Structured Optimal Transport

Alvarez-Melis, David; Jaakkola, Tommi S.; Jegelka, Stefanie

doi:10.48550/arxiv.1712.06199

Cited by 4 publications

(6 citation statements)

References 22 publications

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“…In the past few years, it has attracted significant attention in the machine learning and computer science communities thanks to the availability of fast approximation algorithms [17,21,4,9,29]. Optimal transport is particularly successful in various learning tasks, notably generative mixture models [38,49], image processing [1,25,39,50,63], computer vision and graphics [51,52,56,62,61], clustering [33], dimensionality reduction [12,26,55,58,59], domain adaptation [16,47], signal processing [65] and data-driven distributionally robust optimization [40,7,27,72]. Recent comprehensive survey on optimal transport and its applications can be found in [53,38].…”

Section: Definition 22 (Equalized Odds [32]) a Classifiermentioning

confidence: 99%

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A Statistical Test for Probabilistic Fairness

Taşkesen¹,

Blanchet²,

Kühn³

et al. 2020

Preprint

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Algorithms are now routinely used to make consequential decisions that affect human lives. Examples include college admissions, medical interventions or law enforcement. While algorithms empower us to harness all information hidden in vast amounts of data, they may inadvertently amplify existing biases in the available datasets. This concern has sparked increasing interest in fair machine learning, which aims to quantify and mitigate algorithmic discrimination. Indeed, machine learning models should undergo intensive tests to detect algorithmic biases before being deployed at scale. In this paper, we use ideas from the theory of optimal transport to propose a statistical hypothesis test for detecting unfair classifiers. Leveraging the geometry of the feature space, the test statistic quantifies the distance of the empirical distribution supported on the test samples to the manifold of distributions that render a pre-trained classifier fair. We develop a rigorous hypothesis testing mechanism for assessing the probabilistic fairness of any pre-trained logistic classifier, and we show both theoretically as well as empirically that the proposed test is asymptotically correct. In addition, the proposed framework offers interpretability by identifying the most favorable perturbation of the data so that the given classifier becomes fair.

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Section: Definition 22 (Equalized Odds [32]) a Classifiermentioning

confidence: 99%

“…The pressing needs to redress undesirable algorithmic biases have propelled the rising field of fair machine learning 1 . A building pillar of this field involves the verification task: given a machine learning algorithm, we are interested in verifying if this algorithm satisfies a chosen criterion of fairness.…”

Section: Introductionmentioning

confidence: 99%

A Statistical Test for Probabilistic Fairness

Taşkesen¹,

Blanchet²,

Kühn³

et al. 2020

Preprint

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show abstract

“…The theory of optimal transport [51,52,37], now routinely used to find probabilistic matchings of metric spaces [35], suggests itself as a general strategy to circumvent this combinatorial problem. Several authors have proposed specific methods to match graphs or other structured data using optimal transport [2,11,36,49].…”

Section: Introductionmentioning

confidence: 99%

Hausdorff and Wasserstein metrics on graphs and other structured data

Patterson¹

2019

Preprint

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Optimal transport is widely used in pure and applied mathematics to find probabilistic solutions to hard combinatorial matching problems. We extend the Wasserstein metric and other elements of optimal transport from the matching of sets to the matching of graphs and other structured data. This structurepreserving form of optimal transport relaxes the usual notion of homomorphism between structures. It applies to graphs, directed and undirected, labeled and unlabeled, and to any other structure that can be realized as a C-set for some finitely presented category C. We construct both Hausdorff-style and Wasserstein-style metrics on C-sets and we show that the latter are convex relaxations of the former. Like the classical Wasserstein metric, the Wasserstein metric on C-sets is the value of a linear program and is therefore efficiently computable.

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“…native to the euclidean metric in the context of regularizer of loss functions in image processing allows an intuitive and efficient means of handling spatial motion in videos [9,10,11,12,13,14,15,16,17].…”

Section: Introductionmentioning

confidence: 99%

Wasserstein total variation filtering

Varol¹,

Nejatbakhsh²

2019

Preprint

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In this paper, we expand upon the theory of trend filtering by introducing the use of the Wasserstein metric as a means to control the amount of spatiotemporal variation in filtered time series data. While trend filtering utilizes regularization to produce signal estimates that are piecewise linear, in the case of ℓ 1 regularization, or temporally smooth, in the case of ℓ 2 regularization, it ignores the topology of the spatial distribution of signal. By incorporating the information about the underlying metric space of the pixel layout, the Wasserstein metric is an attractive choice as a regularizer to undercover spatiotemporal trends in time series data. We introduce a globally optimal algorithm for efficiently estimating the filtered signal under a Wasserstein finite differences operator. The efficacy of the proposed algorithm in preserving spatiotemporal trends in time series video is demonstrated in both simulated and fluorescent microscopy videos of the nematode caenorhabditis elegans and compared against standard trend filtering algorithms.

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Structured Optimal Transport

Cited by 4 publications

References 22 publications

A Statistical Test for Probabilistic Fairness

A Statistical Test for Probabilistic Fairness

Hausdorff and Wasserstein metrics on graphs and other structured data

Wasserstein total variation filtering

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