Dataset Information

Markov chain Monte Carlo methods for hierarchical clustering of dynamic causal models.

ABSTRACT: In this article, we address technical difficulties that arise when applying Markov chain Monte Carlo (MCMC) to hierarchical models designed to perform clustering in the space of latent parameters of subject-wise generative models. Specifically, we focus on the case where the subject-wise generative model is a dynamic causal model (DCM) for functional magnetic resonance imaging (fMRI) and clusters are defined in terms of effective brain connectivity. While an attractive approach for detecting mechanistically interpretable subgroups in heterogeneous populations, inverting such a hierarchical model represents a particularly challenging case, since DCM is often characterized by high posterior correlations between its parameters. In this context, standard MCMC schemes exhibit poor performance and extremely slow convergence. In this article, we investigate the properties of hierarchical clustering which lead to the observed failure of standard MCMC schemes and propose a solution designed to improve convergence but preserve computational complexity. Specifically, we introduce a class of proposal distributions which aims to capture the interdependencies between the parameters of the clustering and subject-wise generative models and helps to reduce random walk behaviour of the MCMC scheme. Critically, these proposal distributions only introduce a single hyperparameter that needs to be tuned to achieve good performance. For validation, we apply our proposed solution to synthetic and real-world datasets and also compare it, in terms of computational complexity and performance, to Hamiltonian Monte Carlo (HMC), a state-of-the-art Monte Carlo technique. Our results indicate that, for the specific application domain considered here, our proposed solution shows good convergence performance and superior runtime compared to HMC.

SUBMITTER: Yao Y

PROVIDER: S-EPMC8193526 | biostudies-literature |

REPOSITORIES: biostudies-literature

ACCESS DATA

Similar Datasets

Project description:BackgroundIn quantitative biology, mathematical models are used to describe and analyze biological processes. The parameters of these models are usually unknown and need to be estimated from experimental data using statistical methods. In particular, Markov chain Monte Carlo (MCMC) methods have become increasingly popular as they allow for a rigorous analysis of parameter and prediction uncertainties without the need for assuming parameter identifiability or removing non-identifiable parameters. A broad spectrum of MCMC algorithms have been proposed, including single- and multi-chain approaches. However, selecting and tuning sampling algorithms suited for a given problem remains challenging and a comprehensive comparison of different methods is so far not available.ResultsWe present the results of a thorough benchmarking of state-of-the-art single- and multi-chain sampling methods, including Adaptive Metropolis, Delayed Rejection Adaptive Metropolis, Metropolis adjusted Langevin algorithm, Parallel Tempering and Parallel Hierarchical Sampling. Different initialization and adaptation schemes are considered. To ensure a comprehensive and fair comparison, we consider problems with a range of features such as bifurcations, periodical orbits, multistability of steady-state solutions and chaotic regimes. These problem properties give rise to various posterior distributions including uni- and multi-modal distributions and non-normally distributed mode tails. For an objective comparison, we developed a pipeline for the semi-automatic comparison of sampling results.ConclusionThe comparison of MCMC algorithms, initialization and adaptation schemes revealed that overall multi-chain algorithms perform better than single-chain algorithms. In some cases this performance can be further increased by using a preceding multi-start local optimization scheme. These results can inform the selection of sampling methods and the benchmark collection can serve for the evaluation of new algorithms. Furthermore, our results confirm the need to address exploration quality of MCMC chains before applying the commonly used quality measure of effective sample size to prevent false analysis conclusions.

Project description:In diffusion MRI analysis, advances in biophysical multi-compartment modeling have gained popularity over the conventional Diffusion Tensor Imaging (DTI), because they can obtain a greater specificity in relating the dMRI signal to underlying cellular microstructure. Biophysical multi-compartment models require a parameter estimation, typically performed using either the Maximum Likelihood Estimation (MLE) or the Markov Chain Monte Carlo (MCMC) sampling. Whereas, the MLE provides only a point estimate of the fitted model parameters, the MCMC recovers the entire posterior distribution of the model parameters given in the data, providing additional information such as parameter uncertainty and correlations. MCMC sampling is currently not routinely applied in dMRI microstructure modeling, as it requires adjustment and tuning, specific to each model, particularly in the choice of proposal distributions, burn-in length, thinning, and the number of samples to store. In addition, sampling often takes at least an order of magnitude, more time than non-linear optimization. Here we investigate the performance of the MCMC algorithm variations over multiple popular diffusion microstructure models, to examine whether a single, well performing variation could be applied efficiently and robustly to many models. Using an efficient GPU-based implementation, we showed that run times can be removed as a prohibitive constraint for the sampling of diffusion multi-compartment models. Using this implementation, we investigated the effectiveness of different adaptive MCMC algorithms, burn-in, initialization, and thinning. Finally we applied the theory of the Effective Sample Size, to the diffusion multi-compartment models, as a way of determining a relatively general target for the number of samples needed to characterize parameter distributions for different models and data sets. We conclude that adaptive Metropolis methods increase MCMC performance and select the Adaptive Metropolis-Within-Gibbs (AMWG) algorithm as the primary method. We furthermore advise to initialize the sampling with an MLE point estimate, in which case 100 to 200 samples are sufficient as a burn-in. Finally, we advise against thinning in most use-cases and as a relatively general target for the number of samples, we recommend a multivariate Effective Sample Size of 2,200.

Dataset Information

Markov chain Monte Carlo methods for hierarchical clustering of dynamic causal models.

Similar Datasets

OmicsDI is part of the ELIXIR infrastructure

Tweets