problem in contemporary systems biology. Conventional methods involve repeatedly solving the ODEs by numerical integration, which is computationally onerous and does not scale up to complex systems. Aimed at reducing the computational costs, new concepts based on gradient matching have recently been proposed in the computational statistics and machine learning literature. In a preliminary smoothing step, the time series data are interpolated; then, in a second step, the parameters of the ODEs are optimised so as to minimise some metric measuring the difference between the slopes of the tangents to the interpolants, and the time derivatives from the ODEs. In this way, the ODEs never have to be solved explicitly. This review provides a concise methodological overview of the current state-of-the-art methods for gradient matching in ODEs, followed by an empirical comparative evaluation based on a set of widely used and representative benchmark data
The adaptive interpolation method for proving replica formulas. Applications to the Curie-Weiss and Wigner spike models
In this contribution we give a pedagogic introduction to the newly introduced
adaptive interpolation method to prove in a simple and unified way replica
formulas for Bayesian optimal inference problems. Many aspects of this method
can already be explained at the level of the simple Curie-Weiss spin system.
This provides a new method of solution for this model which does not appear to
be known. We then generalize this analysis to a paradigmatic inference problem,
namely rank-one matrix estimation, also refered to as the Wigner spike model in
statistics. We give many pointers to the recent literature where the method has
been succesfully applied
Accelerating gravitational wave parameter estimation with multi-band template interpolation
Parameter estimation on gravitational wave signals from compact binary
coalescence (CBC) requires the evaluation of computationally intensive waveform
models, typically the bottleneck in the analysis. This cost will increase
further as low frequency sensitivity in later second and third generation
detectors motivates the use of longer waveforms.
We describe a method for accelerating parameter estimation by exploiting the
chirping behaviour of the signals to sample the waveform sparsely for portions
where the full frequency resolution is not required. We demonstrate that the
method can reproduce the original results with a waveform mismatch of , but with a waveform generation cost up to times
lower for computationally costly frequency-domain waveforms starting from below
8 Hz
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