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no code implementations • 24 Oct 2022 • Lingxiao Li, Qiang Liu, Anna Korba, Mikhail Yurochkin, Justin Solomon

These energies rely on mollifier functions -- smooth approximations of the Dirac delta originated from PDE theory.

1 code implementation • 13 Oct 2022 • Yuchen Zeng, Kristjan Greenewald, Kangwook Lee, Justin Solomon, Mikhail Yurochkin

Traditional machine learning models focus on achieving good performance on the overall training distribution, but they often underperform on minority groups.

no code implementations • 18 May 2022 • Christopher Scarvelis, Justin Solomon

We introduce an optimal transport-based model for learning a metric tensor from cross-sectional samples of evolving probability measures on a common Riemannian manifold.

1 code implementation • 5 Feb 2022 • S. Mazdak Abulnaga, Oded Stein, Polina Golland, Justin Solomon

Although shape correspondence is a central problem in geometry processing, most methods for this task apply only to two-dimensional surfaces.

1 code implementation • 3 Feb 2022 • Tal Shnitzer, Mikhail Yurochkin, Kristjan Greenewald, Justin Solomon

We use manifold learning to compare the intrinsic geometric structures of different datasets by comparing their diffusion operators, symmetric positive-definite (SPD) matrices that relate to approximations of the continuous Laplace-Beltrami operator from discrete samples.

no code implementations • 29 Jan 2022 • Rickard Brüel-Gabrielsson, Mikhail Yurochkin, Justin Solomon

As a conservative alternative, we use positional encodings to expand receptive fields to $r$-hop neighborhoods.

no code implementations • 28 Jan 2022 • Lingxiao Li, Noam Aigerman, Vladimir G. Kim, Jiajin Li, Kristjan Greenewald, Mikhail Yurochkin, Justin Solomon

We present an end-to-end method to learn the proximal operator of a family of training problems so that multiple local minima can be quickly obtained from initial guesses by iterating the learned operator, emulating the proximal-point algorithm that has fast convergence.

no code implementations • 28 Jan 2022 • Paul Zhang, Dmitriy Smirnov, Justin Solomon

Trajectories are then computed by advecting keyframes through the velocity field.

1 code implementation • CVPR 2022 • David Palmer, Dmitriy Smirnov, Stephanie Wang, Albert Chern, Justin Solomon

Recent techniques have been successful in reconstructing surfaces as level sets of learned functions (such as signed distance fields) parameterized by deep neural networks.

1 code implementation • 15 Nov 2021 • S. Mazdak Abulnaga, Esra Abaci Turk, Mikhail Bessmeltsev, P. Ellen Grant, Justin Solomon, Polina Golland

However, due to the curved and highly variable in vivo shape of the placenta, interpreting and visualizing these images is difficult.

1 code implementation • NeurIPS 2021 • Yue Wang, Justin Solomon

Our method models 3D object detection as message passing on a dynamic graph, generalizing the DGCNN framework to predict a set of objects.

1 code implementation • 13 Oct 2021 • Yue Wang, Vitor Guizilini, Tianyuan Zhang, Yilun Wang, Hang Zhao, Justin Solomon

This top-down approach outperforms its bottom-up counterpart in which object bounding box prediction follows per-pixel depth estimation, since it does not suffer from the compounding error introduced by a depth prediction model.

no code implementations • 29 Sep 2021 • Kristjan Greenewald, Anming Gu, Mikhail Yurochkin, Justin Solomon, Edward Chien

To better leverage the structure of the data, we extend mixup to $k$-mixup by perturbing $k$-batches of training points in the direction of other $k$-batches using displacement interpolation, i. e. interpolation under the Wasserstein metric.

1 code implementation • CVPR 2021 • Nicolas Girard, Dmitriy Smirnov, Justin Solomon, Yuliya Tarabalka

While state of the art image segmentation models typically output segmentations in raster format, applications in geographic information systems often require vector polygons.

no code implementations • 5 Jun 2021 • Kristjan Greenewald, Anming Gu, Mikhail Yurochkin, Justin Solomon, Edward Chien

Mixup is a popular regularization technique for training deep neural networks that can improve generalization and increase adversarial robustness.

3 code implementations • NeurIPS 2021 • Alexander Korotin, Lingxiao Li, Aude Genevay, Justin Solomon, Alexander Filippov, Evgeny Burnaev

Despite the recent popularity of neural network-based solvers for optimal transport (OT), there is no standard quantitative way to evaluate their performance.

3 code implementations • NeurIPS 2021 • Petr Mokrov, Alexander Korotin, Lingxiao Li, Aude Genevay, Justin Solomon, Evgeny Burnaev

Specifically, Fokker-Planck equations, which model the diffusion of probability measures, can be understood as gradient descent over entropy functionals in Wasserstein space.

1 code implementation • NeurIPS 2021 • Dmitriy Smirnov, Michael Gharbi, Matthew Fisher, Vitor Guizilini, Alexei A. Efros, Justin Solomon

Artists and video game designers often construct 2D animations using libraries of sprites -- textured patches of objects and characters.

no code implementations • 25 Feb 2021 • Gaspard Beugnot, Aude Genevay, Kristjan Greenewald, Justin Solomon

Optimal transport (OT) is a popular tool in machine learning to compare probability measures geometrically, but it comes with substantial computational burden.

2 code implementations • ICLR 2021 • Alexander Korotin, Lingxiao Li, Justin Solomon, Evgeny Burnaev

Wasserstein barycenters provide a geometric notion of the weighted average of probability measures based on optimal transport.

no code implementations • 1 Jan 2021 • Debarghya Mukherjee, Aritra Guha, Justin Solomon, Yuekai Sun, Mikhail Yurochkin

In light of recent advances in solving the OT problem, OT distances are widely used as loss functions in minimum distance estimation.

no code implementations • 13 Dec 2020 • Justin Solomon, Kristjan Greenewald, Haikady N. Nagaraja

We introduce $k$-variance, a generalization of variance built on the machinery of random bipartite matchings.

1 code implementation • 8 Dec 2020 • Lorenzo Najt, Daryl DeFord, Justin Solomon

Second, we analyze the robustness of the qualitative properties of typical districting plans with respect to score functions and a certain lattice-like graph, called the state-dual graph, that is used as a discretization of geographic regions in most districting analysis.

Physics and Society Statistical Mechanics 62P25, 82-05 K.4.1; G.3

no code implementations • 18 Nov 2020 • Amariah Becker, Justin Solomon

Why not have a computer just draw a map?

Data Structures and Algorithms Computers and Society K.4.0

no code implementations • 24 Sep 2020 • Yue Wang, Alireza Fathi, Jiajun Wu, Thomas Funkhouser, Justin Solomon

A common dilemma in 3D object detection for autonomous driving is that high-quality, dense point clouds are only available during training, but not testing.

1 code implementation • NeurIPS 2020 • Lingxiao Li, Aude Genevay, Mikhail Yurochkin, Justin Solomon

Leveraging a new dual formulation for the regularized Wasserstein barycenter problem, we introduce a stochastic algorithm that constructs a continuous approximation of the barycenter.

1 code implementation • ECCV 2020 • Yue Wang, Alireza Fathi, Abhijit Kundu, David Ross, Caroline Pantofaru, Thomas Funkhouser, Justin Solomon

We present a simple and flexible object detection framework optimized for autonomous driving.

1 code implementation • ICML 2020 • Sebastian Claici, Mikhail Yurochkin, Soumya Ghosh, Justin Solomon

Our algorithm relies on a mean field assumption for both the fused model and the individual dataset posteriors and proceeds using a simple assign-and-average approach.

2 code implementations • 30 Apr 2020 • Nicolas Girard, Dmitriy Smirnov, Justin Solomon, Yuliya Tarabalka

While state of the art image segmentation models typically output segmentations in raster format, applications in geographic information systems often require vector polygons.

no code implementations • 22 Jan 2020 • Rafael B. Fricks, Justin Solomon, Ehsan Samei

Imaging phantoms are test patterns used to measure image quality in computer tomography (CT) systems.

no code implementations • 16 Dec 2019 • Charlie Frogner, Sebastian Claici, Edward Chien, Justin Solomon

We examine the performance of this new formulation on 14 real datasets and find that it often yields effective classifiers with nontrivial performance guarantees in situations where conventional DRL produces neither.

1 code implementation • NeurIPS 2019 • Pierre Monteiller, Sebastian Claici, Edward Chien, Farzaneh Mirzazadeh, Justin Solomon, Mikhail Yurochkin

Label switching is a phenomenon arising in mixture model posterior inference that prevents one from meaningfully assessing posterior statistics using standard Monte Carlo procedures.

4 code implementations • 31 Oct 2019 • Daryl DeFord, Moon Duchin, Justin Solomon

Redistricting is the problem of partitioning a set of geographical units into a fixed number of districts, subject to a list of often-vague rules and priorities.

Computers and Society Physics and Society 60J10, 05C70, 91F10

1 code implementation • 15 Aug 2019 • David Palmer, David Bommes, Justin Solomon

A key challenge in extending these methods to three dimensions, however, is representation of field values.

Graphics

1 code implementation • NeurIPS 2019 • Mikhail Yurochkin, Sebastian Claici, Edward Chien, Farzaneh Mirzazadeh, Justin Solomon

The ability to measure similarity between documents enables intelligent summarization and analysis of large corpora.

2 code implementations • 8 May 2019 • Charlie Frogner, Farzaneh Mirzazadeh, Justin Solomon

Euclidean embeddings of data are fundamentally limited in their ability to capture latent semantic structures, which need not conform to Euclidean spatial assumptions.

no code implementations • ICLR 2019 • Charlie Frogner, Farzaneh Mirzazadeh, Justin Solomon

Despite their prevalence, Euclidean embeddings of data are fundamentally limited in their ability to capture latent semantic structures, which need not conform to Euclidean spatial assumptions.

1 code implementation • CVPR 2020 • Dmitriy Smirnov, Matthew Fisher, Vladimir G. Kim, Richard Zhang, Justin Solomon

Many tasks in graphics and vision demand machinery for converting shapes into consistent representations with sparse sets of parameters; these representations facilitate rendering, editing, and storage.

1 code implementation • 12 Mar 2019 • S. Mazdak Abulnaga, Esra Abaci Turk, Mikhail Bessmeltsev, P. Ellen Grant, Justin Solomon, Polina Golland

We formulate our method as a map from the in vivo shape to a flattened template that minimizes the symmetric Dirichlet energy to control distortion throughout the volume.

1 code implementation • 19 Sep 2018 • Hugo Lavenant, Sebastian Claici, Edward Chien, Justin Solomon

We propose a technique for interpolating between probability distributions on discrete surfaces, based on the theory of optimal transport.

Analysis of PDEs Numerical Analysis Numerical Analysis Optimization and Control

no code implementations • 18 May 2018 • Sebastian Claici, Aude Genevay, Justin Solomon

The proliferation of large data sets and Bayesian inference techniques motivates demand for better data sparsification.

1 code implementation • 7 Mar 2018 • Richard Barnes, Justin Solomon

As a case study demonstrating the effect, we show that commonly-used measures of geometric compactness for district boundaries are affected by several factors irrelevant to fairness or compliance with civil rights law.

Computers and Society Computational Geometry

3 code implementations • ICML 2018 • Sebastian Claici, Edward Chien, Justin Solomon

We present a stochastic algorithm to compute the barycenter of a set of probability distributions under the Wasserstein metric from optimal transport.

no code implementations • 23 Jan 2018 • Justin Solomon

Inspired by the matching of supply to demand in logistical problems, the optimal transport (or Monge--Kantorovich) problem involves the matching of probability distributions defined over a geometric domain such as a surface or manifold.

1 code implementation • 21 Jul 2017 • Yu Wang, Mirela Ben-Chen, Iosif Polterovich, Justin Solomon

We propose using the Dirichlet-to-Neumann operator as an extrinsic alternative to the Laplacian for spectral geometry processing and shape analysis.

Graphics

1 code implementation • NeurIPS 2017 • Matthew Staib, Sebastian Claici, Justin Solomon, Stefanie Jegelka

Our method is even robust to nonstationary input distributions and produces a barycenter estimate that tracks the input measures over time.

1 code implementation • 20 Dec 2016 • Gabriel Peyré, Lenaïc Chizat, François-Xavier Vialard, Justin Solomon

This "quantum" formulation of OT (Q-OT) corresponds to a relaxed version of the classical Kantorovich transport problem, where the fidelity between the input PSD-valued measures is captured using the geometry of the Von-Neumann quantum entropy.

Graphics

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