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Unbalanced Optimal Transport through Non-negative Penalized Linear Regression [article]

Laetitia Chapel, Rémi Flamary, Haoran Wu, Cédric Févotte, Gilles Gasso
2021 arXiv   pre-print
In this context, we show that the corresponding optimization problem can be reformulated as a non-negative penalized linear regression problem.  ...  This paper addresses the problem of Unbalanced Optimal Transport (UOT) in which the marginal conditions are relaxed (using weighted penalties in lieu of equality) and no additional regularization is enforced  ...  dealing with non-negative penalized linear regression.  ... 
arXiv:2106.04145v1 fatcat:bfxdj566mncqbncqxqvgs7klky

ROKET: Associating Somatic Mutation with Clinical Outcomes through Kernel Regression and Optimal Transport [article]

Paul Little, Li Hsu, Wei Sun
2021 bioRxiv   pre-print
Building on the optimal transport method, we propose a principled approach to estimate the similarity of somatic mutation profiles of multiple genes between tumor samples, while accounting for gene-gene  ...  Using such similarities, we can assess the associations between somatic mutations and clinical outcomes by kernel regression.  ...  We adjust for baseline covariates through a parametric component X T i β and the high-dimensional covariate through the non-parametric component f (Z i ).  ... 
doi:10.1101/2021.12.23.474064 fatcat:kuendu3b4vetzgee5jpo7iy4ee

Wasserstein regularization for sparse multi-task regression [article]

Hicham Janati and Marco Cuturi and Alexandre Gramfort
2019 arXiv   pre-print
Our regularizer is based on unbalanced optimal transport (OT) theory, and can take into account a prior geometric knowledge on the regressor variables, without necessarily requiring overlapping supports  ...  In this paper, we propose a convex regularizer for multi-task regression that encodes a more flexible geometry.  ...  Large values of γ > 0 tend to strongly penalize unbalanced transports, and as a result penalize discrepancies between the marginals of P and θ 1 , θ 2 .  ... 
arXiv:1805.07833v3 fatcat:yrgyudpnlrfufbgpcbwn2s4ki4

Group level MEG/EEG source imaging via optimal transport: minimum Wasserstein estimates [article]

Hicham Janati , Bertrand Thirion , Alexandre Gramfort
2019 arXiv   pre-print
Second, MWE are defined through Optimal Transport (OT) metrics which provide a tool to model spatial proximity between cortical sources of different subjects, hence not enforcing identical source location  ...  Magnetoencephalography (MEG) and electroencephalogra-phy (EEG) are non-invasive modalities that measure the weak electromagnetic fields generated by neural activity.  ...  MTW is defined through an Unbalanced Optimal Transport (UOT) metric that promotes support proximity across regression coefficients.  ... 
arXiv:1902.04812v1 fatcat:kl7gqp4wqbh2tgrwdncmtfqope

Theories and Methods for Labeling Cognitive Workload: Classification and Transfer Learning

Ryan McKendrick, Bradley Feest, Amanda Harwood, Brian Falcone
2019 Frontiers in Human Neuroscience  
We included these polynomials because previous research (McKendrick and Harwood, under review) has shown that participants' hemodynamic response is non-linear as they transition through mental workload  ...  After, we optimized the 36 models described in the section Overall Processing and Optimization, we performed six linear regressions to test the effects of manipulating labeling, algorithms, and class balancing  ... 
doi:10.3389/fnhum.2019.00295 pmid:31572146 pmcid:PMC6749052 fatcat:7dachhlbtvhv3jhy3k6ev6l7fq

Multi-subject MEG/EEG source imaging with sparse multi-task regression [article]

Hicham Janati, Thomas Bazeille, Bertrand Thirion, Marco Cuturi, Alexandre Gramfort
2019 arXiv   pre-print
The Minimum Wasserstein Estimates (MWE) promotes focal activations that do not perfectly overlap for all subjects, thanks to a regularizer based on Optimal Transport (OT) metrics.  ...  Magnetoencephalography and electroencephalography (M/EEG) are non-invasive modalities that measure the weak electromagnetic fields generated by neural activity.  ...  MTW is defined through an Unbalanced Optimal Transport (UOT) metric that promotes support proximity across regression coefficients.  ... 
arXiv:1910.01914v2 fatcat:4ktnmi7h7va5vclbieucswyl3m

Multi-subject MEG/EEG source imaging with sparse multi-task regression

Hicham Janati, Thomas Bazeille, Bertrand Thirion, Marco Cuturi, Alexandre Gramfort
2020 NeuroImage  
Thanks to a new joint regression method based on optimal transport (OT) metrics, MWE does not enforce perfect overlap of activation foci for all subjects but rather promotes spatial proximity on the cortical  ...  Here we show how the coupling of the different regression problems can be done through a multi-task regularization that promotes focal source estimates.  ...  Moreover, while coordinate descent iterations are linear in 221 the number of sources p, optimal transport iterations are linear in the number of subjects S 222 and quadratic in the number of sources p  ... 
doi:10.1016/j.neuroimage.2020.116847 pmid:32438046 fatcat:4zycfenpvnekzltdhhcqpoakm4

Particles to Partial Differential Equations Parsimoniously [article]

Hassan Arbabi, Ioannis Kevrekidis
2020 arXiv   pre-print
We also propose using a data-driven approach, based on manifold learning and unnormalized optimal transport of distributions, to identify macro-scale dependent variable(s) suitable for the data-driven  ...  However, in Appendix B, we present pairwise distance matrices computed using the unbalanced optimal transport formulation in [18] as well as a non-transport based, moments formulation.  ...  The parameter α determines how much the violation of marginals is penalized in realizing the optimal transport plan.  ... 
arXiv:2011.04517v1 fatcat:hvakptptsbhippndt3p2syxk2u

Spatio-Temporal Alignments: Optimal transport through space and time [article]

Hicham Janati, Marco Cuturi, Alexandre Gramfort
2019 arXiv   pre-print
In this paper, we propose Spatio-Temporal Alignments (STA), a new differentiable formulation of DTW, in which spatial differences between time samples are accounted for using regularized optimal transport  ...  The cost matrix within soft-DTW that we use are computed using unbalanced OT, to handle the case in which observations are not normalized probabilities.  ...  Non-negativity We show that S is non-negative, we assume that the kernel K = e − M ε is positive semidefinite.  ... 
arXiv:1910.03860v3 fatcat:piwndm7x6bhnzk46krjng2svmq

Using Ensembles for Accurate Modelling of Manufacturing Processes in an IoT Data-Acquisition Solution

José Luis Garrido-Labrador, Daniel Puente-Gabarri, José Miguel Ramírez-Sanz, David Ayala-Dulanto, Jesus Maudes
2020 Applied Sciences  
The results show the superiority of the ensembles for both classification problems under analysis and all four regression problems.  ...  This evaluation, completed under real industrial conditions, includes very limited information on the machining workload of the machining center and unbalanced datasets.  ...  As in the case of linear regression, we also have a model that is a linear combination of the input variables (i.e., a hyperplane), but this time the optimization process ignores the instances that are  ... 
doi:10.3390/app10134606 fatcat:xgtpghdzyffcjdyb7zv4s47xv4

On Deep Unsupervised Active Learning

Changsheng Li, Handong Ma, Zhao Kang, Ye Yuan, Xiao-Yu Zhang, Guoren Wang
2020 Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence  
Most existing works are based on shallow linear models by assuming that each sample can be well approximated by the span (i.e., the set of all linear combinations) of certain selected samples, and then  ...  DUAL can explicitly learn a nonlinear embedding to map each input into a latent space through an encoder-decoder architecture, and introduce a selection block to select representative samples in the the  ...  R + denotes the set of all non-negative real number. R N S ×N G + denotes the set of all positive semi-define matrices on R N S ×N G .  ... 
doi:10.24963/ijcai.2020/360 dblp:conf/ijcai/LuoPH20 fatcat:ffz3ibek6nbi7hewsqzdxtzlvu

Predicting Prevalence of Influenza-Like Illness From Geo-Tagged Tweets

Kewei Zhang, Reza Arablouei, Raja Jurdak
2017 Proceedings of the 26th International Conference on World Wide Web Companion - WWW '17 Companion  
Then, we establish a state-level linear regression model between the number of ILI-related tweets and the number of real influenza notifications.  ...  Our results indicate that: 1) a strong positive linear correlation exists between the number of ILI-related tweets and the number of recorded influenza notifications at state scale; 2) Twitter data has  ...  The classifier Cs is highly penalized for including false positives (mistakenly labeling an "other" tweet as a "sick" one) and the classifier Co is highly penalized for including false negatives (classifying  ... 
doi:10.1145/3041021.3051150 dblp:conf/www/ZhangAJ17 fatcat:lufuaab7onhuzhy4yakfjhufdi

Distributionally-Constrained Policy Optimization via Unbalanced Optimal Transport [article]

Arash Givchi, Pei Wang, Junqi Wang, Patrick Shafto
2021 arXiv   pre-print
Given these distributions, we formulate policy optimization as unbalanced optimal transport over the space of occupancy measures.  ...  We propose a general purpose RL objective based on Bregman divergence and optimize it using Dykstra's algorithm.  ...  Recent works have expanded linear programming view through a more general convex optimization framework.  ... 
arXiv:2102.07889v1 fatcat:odv5fkauf5fdpbbfxee7gc5jpu

Aligning individual brains with Fused Unbalanced Gromov-Wasserstein [article]

Alexis Thual, Huy Tran, Tatiana Zemskova, Nicolas Courty, Rémi Flamary, Stanislas Dehaene, Bertrand Thirion
2022 arXiv   pre-print
In this work, we present a novel method for inter-subject alignment based on Optimal Transport, denoted as Fused Unbalanced Gromov Wasserstein (FUGW).  ...  The unbalanced feature allows to deal with the fact that functional areas vary in size across subjects.  ...  The numerical optimization problem (2) is solved using a classical strategy that consists in linearizing the loss 1 at each iteration, similar to [39, 34] , then solving the resulting entropic unbalanced  ... 
arXiv:2206.09398v1 fatcat:hy2n7u4bxffqvby2gwuwcblycq

The best of two worlds: Balancing model strength and comprehensibility in business failure prediction using spline-rule ensembles

Koen W. De Bock
2017 Expert systems with applications  
L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche  ...  linear regression.  ...  of rules) as well as linear terms (through the inclusion of winsorized linear terms).  ... 
doi:10.1016/j.eswa.2017.07.036 fatcat:xookibdyurbfxhsqk27lmjb76q
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