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Unbalanced Optimal Transport through Non-negative Penalized Linear Regression
[article]
2021
arXiv
pre-print
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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]
2021
bioRxiv
pre-print
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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]
2019
arXiv
pre-print
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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]
2019
arXiv
pre-print
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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
2019
Frontiers in Human Neuroscience
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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]
2019
arXiv
pre-print
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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
2020
NeuroImage
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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]
2020
arXiv
pre-print
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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]
2019
arXiv
pre-print
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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
2020
Applied Sciences
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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
2020
Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence
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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
2017
Proceedings of the 26th International Conference on World Wide Web Companion - WWW '17 Companion
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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]
2021
arXiv
pre-print
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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]
2022
arXiv
pre-print
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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
2017
Expert systems with applications
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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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