# Inference via low-dimensional couplings

arXiv: https://arxiv.org/abs/1703.06131 · HTML: https://mlsanity.com/paper/1703.06131/

## Key facts

- Cited by 44 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Mar 2017.

## Built on by (most cited first, 30 of 44)

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- [Score matching through the roof: linear, nonlinear, and latent variables causal discovery](https://mlsanity.com/paper/2407.18755/) (2024)
- [Ensemble transport smoothing. Part II: Nonlinear updates](https://mlsanity.com/paper/2210.17435/) (2022)
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- [LazyDINO: Fast, scalable, and efficiently amortized Bayesian inversion via structure-exploiting and surrogate-driven measure transport](https://mlsanity.com/paper/2411.12726/) (2024)
- [Heavy-tailed Sampling via Transformed Unadjusted Langevin Algorithm](https://mlsanity.com/paper/2201.08349/) (2022)
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- [Learning Causal Graphs via Monotone Triangular Transport Maps](https://mlsanity.com/paper/2305.18210/) (2023)
- [Expected information gain estimation via density approximations: Sample allocation and dimension reduction](https://mlsanity.com/paper/2411.08390/) (2024)
- [A friendly introduction to triangular transport](https://mlsanity.com/paper/2503.21673/) (2025)
- [Self-reinforced polynomial approximation methods for concentrated probability densities](https://mlsanity.com/paper/2303.02554/) (2023)
- [A transport approach to sequential simulation-based inference](https://mlsanity.com/paper/2308.13940/) (2023)
- [Density Estimation via Measure Transport: Outlook for Applications in the Biological Sciences](https://mlsanity.com/paper/2309.15366/) (2023)
- [Nonstationary Time Series Forecasting via Unknown Distribution Adaptation](https://mlsanity.com/paper/2402.12767/) (2024)
- [Learning local neighborhoods of non-Gaussian graphical models: A measure transport approach](https://mlsanity.com/paper/2503.13899/) (2025)
- [Neural Triangular Transport Maps: A New Approach Towards Sampling in Lattice QCD](https://mlsanity.com/paper/2510.13112/) (2025)
- [Deep importance sampling using tensor trains with application to a priori and a posteriori rare event estimation](https://mlsanity.com/paper/2209.01941/) (2022)

## Abstract (arXiv)

We investigate the low-dimensional structure of deterministic transformations between random variables, i.e., transport maps between probability measures. In the context of statistics and machine learning, these transformations can be used to couple a tractable "reference" measure (e.g., a standard Gaussian) with a target measure of interest. Direct simulation from the desired measure can then be achieved by pushing forward reference samples through the map. Yet characterizing such a map---e.g., representing and evaluating it---grows challenging in high dimensions. The central contribution of this paper is to establish a link between the Markov properties of the target measure and the existence of low-dimensional couplings, induced by transport maps that are sparse and/or decomposable. Our analysis not only facilitates the construction of transformations in high-dimensional settings, but also suggests new inference methodologies for continuous non-Gaussian graphical models. For instance, in the context of nonlinear state-space models, we describe new variational algorithms for filtering, smoothing, and sequential parameter inference. These algorithms can be understood as the natural generalization---to the non-Gaussian case---of the square-root Rauch-Tung-Striebel Gaussian smoother.