# Exponential Family Estimation via Adversarial Dynamics Embedding

arXiv: https://arxiv.org/abs/1904.12083 · HTML: https://mlsanity.com/paper/1904.12083/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Apr 2019.

## Built on by (most cited first, 30 of 30)

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- [Towards Understanding the Generative Capability of Adversarially Robust Classifiers](https://mlsanity.com/paper/2108.09093/) (2021)
- [Discrete Langevin Sampler via Wasserstein Gradient Flow](https://mlsanity.com/paper/2206.14897/) (2022)
- [S2AC: Energy-Based Reinforcement Learning with Stein Soft Actor Critic](https://mlsanity.com/paper/2405.00987/) (2024)
- [Diffusion Spectral Representation for Reinforcement Learning](https://mlsanity.com/paper/2406.16121/) (2024)
- [Two-Scale Gradient Descent Ascent Dynamics Finds Mixed Nash Equilibria of Continuous Games: A Mean-Field Perspective](https://mlsanity.com/paper/2212.08791/) (2022)
- [Designing Perceptual Puzzles by Differentiating Probabilistic Programs](https://mlsanity.com/paper/2204.12301/) (2022)
- [A Computationally Efficient Method for Learning Exponential Family Distributions](https://mlsanity.com/paper/2110.15397/) (2021)
- [Revisiting Energy Based Models as Policies: Ranking Noise Contrastive Estimation and Interpolating Energy Models](https://mlsanity.com/paper/2309.05803/) (2023)
- [Dual Training of Energy-Based Models with Overparametrized Shallow Neural Networks](https://mlsanity.com/paper/2107.05134/) (2021)
- [Planning with Sequence Models through Iterative Energy Minimization](https://mlsanity.com/paper/2303.16189/) (2023)
- [Pseudo-Spherical Contrastive Divergence](https://mlsanity.com/paper/2111.00780/) (2021)
- [Exponential Family Model-Based Reinforcement Learning via Score Matching](https://mlsanity.com/paper/2112.14195/) (2021)
- [Persistently Trained, Diffusion-assisted Energy-based Models](https://mlsanity.com/paper/2304.10707/) (2023)
- [Balanced Training of Energy-Based Models with Adaptive Flow Sampling](https://mlsanity.com/paper/2306.00684/) (2023)
- [Maximum Entropy Inverse Reinforcement Learning of Diffusion Models with Energy-Based Models](https://mlsanity.com/paper/2407.00626/) (2024)
- [Improving Generative Flow Networks with Path Regularization](https://mlsanity.com/paper/2209.15092/) (2022)
- [Failing Forward: Adaptive Failure-Informed Learning for Vision-Language-Action Models](https://mlsanity.com/paper/2605.08434/) (2026)
- [Simultaneous Transport Evolution for Minimax Equilibria on Measures](https://mlsanity.com/paper/2202.06460/) (2022)
- [On Computationally Efficient Learning of Exponential Family Distributions](https://mlsanity.com/paper/2309.06413/) (2023)
- [Divergences induced by dual subtractive and divisive normalizations of exponential families and their convex deformations](https://mlsanity.com/paper/2312.12849/) (2023)
- [AmorLIP: Efficient Language-Image Pretraining via Amortization](https://mlsanity.com/paper/2505.18983/) (2025)
- [A Unified View of cGANs with and without Classifiers](https://mlsanity.com/paper/2111.01035/) (2021)
- [Robust Estimation for Kernel Exponential Families with Smoothed Total Variation Distances](https://mlsanity.com/paper/2410.20760/) (2024)
- [Scalable Personalised Item Ranking through Parametric Density Estimation](https://mlsanity.com/paper/2105.04769/) (2021)
- [Spectral Ghost in Representation Learning: from Component Analysis to Self-Supervised Learning](https://mlsanity.com/paper/2601.20154/) (2026)

## Abstract (arXiv)

We present an efficient algorithm for maximum likelihood estimation (MLE) of exponential family models, with a general parametrization of the energy function that includes neural networks. We exploit the primal-dual view of the MLE with a kinetics augmented model to obtain an estimate associated with an adversarial dual sampler. To represent this sampler, we introduce a novel neural architecture, dynamics embedding, that generalizes Hamiltonian Monte-Carlo (HMC). The proposed approach inherits the flexibility of HMC while enabling tractable entropy estimation for the augmented model. By learning both a dual sampler and the primal model simultaneously, and sharing parameters between them, we obviate the requirement to design a separate sampling procedure once the model has been trained, leading to more effective learning. We show that many existing estimators, such as contrastive divergence, pseudo/composite-likelihood, score matching, minimum Stein discrepancy estimator, non-local contrastive objectives, noise-contrastive estimation, and minimum probability flow, are special cases of the proposed approach, each expressed by a different (fixed) dual sampler. An empirical investigation shows that adapting the sampler during MLE can significantly improve on state-of-the-art estimators.