# Simulation-based Inference for High-dimensional Data using Surjective Sequential Neural Likelihood Estimation

arXiv: https://arxiv.org/abs/2308.01054 · HTML: https://mlsanity.com/paper/2308.01054/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 51 of its 87 references that are in the map.
- First posted on arXiv 2 Aug 2023.

## Builds on (most cited first, 30 of 51)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Improving Variational Inference with Inverse Autoregressive Flow](https://mlsanity.com/paper/1606.04934/) (2016)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models](https://mlsanity.com/paper/1810.01367/) (2018)
- [The frontier of simulation-based inference](https://mlsanity.com/paper/1911.01429/) (2019)
- [MADE: Masked Autoencoder for Distribution Estimation](https://mlsanity.com/paper/1502.03509/) (2015)
- [A note on the evaluation of generative models](https://mlsanity.com/paper/1511.01844/) (2015)
- [Revisiting Classifier Two-Sample Tests](https://mlsanity.com/paper/1610.06545/) (2016)
- [On Neural Differential Equations](https://mlsanity.com/paper/2202.02435/) (2022)
- [Flow++: Improving Flow-Based Generative Models with Variational Dequantization and Architecture Design](https://mlsanity.com/paper/1902.00275/) (2019)
- [Sequential Neural Likelihood: Fast Likelihood-free Inference with Autoregressive Flows](https://mlsanity.com/paper/1805.07226/) (2018)
- [Automatic Posterior Transformation for Likelihood-Free Inference](https://mlsanity.com/paper/1905.07488/) (2019)
- [Neural Autoregressive Flows](https://mlsanity.com/paper/1804.00779/) (2018)
- [Flexible statistical inference for mechanistic models of neural dynamics](https://mlsanity.com/paper/1711.01861/) (2017)
- [Benchmarking Simulation-Based Inference](https://mlsanity.com/paper/2101.04653/) (2021)
- [Validating Bayesian Inference Algorithms with Simulation-Based Calibration](https://mlsanity.com/paper/1804.06788/) (2018)
- [Flow Matching for Scalable Simulation-Based Inference](https://mlsanity.com/paper/2305.17161/) (2023)
- [Generative Models and Model Criticism via Optimized Maximum Mean Discrepancy](https://mlsanity.com/paper/1611.04488/) (2016)
- [On Contrastive Learning for Likelihood-free Inference](https://mlsanity.com/paper/2002.03712/) (2020)
- [Approximating Likelihood Ratios with Calibrated Discriminative Classifiers](https://mlsanity.com/paper/1506.02169/) (2015)
- [Likelihood-free inference by ratio estimation](https://mlsanity.com/paper/1611.10242/) (2016)
- [Real-time gravitational-wave science with neural posterior estimation](https://mlsanity.com/paper/2106.12594/) (2021)
- [Neural Approximate Sufficient Statistics for Implicit Models](https://mlsanity.com/paper/2010.10079/) (2020)
- [SurVAE Flows: Surjections to Bridge the Gap between VAEs and Flows](https://mlsanity.com/paper/2007.02731/) (2020)
- [Scikit-dimension: a Python package for intrinsic dimension estimation](https://mlsanity.com/paper/2109.02596/) (2021)

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

- [A Kernel-Based Conditional Two-Sample Test Using Nearest Neighbors (with Applications to Calibration, Regression Curves, and Simulation-Based Inference)](https://mlsanity.com/paper/2407.16550/) (2024)
- [Unifying Simulation and Inference with Normalizing Flows](https://mlsanity.com/paper/2404.18992/) (2024)
- [Simulation-based Inference with the Python Package sbijax](https://mlsanity.com/paper/2409.19435/) (2024)
- [Causal Posterior Estimation](https://mlsanity.com/paper/2505.21468/) (2025)
- [Uncertainty quantification and out-of-distribution detection using surjective normalizing flows](https://mlsanity.com/paper/2311.00377/) (2023)
- [Generative AI-enhanced Probabilistic Multi-Fidelity Surrogate Modeling Via Transfer Learning](https://mlsanity.com/paper/2602.00072/) (2026)
- [Pre-trained Tabular Foundation Models as Versatile Summary Networks for Neural Posterior Estimation](https://mlsanity.com/paper/2605.07765/) (2026)
- [Neural composite likelihood estimation: simulation based inference for time series](https://mlsanity.com/paper/2609.21762/) (2026)

## Abstract (arXiv)

Neural likelihood estimation methods for simulation-based inference can suffer from performance degradation when the modeled data is very high-dimensional or lies along a lower-dimensional manifold, which is due to the inability of the density estimator to accurately estimate a density function. We present Surjective Sequential Neural Likelihood (SSNL) estimation, a novel member in the family of methods for simulation-based inference (SBI). SSNL fits a dimensionality-reducing surjective normalizing flow model and uses it as a surrogate likelihood function, which allows for computational inference via Markov chain Monte Carlo or variational Bayes methods. Among other benefits, SSNL avoids the requirement to manually craft summary statistics for inference of high-dimensional data sets, since the lower-dimensional representation is computed simultaneously with learning the likelihood and without additional computational overhead. We evaluate SSNL on a wide variety of experiments, including two challenging real-world examples from the astrophysics and neuroscience literatures, and show that it either outperforms or is on par with state-of-the-art methods, making it an excellent off-the-shelf estimator for SBI for high-dimensional data sets.