# Parameter Estimation in DAGs from Incomplete Data via Optimal Transport

arXiv: https://arxiv.org/abs/2305.15927 · HTML: https://mlsanity.com/paper/2305.15927/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 93 references that are in the map.
- First posted on arXiv 25 May 2023.

## Builds on (most cited first, 30 of 40)

- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Fast R-CNN](https://mlsanity.com/paper/1504.08083/) (2015)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [Image Transformer](https://mlsanity.com/paper/1802.05751/) (2018)
- [Vector-quantized Image Modeling with Improved VQGAN](https://mlsanity.com/paper/2110.04627/) (2021)
- [Improving Variational Inference with Inverse Autoregressive Flow](https://mlsanity.com/paper/1606.04934/) (2016)
- [Wasserstein Auto-Encoders](https://mlsanity.com/paper/1711.01558/) (2017)
- [DAG-GNN: DAG Structure Learning with Graph Neural Networks](https://mlsanity.com/paper/1904.10098/) (2019)
- [Black Box Variational Inference](https://mlsanity.com/paper/1401.0118/) (2013)
- [Autoencoding Variational Inference For Topic Models](https://mlsanity.com/paper/1703.01488/) (2017)
- [R'enyi Divergence Variational Inference](https://mlsanity.com/paper/1602.02311/) (2016)
- [Deep End-to-end Causal Inference](https://mlsanity.com/paper/2202.02195/) (2022)
- [Hierarchical Variational Models](https://mlsanity.com/paper/1511.02386/) (2015)
- [SQ-VAE: Variational Bayes on Discrete Representation with Self-annealed Stochastic Quantization](https://mlsanity.com/paper/2205.07547/) (2022)
- [Banach Wasserstein GAN](https://mlsanity.com/paper/1806.06621/) (2018)
- [Semi-Implicit Variational Inference](https://mlsanity.com/paper/1805.11183/) (2018)
- [The Usual Suspects? Reassessing Blame for VAE Posterior Collapse](https://mlsanity.com/paper/1912.10702/) (2019)
- [Topic Modelling Meets Deep Neural Networks: A Survey](https://mlsanity.com/paper/2103.00498/) (2021)
- [Neural Topic Model via Optimal Transport](https://mlsanity.com/paper/2008.13537/) (2020)
- [Multilevel Clustering via Wasserstein Means](https://mlsanity.com/paper/1706.03883/) (2017)
- [Variance reduction properties of the reparameterization trick](https://mlsanity.com/paper/1809.10330/) (2018)
- [Black-box α-divergence Minimization](https://mlsanity.com/paper/1511.03243/) (2015)
- [A Unified Wasserstein Distributional Robustness Framework for Adversarial Training](https://mlsanity.com/paper/2202.13437/) (2022)
- [Representing Mixtures of Word Embeddings with Mixtures of Topic Embeddings](https://mlsanity.com/paper/2203.01570/) (2022)
- [Unbiased Implicit Variational Inference](https://mlsanity.com/paper/1808.02078/) (2018)

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

- [Optimal Transport for Structure Learning Under Missing Data](https://mlsanity.com/paper/2402.15255/) (2024)

## Abstract (arXiv)

Estimating the parameters of a probabilistic directed graphical model from incomplete data is a long-standing challenge. This is because, in the presence of latent variables, both the likelihood function and posterior distribution are intractable without assumptions about structural dependencies or model classes. While existing learning methods are fundamentally based on likelihood maximization, here we offer a new view of the parameter learning problem through the lens of optimal transport. This perspective licenses a general framework that operates on any directed graphs without making unrealistic assumptions on the posterior over the latent variables or resorting to variational approximations. We develop a theoretical framework and support it with extensive empirical evidence demonstrating the versatility and robustness of our approach. Across experiments, we show that not only can our method effectively recover the ground-truth parameters but it also performs comparably or better than competing baselines on downstream applications.