# Unifying Likelihood-free Inference with Black-box Optimization and Beyond

arXiv: https://arxiv.org/abs/2110.03372 · HTML: https://mlsanity.com/paper/2110.03372/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 74 references that are in the map.
- First posted on arXiv 6 Oct 2021.

## Builds on (most cited first, 30 of 31)

- [Regularized Evolution for Image Classifier Architecture Search](https://mlsanity.com/paper/1802.01548/) (2018)
- [Automatic chemical design using a data-driven continuous representation of molecules](https://mlsanity.com/paper/1610.02415/) (2016)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Evolution Strategies as a Scalable Alternative to Reinforcement Learning](https://mlsanity.com/paper/1703.03864/) (2017)
- [GraphAF: a Flow-based Autoregressive Model for Molecular Graph Generation](https://mlsanity.com/paper/2001.09382/) (2020)
- [Evaluating Protein Transfer Learning with TAPE](https://mlsanity.com/paper/1906.08230/) (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)
- [Optimization of Molecules via Deep Reinforcement Learning](https://mlsanity.com/paper/1810.08678/) (2018)
- [Flexible statistical inference for mechanistic models of neural dynamics](https://mlsanity.com/paper/1711.01861/) (2017)
- [ProtTrans: Towards Cracking the Language of Life's Code Through Self-Supervised Deep Learning and High Performance Computing](https://mlsanity.com/paper/2007.06225/) (2020)
- [Objective-Reinforced Generative Adversarial Networks (ORGAN) for Sequence Generation Models](https://mlsanity.com/paper/1705.10843/) (2017)
- [Conditioning by adaptive sampling for robust design](https://mlsanity.com/paper/1901.10060/) (2019)
- [Likelihood-free inference by ratio estimation](https://mlsanity.com/paper/1611.10242/) (2016)
- [Neural Approximate Sufficient Statistics for Implicit Models](https://mlsanity.com/paper/2010.10079/) (2020)
- [Augmenting Genetic Algorithms with Deep Neural Networks for Exploring the Chemical Space](https://mlsanity.com/paper/1909.11655/) (2019)
- [Likelihood-free inference with emulator networks](https://mlsanity.com/paper/1805.09294/) (2018)
- [Mining gold from implicit models to improve likelihood-free inference](https://mlsanity.com/paper/1805.12244/) (2018)
- [Learning To Navigate The Synthetically Accessible Chemical Space Using Reinforcement Learning](https://mlsanity.com/paper/2004.12485/) (2020)
- [Fast ε-free Inference of Simulation Models with Bayesian Conditional Density Estimation](https://mlsanity.com/paper/1605.06376/) (2016)
- [Guiding Deep Molecular Optimization with Genetic Exploration](https://mlsanity.com/paper/2007.04897/) (2020)
- [Design by adaptive sampling](https://mlsanity.com/paper/1810.03714/) (2018)
- [A Likelihood-Free Inference Framework for Population Genetic Data using Exchangeable Neural Networks](https://mlsanity.com/paper/1802.06153/) (2018)
- [Population-Based Black-Box Optimization for Biological Sequence Design](https://mlsanity.com/paper/2006.03227/) (2020)
- [High-Dimensional Density Ratio Estimation with Extensions to Approximate Likelihood Computation](https://mlsanity.com/paper/1404.7063/) (2014)
- [Likelihood-free inference via classification](https://mlsanity.com/paper/1407.4981/) (2014)
- [Variational Bayes with Intractable Likelihood](https://mlsanity.com/paper/1503.08621/) (2015)
- [Adaptive Gaussian Copula ABC](https://mlsanity.com/paper/1902.10704/) (2019)
- [Approximating the Likelihood in Approximate Bayesian Computation](https://mlsanity.com/paper/1803.06645/) (2018)
- [Derivative free optimization via repeated classification](https://mlsanity.com/paper/1804.03761/) (2018)

## Built on by (most cited first, 11 of 11)

- [Diffusion Generative Flow Samplers: Improving learning signals through partial trajectory optimization](https://mlsanity.com/paper/2310.02679/) (2023)
- [Diffusion Models as Constrained Samplers for Optimization with Unknown Constraints](https://mlsanity.com/paper/2402.18012/) (2024)
- [Distributional GFlowNets with Quantile Flows](https://mlsanity.com/paper/2302.05793/) (2023)
- [Unifying Generative Models with GFlowNets and Beyond](https://mlsanity.com/paper/2209.02606/) (2022)
- [Plug & Play Directed Evolution of Proteins with Gradient-based Discrete MCMC](https://mlsanity.com/paper/2212.09925/) (2022)
- [Pre-Training and Fine-Tuning Generative Flow Networks](https://mlsanity.com/paper/2310.03419/) (2023)
- [Latent State Marginalization as a Low-cost Approach for Improving Exploration](https://mlsanity.com/paper/2210.00999/) (2022)
- [Importance Weighted Expectation-Maximization for Protein Sequence Design](https://mlsanity.com/paper/2305.00386/) (2023)
- [ProSpero: Active Learning for Robust Protein Design Beyond Wild-Type Neighborhoods](https://mlsanity.com/paper/2505.22494/) (2025)
- [BOAT: Navigating the Sea of In Silico Predictors for Antibody Design via Multi-Objective Bayesian Optimization](https://mlsanity.com/paper/2604.13980/) (2026)
- [Predictor-Guided Latent Space Codon Optimization for Maximizing Protein Expression](https://mlsanity.com/paper/2610.03098/) (2026)

## Abstract (arXiv)

Black-box optimization formulations for biological sequence design have drawn recent attention due to their promising potential impact on the pharmaceutical industry. In this work, we propose to unify two seemingly distinct worlds: likelihood-free inference and black-box optimization, under one probabilistic framework. In tandem, we provide a recipe for constructing various sequence design methods based on this framework. We show how previous optimization approaches can be "reinvented" in our framework, and further propose new probabilistic black-box optimization algorithms. Extensive experiments on sequence design application illustrate the benefits of the proposed methodology.