Monte Carlo samplers for efficient network inference

Abstract

Accessing information on an underlying network driving a biological process often involves interrupting the process and collecting snapshot data. When snapshot data are stochastic, the data’s structure necessitates a probabilistic description to infer underlying reaction networks. As an example, we may imagine wanting to learn gene state networks from the type of data collected in single molecule RNA fluorescence in situ hybridization (RNA-FISH). In the networks we consider, nodes represent network states, and edges represent biochemical reaction rates linking states. Simultaneously estimating the number of nodes and constituent parameters from snapshot data remains a challenging task in part on account of data uncertainty and timescale separations between kinetic parameters mediating the network. While parametric Bayesian methods learn parameters given a network structure (with known node numbers) with rigorously propagated measurement uncertainty, learning the number of nodes and parameters with potentially large timescale separations remain open questions. Here, we propose a Bayesian nonparametric framework and describe a hybrid Bayesian Markov Chain Monte Carlo (MCMC) sampler directly addressing these challenges. In particular, in our hybrid method, Hamiltonian Monte Carlo (HMC) leverages local posterior geometries in inference to explore the parameter space; Adaptive Metropolis Hastings (AMH) learns correlations between plausible parameter sets to efficiently propose probable models; and Parallel Tempering takes into account multiple models simultaneously with tempered information content to augment sampling efficiency. We apply our method to synthetic data mimicking single molecule RNA-FISH, a popular snapshot method in probing transcriptional networks to illustrate the identified challenges inherent to learning dynamical models from these snapshots and how our method addresses them.

From Average Transient Transporter Currents to Microscopic Mechanism─A Bayesian Analysis

“…We found that the BI methods were the most computationally expensive but had a comparable efficiency (number of likelihood calculations per second) as MLE methods such as differential evolution (see Figure SI 19), while generating full posterior distributions rather than point estimates. On the whole, our data on what might be considered a simple model with synthetic data clearly demonstrate the technical challenges of BI , and highlight the need for careful evaluation of MCMC sampling and MLE optimization.…”

Bayesian Mechanistic Inference, Statistical Mechanics, and a New Era for Monte Carlo

“…While we only discuss a few selected algorithms and their trade-offs, it is important to note that there are hybrid approaches that combine multiple methods. 32 The random walk Metropolis−Hastings (MH) algorithm 20 is a well established, basic method for Markov chain Monte Carlo sampling. Briefly, for each iteration, a random jump from the current parameter set to a new parameter set is performed using a proposal (jump) distribution.…”

“…Fixed-temperature algorithms are stand-alone sampling procedures that can be integrated into a larger multi-temperature sampler. While we only discuss a few selected algorithms and their trade-offs, it is important to note that there are hybrid approaches that combine multiple methods …”