# ABC-CDE: Towards Approximate Bayesian Computation with Complex High-Dimensional Data and Limited Simulations

arXiv: https://arxiv.org/abs/1805.05480 · HTML: https://mlsanity.com/paper/1805.05480/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 May 2018.

## Built on by (most cited first, 8 of 8)

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- [CP4SBI: Local Conformal Calibration of Credible Sets in Simulation-Based Inference](https://mlsanity.com/paper/2508.17077/) (2025)
- [Efficient identification of informative features in simulation-based inference](https://mlsanity.com/paper/2210.11915/) (2022)
- [A Bayesian Optimization approach for calibrating large-scale activity-based transport models](https://mlsanity.com/paper/2302.03480/) (2023)
- [Conformal Calibration of Statistical Confidence Sets](https://mlsanity.com/paper/2411.19368/) (2024)
- [A Three-Way Testing Framework for Quantifying Epistemic Calibration Uncertainty in SBI](https://mlsanity.com/paper/2609.24419/) (2026)

## Abstract (arXiv)

Approximate Bayesian Computation (ABC) is typically used when the likelihood is either unavailable or intractable but where data can be simulated under different parameter settings using a forward model. Despite the recent interest in ABC, high-dimensional data and costly simulations still remain a bottleneck in some applications. There is also no consensus as to how to best assess the performance of such methods without knowing the true posterior. We show how a nonparametric conditional density estimation (CDE) framework, which we refer to as ABC-CDE, help address three nontrivial challenges in ABC: (i) how to efficiently estimate the posterior distribution with limited simulations and different types of data, (ii) how to tune and compare the performance of ABC and related methods in estimating the posterior itself, rather than just certain properties of the density, and (iii) how to efficiently choose among a large set of summary statistics based on a CDE surrogate loss. We provide theoretical and empirical evidence that justify ABC-CDE procedures that em directly estimate and assess the posterior based on an initial ABC sample, and we describe settings where standard ABC and regression-based approaches are inadequate.