A survey of some recent applications of optimal transport methods to econometrics

Galichon, Alfred

doi:10.1111/ectj.12083

Cited by 24 publications

(14 citation statements)

References 38 publications

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“…This paper contributes to the large literature on the optimal transport problem and its applications (e.g., Rachev and Rüschendorf [1998] or Villani [2003Villani [ , 2008, and the references therein). Applications to economics are discussed in Galichon [2016Galichon [ , 2017 and to risk measures in Rüschendorf [2013]. Optimal transport, and the related martingale optimal transport problem have also been applied to the problem of calculating bounds for prices of financial instruments (e.g., Galichon et al [2014], Beiglböck et al [2013], or Henry-Labordère [2017], and the references therein).…”

Section: Related Literaturementioning

confidence: 99%

Maximum Spectral Measures of Risk with given Risk Factor Marginal Distributions

Ghossoub¹,

Hall²,

Saunders³

2020

Preprint

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We consider the problem of determining an upper bound for the value of a spectral risk measure of a loss that is a general nonlinear function of two factors whose marginal distributions are known, but whose joint distribution is unknown. The factors may take values in complete separable metric spaces. We introduce the notion of Maximum Spectral Measure (MSP), as a worst-case spectral risk measure of the loss with respect to the dependence between the factors. The MSP admits a formulation as a solution to an optimization problem that has the same constraint set as the optimal transport problem, but with a more general objective function. We present results analogous to the Kantorovich duality, and we investigate the continuity properties of the optimal value function and optimal solution set with respect to perturbation of the marginal distributions. Additionally, we provide an asymptotic result characterizing the limiting distribution of the optimal value function when the factor distributions are simulated from finite sample spaces. The special case of Expected Shortfall and the resulting Maximum Expected Shortfall is also examined.

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Section: Related Literaturementioning

confidence: 99%

Maximum Spectral Measures of Risk with given Risk Factor Marginal Distributions

Ghossoub¹,

Hall²,

Saunders³

2020

Preprint

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“…An emerging number of applications, including several in biology, are using optimal transport to learn a mapping between data distributions [9, 10]. Optimal transport finds the most cost-effective way to move data points from one domain to another.…”

Section: Introductionmentioning

confidence: 99%

Gromov-Wasserstein optimal transport to align single-cell multi-omics data

Demetçi

Santorella

Sandstede

et al. 2020

Preprint

101

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Data integration of single-cell measurements is critical for our understanding of cell development and disease, but the lack of correspondence between different types of single-cell measurements makes such efforts challenging. Several unsupervised algorithms are capable of aligning heterogeneous types of single-cell measurements in a shared space, enabling the creation of mappings between single cells in different data modalities. We present Single-Cell alignment using Optimal Transport (SCOT), an unsupervised learning algorithm that uses Gromov Wasserstein-based optimal transport to align single-cell multi-omics datasets. SCOT calculates a probabilistic coupling matrix that matches cells across two datasets. The optimization uses k-nearest neighbor graphs, thus preserving the local geometry of the data. We use the resulting coupling matrix to project one singlecell dataset onto another via a barycentric projection. We compare the alignment performance of SCOT with state-of-the-art algorithms on three simulated and two real datasets. Our results demonstrate that SCOT yields results that are comparable in quality to those of competing methods, but SCOT is significantly faster and requires tuning fewer hyperparameters. The code is available at https://github.com/rsinghlab/SCOT

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“…Recently, there has been intensive interest in comparing distributions with the Wasserstein distance, both in theory and applications (e.g. Bolstad et al, 2003;Bigot et al, 2017;Galichon, 2017;Cazelles et al, 2018;Bigot et al, 2019), and in visualization (e.g. Delicado and Vieu, 2017).…”

Section: Introductionmentioning

confidence: 99%

Wasserstein gradients for the temporal evolution of probability distributions

Chen

Müller

2021

Electron. J. Statist.

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Many studies have been conducted on flows of probability measures, often in terms of gradient flows. We utilize a generalized notion of derivatives with respect to time to model the instantaneous evolution of empirically observed one-dimensional distributions that vary over time and develop consistent estimates for these derivatives. Employing local Fréchet regression and working in local tangent spaces with regard to the Wasserstein metric, we derive the rate of convergence of the proposed estimators. The resulting time dynamics are illustrated with time-varying distribution data that include yearly income distributions and the evolution of mortality over calendar years.

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A survey of some recent applications of optimal transport methods to econometrics

Abstract: This paper surveys recent applications of methods from the theory of optimal transport to econometric problems.

Cited by 24 publications

References 38 publications

Maximum Spectral Measures of Risk with given Risk Factor Marginal Distributions

Maximum Spectral Measures of Risk with given Risk Factor Marginal Distributions

Gromov-Wasserstein optimal transport to align single-cell multi-omics data

Wasserstein gradients for the temporal evolution of probability distributions

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