Search Results for author: Gilad Lerman

Found 36 papers, 11 papers with code

Message Passing Least Squares: A Unified Framework for Fast and Robust Group Synchronization

no code implementations ICML 2020 Yunpeng Shi, Gilad Lerman

We propose an efficient algorithm for solving robust group synchronization given adversarially corrupted group ratios.

Cubic-Regularized Newton for Spectral Constrained Matrix Optimization and its Application to Fairness

no code implementations2 Sep 2022 Casey Garner, Gilad Lerman, Shuzhong Zhang

Matrix functions are utilized to rewrite smooth spectral constrained matrix optimization problems as smooth unconstrained problems over the set of symmetric matrices which are then solved via the cubic-regularized Newton method.


Robust Group Synchronization via Quadratic Programming

1 code implementation17 Jun 2022 Yunpeng Shi, Cole Wyeth, Gilad Lerman

We propose a novel quadratic programming formulation for estimating the corruption levels in group synchronization, and use these estimates to solve this problem.

An Unpooling Layer for Graph Generation

1 code implementation4 Jun 2022 Yinglong Guo, Dongmian Zou, Gilad Lerman

Since this unpooling layer is trainable, it can be applied to graph generation either in the decoder of a variational autoencoder or in the generator of a generative adversarial network (GAN).

Graph Generation

Fast, Accurate and Memory-Efficient Partial Permutation Synchronization

no code implementations CVPR 2022 Shaohan Li, Yunpeng Shi, Gilad Lerman

Previous partial permutation synchronization (PPS) algorithms, which are commonly used for multi-object matching, often involve computation-intensive and memory-demanding matrix operations.

Stochastic and Private Nonconvex Outlier-Robust PCA

no code implementations17 Mar 2022 Tyler Maunu, Chenyu Yu, Gilad Lerman

Our results emphasize the advantages of the nonconvex methods over another convex approach to solving this problem in the differentially private setting.

Robust Vector Quantized-Variational Autoencoder

no code implementations4 Feb 2022 Chieh-Hsin Lai, Dongmian Zou, Gilad Lerman

We experimentally demonstrate that RVQ-VAE is able to generate examples from inliers even if a large portion of the training data points are corrupted.


Scalable Cluster-Consistency Statistics for Robust Multi-Object Matching

1 code implementation13 Jan 2022 Yunpeng Shi, Shaohan Li, Tyler Maunu, Gilad Lerman

We develop new statistics for robustly filtering corrupted keypoint matches in the structure from motion pipeline.

Ensemble Riemannian Data Assimilation over the Wasserstein Space

no code implementations7 Sep 2020 Sagar K. Tamang, Ardeshir Ebtehaj, Peter J. Van Leeuwen, Dongmian Zou, Gilad Lerman

Unlike the Eulerian penalization of error in the Euclidean space, the Wasserstein metric can capture translation and difference between the shapes of square-integrable probability distributions of the background state and observations -- enabling to formally penalize geophysical biases in state-space with non-Gaussian distributions.


Message Passing Least Squares Framework and its Application to Rotation Synchronization

1 code implementation27 Jul 2020 Yunpeng Shi, Gilad Lerman

We propose an efficient algorithm for solving group synchronization under high levels of corruption and noise, while we focus on rotation synchronization.

Novelty Detection via Robust Variational Autoencoding

1 code implementation9 Jun 2020 Chieh-Hsin Lai, Dongmian Zou, Gilad Lerman

We establish both robustness to outliers and suitability to low-rank modeling of the Wasserstein metric as opposed to the KL divergence.

Dimensionality Reduction

Depth Descent Synchronization in $\mathrm{SO}(D)$

no code implementations13 Feb 2020 Tyler Maunu, Gilad Lerman

We give robust recovery results for synchronization on the rotation group, $\mathrm{SO}(D)$.

Robust Group Synchronization via Cycle-Edge Message Passing

2 code implementations24 Dec 2019 Gilad Lerman, Yunpeng Shi

We then establish exact recovery and linear convergence guarantees for the proposed message passing procedure under a deterministic setting with adversarial corruption.

Robust Subspace Recovery with Adversarial Outliers

no code implementations5 Apr 2019 Tyler Maunu, Gilad Lerman

The two estimators are fast to compute and achieve state-of-the-art theoretical performance in a noiseless RSR setting with adversarial outliers.

Analysis and algorithms for $\ell_p$-based semi-supervised learning on graphs

no code implementations15 Jan 2019 Mauricio Flores, Jeff Calder, Gilad Lerman

In the first part of the paper we prove new discrete to continuum convergence results for $p$-Laplace problems on $k$-nearest neighbor ($k$-NN) graphs, which are more commonly used in practice than random geometric graphs.

General Classification

Solving Jigsaw Puzzles By the Graph Connection Laplacian

3 code implementations7 Nov 2018 Vahan Huroyan, Gilad Lerman, Hau-Tieng Wu

The main contribution of this work is a method for recovering the rotations of the pieces when both shuffles and rotations are unknown.

Encoding Robust Representation for Graph Generation

1 code implementation28 Sep 2018 Dongmian Zou, Gilad Lerman

The decoder is a simple fully connected network that is adapted to specific tasks, such as link prediction, signal generation on graphs and full graph and signal generation.

Graph Generation Link Prediction

Graph Generation via Scattering

no code implementations27 Sep 2018 Dongmian Zou, Gilad Lerman

These results are in contrast to experience with Euclidean data, where it is difficult to form a generative scattering network that performs as well as state-of-the-art methods.

Graph Generation Link Prediction

Graph Convolutional Neural Networks via Scattering

1 code implementation31 Mar 2018 Dongmian Zou, Gilad Lerman

We generalize the scattering transform to graphs and consequently construct a convolutional neural network on graphs.

Node Classification

An Overview of Robust Subspace Recovery

no code implementations2 Mar 2018 Gilad Lerman, Tyler Maunu

This paper will serve as an introduction to the body of work on robust subspace recovery.

Exact Camera Location Recovery by Least Unsquared Deviations

no code implementations27 Sep 2017 Gilad Lerman, Yunpeng Shi, Teng Zhang

We establish exact recovery for the Least Unsquared Deviations (LUD) algorithm of Ozyesil and Singer.

A Well-Tempered Landscape for Non-convex Robust Subspace Recovery

no code implementations13 Jun 2017 Tyler Maunu, Teng Zhang, Gilad Lerman

The practicality of the deterministic condition is demonstrated on some statistical models of data, and the method achieves almost state-of-the-art recovery guarantees on the Haystack Model for different regimes of sample size and ambient dimension.

Distributed Robust Subspace Recovery

no code implementations25 May 2017 Vahan Huroyan, Gilad Lerman

We propose distributed solutions to the problem of Robust Subspace Recovery (RSR).

Enhancing Feature Tracking With Gyro Regularization

no code implementations4 Nov 2015 Bryan Poling, Gilad Lerman

We present a deeply integrated method of exploiting low-cost gyroscopes to improve general purpose feature tracking.

Optical Flow Estimation

Fast Landmark Subspace Clustering

no code implementations28 Oct 2015 Xu Wang, Gilad Lerman

Kernel methods obtain superb performance in terms of accuracy for various machine learning tasks since they can effectively extract nonlinear relations.

Riemannian Multi-Manifold Modeling

no code implementations1 Oct 2014 Xu Wang, Konstantinos Slavakis, Gilad Lerman

This paper advocates a novel framework for segmenting a dataset in a Riemannian manifold $M$ into clusters lying around low-dimensional submanifolds of $M$.

Fast, Robust and Non-convex Subspace Recovery

no code implementations24 Jun 2014 Gilad Lerman, Tyler Maunu

Further, under a special model of data, FMS converges to a point which is near to the global minimum with overwhelming probability.

Better Feature Tracking Through Subspace Constraints

no code implementations CVPR 2014 Bryan Poling, Gilad Lerman, Arthur Szlam

Our approach does not require direct modeling of the structure or the motion of the scene, and runs in real time on a single CPU core.

On the Sample Complexity of Robust PCA

no code implementations NeurIPS 2012 Matthew Coudron, Gilad Lerman

This estimator is used in a convex algorithm for robust subspace recovery (i. e., robust PCA).

Robust computation of linear models by convex relaxation

no code implementations18 Feb 2012 Gilad Lerman, Michael McCoy, Joel A. Tropp, Teng Zhang

Consider a dataset of vector-valued observations that consists of noisy inliers, which are explained well by a low-dimensional subspace, along with some number of outliers.

A Novel M-Estimator for Robust PCA

no code implementations20 Dec 2011 Teng Zhang, Gilad Lerman

That is, we assume a data set that some of its points are sampled around a fixed subspace and the rest of them are spread in the whole ambient space, and we aim to recover the fixed underlying subspace.

lp-Recovery of the Most Significant Subspace among Multiple Subspaces with Outliers

no code implementations18 Dec 2010 Gilad Lerman, Teng Zhang

We say that one of the underlying subspaces of the model is most significant if its mixture weight is higher than the sum of the mixture weights of all other subspaces.

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