# Dimension-reduced Reconstruction Map Learning for Parameter Estimation in Likelihood-Free Inference Problems

arXiv: https://arxiv.org/abs/2407.13971 · HTML: https://mlsanity.com/paper/2407.13971/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 48 references that are in the map.
- First posted on arXiv 19 Jul 2024.

## Builds on (most cited first, 6 of 6)

- [Sequential Neural Likelihood: Fast Likelihood-free Inference with Autoregressive Flows](https://mlsanity.com/paper/1805.07226/) (2018)
- [Flexible statistical inference for mechanistic models of neural dynamics](https://mlsanity.com/paper/1711.01861/) (2017)
- [Neural Networks for Parameter Estimation in Intractable Models](https://mlsanity.com/paper/2107.14346/) (2021)
- [Parameter Estimation with Dense and Convolutional Neural Networks Applied to the FitzHugh-Nagumo ODE](https://mlsanity.com/paper/2012.06691/) (2020)
- [Parameter Estimation in Hidden Markov Models with Intractable Likelihoods Using Sequential Monte Carlo](https://mlsanity.com/paper/1311.4117/) (2013)
- [Exponential random graph model parameter estimation for very large directed networks](https://mlsanity.com/paper/1904.08063/) (2019)

## Built on by (most cited first, 1 of 1)

- [False Frontiers: Diagnosing and Mitigating Co-Cheating in Self-Evolving Search Agents](https://mlsanity.com/paper/2609.39102/) (2026)

## Abstract (arXiv)

Many application areas rely on models that can be readily simulated but lack a closed-form likelihood, or an accurate approximation under arbitrary parameter values. Existing parameter estimation approaches in this setting are generally approximate. Recent work on using neural network models to reconstruct the mapping from the data space to the parameters from a set of synthetic parameter-data pairs suffers from the curse of dimensionality, resulting in inaccurate estimation as the data size grows. We propose a dimension-reduced approach to likelihood-free estimation which combines the ideas of reconstruction map estimation with dimension-reduction approaches based on subject-specific knowledge. We examine the properties of reconstruction map estimation with and without dimension reduction and explore the trade-off between approximation error due to information loss from reducing the data dimension and approximation error. Numerical examples show that the proposed approach compares favorably with reconstruction map estimation, approximate Bayesian computation, and synthetic likelihood estimation.