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Parameter Estimation in Finite Mixture Models by Regularized Optimal Transport: A Unified Framework for Hard and Soft Clustering [article]

Arnaud Dessein and Nicolas Papadakis and Charles-Alban Deledalle
2017 arXiv   pre-print
The proposed framework unifies hard and soft clustering methods for general mixture models.  ...  In this short paper, we formulate parameter estimation for finite mixture models in the context of discrete optimal transportation with convex regularization.  ...  Acknowledgment This study has been carried out with financial support from the French State, managed by the French National Research Agency (ANR) in the frame of the "Investments for the future" Program  ... 
arXiv:1711.04366v1 fatcat:qig57yrbanhgxjrvx72tnjsfdq

Gaussian Mixture Reduction with Composite Transportation Divergence [article]

Qiong Zhang, Archer Gong Zhang, Jiahua Chen
2021 arXiv   pre-print
It is widely used in density estimation, recursive tracking in hidden Markov model, and belief propagation.  ...  Gaussian mixture reduction (GMR) is the problem of approximating a high order Gaussian mixture by one with lower order.  ...  This research was enabled in part by support provided by WestGrid (www.westgrid.ca) and Compute Canada Calcul Canada (www.computecanada.ca).  ... 
arXiv:2002.08410v2 fatcat:ciudjw7fojebjcotsd4tws6gim

Computational Optimal Transport: With Applications to Data Science

Gabriel Peyré, Marco Cuturi
2019 Foundations and Trends® in Machine Learning  
Gabriel Peyré and Marco Cuturi (2019), "Computational Optimal Transport", Foundations and Trends R in Machine Learning: Vol. 11, No. 5-6, pp 355-607. DOI: 10.1561/2200000073.  ...  "Parameter estimation in finite mixture models by regularized optimal transport: a unified framework for hard and soft clustering". arXiv preprint arXiv:1711.04366. Dessein, A., N. Papadakis, and J.  ...  Dantzig solved it numerically in 1949 within the framework of linear programming, giving OT a firm footing in optimization.  ... 
doi:10.1561/2200000073 fatcat:qxumbjeeojf6hkbkaqescsfffy

Regularized Optimal Transport and the Rot Mover's Distance [article]

Arnaud Dessein and Nicolas Papadakis and Jean-Luc Rouas
2018 arXiv   pre-print
This paper presents a unified framework for smooth convex regularization of discrete optimal transport problems.  ...  In this context, the regularized optimal transport turns out to be equivalent to a matrix nearness problem with respect to Bregman divergences.  ...  Acknowledgments This study has been carried out with financial support from the French State, managed by the French National Research Agency (ANR) in the frame of the "Investments for the future" Program  ... 
arXiv:1610.06447v4 fatcat:ao5fxjj2nneglodu245h4b4mbq

Computational Optimal Transport [article]

Gabriel Peyré, Marco Cuturi
2020 arXiv   pre-print
Optimal transport (OT) theory can be informally described using the words of the French mathematician Gaspard Monge (1746-1818): A worker with a shovel in hand has to move a large pile of sand lying on  ...  This short book reviews OT with a bias toward numerical methods and their applications in data sciences, and sheds lights on the theoretical properties of OT that make it particularly useful for some of  ...  Let P be an extremal point of the polytope U(a, b).  ... 
arXiv:1803.00567v4 fatcat:zgannw6i6beqde5bx7pj62uyry

Semi-Discrete Optimal Transport: Hardness, Regularization and Numerical Solution [article]

Bahar Taskesen, Soroosh Shafieezadeh-Abadeh, Daniel Kuhn
2022 arXiv   pre-print
As a byproduct, we discover an intimate relation between semi-discrete optimal transport problems and discrete choice models traditionally studied in psychology and economics.  ...  Semi-discrete optimal transport problems, which evaluate the Wasserstein distance between a discrete and a generic (possibly non-discrete) probability measure, are believed to be computationally hard.  ...  The research of the second author is supported by an Early Postdoc.Mobility Fellowship, grant agreement P2ELP2_195149.  ... 
arXiv:2103.06263v2 fatcat:aiqn2u3oszes5nqc37htae2d4e

Polynomial-time algorithms for Multimarginal Optimal Transport problems with structure [article]

Jason M. Altschuler, Enric Boix-Adsera
2021 arXiv   pre-print
We develop a unified algorithmic framework for solving MOT in poly(n,k) time by characterizing the "structure" that different algorithms require in terms of simple variants of the dual feasibility oracle  ...  Multimarginal Optimal Transport (MOT) has attracted significant interest due to applications in machine learning, statistics, and the sciences.  ...  We are grateful to Jonathan Niles-Weed, Pablo Parrilo, and Philippe Rigollet for insightful conversations; to Frederic Koehler for suggesting a simpler proof of Lemma 3.7; and to Ben Edelman and Siddhartha  ... 
arXiv:2008.03006v3 fatcat:i3iz4krphremxiihr4beiw5nue

Anomalous transport in the crowded world of biological cells

Felix Höfling, Thomas Franosch
2013 Reports on progress in physics (Print)  
media, the CTRW model, and the Lorentz model describing obstructed transport in a heterogeneous environment.  ...  Emphasis is put on the spatio-temporal properties of the transport in terms of 2-point correlation functions, dynamic scaling behaviour, and how the models are distinguished by their propagators even for  ...  Spatially resolved transport The scaling form of the propagator is more involved than for the models discussed so far due to the presence of finite clusters and the finite correlation length.  ... 
doi:10.1088/0034-4885/76/4/046602 pmid:23481518 fatcat:ag4ldxmp4vgddgm5euucicnl6e

A contribution to Optimal Transport on incomparable spaces [article]

Titouan Vayer
2020 arXiv   pre-print
How can it be adapted when the data are varied and not embedded in the same metric space? This thesis proposes a set of Optimal Transport tools for these different cases.  ...  In particular we address the following questions: how to define and apply Optimal Transport between graphs, between structured data?  ...  (left) Example images from the dataset, (center) centroids estimated by COOT (right) clustering of the pixels estimated by COOT where each color represents a cluster.  ... 
arXiv:2011.04447v1 fatcat:qnmq5pgqqnaphodg7gcn5j2dt4

Modelling the dynamic pattern of surface area in basketball and its effects on team performance

Rodolfo Metulini, Marica Manisera, Paola Zuccolotto
2018 Journal of Quantitative Analysis in Sports (JQAS)  
Specifically, we first employ a Markov Switching Model (MSM) to detect structural changes in the surface area.  ...  Finally, we assess the relation between the regime probabilities and the scored points by means of Vector Auto Regressive (VAR) models.  ...  TMLE is a framework for estimation of causal parameters that combines data-adaptive estimation with a targeting procedure tailored to optimal estimation of a specific low-dimensional parameter of interest  ... 
doi:10.1515/jqas-2018-0041 fatcat:b3qwsi7tqjg2vdo7gbjtiorv6m

Model-Based Experimental Analysis of Kinetic Phenomena in Multi-Phase Reactive Systems

W. Marquardt
2005 Chemical engineering research & design  
The approach aims at the integration of high resolution measurements, modelling on multiple scales and the formulation and solution of inverse problems in a unifying framework.  ...  T his contribution will introduce a novel concept for mechanistic modelling of complex kinetic phenomena and will explore its potential for multi-phase reaction systems modelling.  ...  In particular, the contributions of and the fruitful discussions with A. Bardow, D. Bonvin, M. Brendel, O. Kahrs and A. Mhamdi are gratefully acknowledged.  ... 
doi:10.1205/cherd.05086 fatcat:rqeoqstt4fanvkypnr7i5zuooi

Sequential updating of multimodal hydrogeologic parameter fields using localization and clustering techniques

Alexander Y. Sun, Alan P. Morris, Sitakanta Mohanty
2009 Water Resources Research  
In this study, we combine an ensemble Kalman filter with grid-based localization and a Gaussian mixture model (GMM) clustering techniques for updating high-dimensional, multimodal parameter distributions  ...  1] Estimated parameter distributions in groundwater models may contain significant uncertainties because of data insufficiency.  ...  This work was supported by the Southwest Research Institute through an internal research and development fund (R9704).  ... 
doi:10.1029/2008wr007443 fatcat:ed4qbjkekjhwlf7mplb353uqtm

Distributionally Robust Optimization: A Review [article]

Hamed Rahimian, Sanjay Mehrotra
2019 arXiv   pre-print
A modeling framework, called distributionally robust optimization (DRO), has recently received significant attention in both the operations research and statistical learning communities.  ...  Statistical learning community has also witnessed a rapid theoretical and applied growth by relying on these concepts.  ...  In fact, by showing that standard DRO is concave in , they solve the soft robust model by a bisection method.  ... 
arXiv:1908.05659v1 fatcat:cliwiafz4vffvj2j3b67uix5nm

Sap flow and sugar transport in plants

K. H. Jensen, K. Berg-Sørensen, H. Bruus, N. M. Holbrook, J. Liesche, A. Schulz, M. A. Zwieniecki, T. Bohr
2016 Reviews of Modern Physics  
Then water transport in the xylem is discussed with a focus on embolism dynamics, conduit optimization, and couplings between water and sugar transport.  ...  The article begins with an overview of low-Reynolds-number transport processes, followed by an introduction to the anatomy and physiology of vascular transport in the phloem and xylem.  ...  In plants, however, we can estimate the parameter β ¼ a 2 u=ð6LDÞ ≃ 3 × 10 −6 for a¼10 −5 m, u¼10 −4 m=s, L¼1 m, and D¼5×10 −10 m 2 =s.  ... 
doi:10.1103/revmodphys.88.035007 fatcat:u66czchdkjawxaq2mgzj534hba

Meshless techniques for anisotropic diffusion

Annamaria Mazzia, Giorgio Pini, Flavio Sartoretto
2014 Applied Mathematics and Computation  
Transport processes are common in geoscience applications, and find their way into models of, e.g., the atmosphere, oceans, shallow water, subsurface, seismic inversion, and deep earth.  ...  A good numerical method would be locally mass conservative, produce no or minimal over/under-shoots, produce minimal numerical diffusion, and require no CFL time-step limit for stability.  ...  We present complex scenarios of multicomponent reactive transport in 2-D and in 3-D. These scenarios are further developments of the setting given by the MoMaS benchmark.  ... 
doi:10.1016/j.amc.2014.03.032 fatcat:c527226gyfgbffnq4p67qxd7wi
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