Cost-aware simulation-based inference

TL;DR

The paper addresses the high computational cost of simulation-based inference (SBI) when simulator cost varies across parameter space. It introduces cost-aware sampling by constructing a cost-sensitive proposal and using self-normalised importance sampling to bias toward cheaper parameter regions, complemented by a penalty function and a computional gain metric. The approach comes with theoretical guarantees on consistency and finite-variance and is demonstrated across ABC, NPE, and NLE, with applications to a Gamma toy, epidemiology SIR models, and a radio propagation simulator, achieving substantial cost reductions while preserving posterior accuracy. It further highlights practical benefits such as parallelization and situates the method as complementary to existing SBI techniques, with clear avenues for extension and adaptation.

Abstract

Simulation-based inference (SBI) is the preferred framework for estimating parameters of intractable models in science and engineering. A significant challenge in this context is the large computational cost of simulating data from complex models, and the fact that this cost often depends on parameter values. We therefore propose \textit{cost-aware SBI methods} which can significantly reduce the cost of existing sampling-based SBI methods, such as neural SBI and approximate Bayesian computation. This is achieved through a combination of rejection and self-normalised importance sampling, which significantly reduces the number of expensive simulations needed. Our approach is studied extensively on models from epidemiology to telecommunications engineering, where we obtain significant reductions in the overall cost of inference.

Figures (13)

• Figure 1: Estimated cost of the temporal susceptible-infected-recovered model considered in \ref{['sec:experiments_epidemiology']}.
• Figure 2: Flowchart of SBI and Ca-SBI. Ca-SBI utilises the cost function $c$ and a penalty function $g$ to (i) sample from the cost-aware proposal $\tilde{p}_g$, and (ii) compute the cost-aware weights. Step 1 reduces the overall cost from using the simulator, while step 2 guarantees we are sampling from the target SBI posterior.
• Figure 3: Left: Cost-aware prior $\tilde{p}_g(\theta)$ for different penalty functions $g(z) = z^k$ using prior $\mathcal{U}(10^2,10^3)$ for the Gamma experiment. The cost increases linearly with $\theta$, see \ref{['fig:gamma_experiment_npe']}(a). Right: Acceptance probability $A(\theta)$ as a function of $\theta$ for different $g$ functions.
• Figure 4: The Gamma experiment. (a) Cost of simulating $n$ data-points, each with $m=500$ Gamma samples, using the prior and different cost-aware proposals. (b)-(d) MMD between the ABC posteriors and the true posterior for different values of $\theta_{\mathrm{true}}$ over five independent runs with $n=50,000$ and $\epsilon = 0.05$. Sample mean and standard deviation of $m$ points are taken as statistics. The corresponding NPE plots are shown in \ref{['app:gamma_additional']}.
• Figure 5: Cost function estimate of the temporal SIR model at varying levels of accuracy. (a) The real cost function estimated using a $20\times20$ grid with 50 samples for each grid (same as \ref{['fig:intro']}). (b) Estimated cost using a GP model trained on 200 data points. (c) Estimated cost using a GP model trained on only 15 data points. (d) Estimated cost using a linear model trained on 200 data points.

Theorems & Definitions (8)

• Proposition 1
• Proposition 2
• Proposition 3
• Proposition 4
• proof
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• proof