Efficient approximate Bayesian inference for large, heterogeneous biological datasets

Abstract

Simulation-based inference (SBI) offers a route to connect biological data with mechanistic models. At the frontier of biology, datasets continue to grow in scale and richness, and increasingly record heterogeneity between individual observations that a mechanistic model can take into account. Approximate Bayesian Computation (ABC) remains a popular approach to SBI due to its ease of use, but incorporating this heterogeneity often requires a separate simulation of each observation, which is prohibitively expensive at scale. A previously proposed technique, minibatch Sequential Monte Carlo ABC (SMC ABC), reduces this cost by simulating a fixed-size random subset of observations for each proposal, at the price of sampling noise that limits precision. Here, we present an adaptive minibatch approach that uses small batches during early exploration and increases the batch size as the posterior is refined. The adaptive batch size is set by the target precision and does not grow with the size of the dataset, so the savings over full-data SMC ABC increase for larger datasets. We demonstrate the method on synthetic biological models and on real single-cell gene-expression data that vary in scale and type of heterogeneity, including cell geometry and initial condition. In each case, the adaptive scheme obtains posteriors close to those of full-data SMC ABC at a fraction of the cost. Altogether, adaptive minibatching improves the tradeoff between speed and precision in SMC ABC and opens the door to mechanistic inference on large, heterogeneous biological datasets.