Alternating minimization algorithm with initialization analysis for r-local and k-sparse unlabeled sensing

• URL: http://arxiv.org/abs/2211.07621v1
• Date: Mon, 14 Nov 2022 18:44:55 GMT
• Title: Alternating minimization algorithm with initialization analysis for r-local and k-sparse unlabeled sensing
• Authors: Ahmed Abbasi, Abiy Tasissa, Shuchin Aeron
• Abstract summary: Unlabeled sensing problem is to recover an unknown signal from permuted linear measurements. We propose an alternating minimization algorithm with a suitable initialization for the widely considered k-sparse permutation model. Our algorithm is computationally scalable and, compared to baseline methods, achieves superior performance on real and synthetic datasets.
• Score: 10.751269349279912
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: The unlabeled sensing problem is to recover an unknown signal from permuted linear measurements. We propose an alternating minimization algorithm with a suitable initialization for the widely considered k-sparse permutation model. Assuming either a Gaussian measurement matrix or a sub-Gaussian signal, we upper bound the initialization error for the r-local and k-sparse permutation models in terms of the block size $r$ and the number of shuffles k, respectively. Our algorithm is computationally scalable and, compared to baseline methods, achieves superior performance on real and synthetic datasets.

Related papers

• Riemannian Optimization for Non-convex Euclidean Distance Geometry with Global Recovery Guarantees [6.422262171968397]
  Two algorithms are proposed to solve the Euclidean Distance Geometry problem. First algorithm converges linearly to the true solution. Second algorithm demonstrates strong numerical performance on both synthetic and real data.
  arXiv  Detail & Related papers  (2024-10-08T21:19:22Z)
• A Sample Efficient Alternating Minimization-based Algorithm For Robust Phase Retrieval [56.67706781191521]
  In this work, we present a robust phase retrieval problem where the task is to recover an unknown signal. Our proposed oracle avoids the need for computationally spectral descent, using a simple gradient step and outliers.
  arXiv  Detail & Related papers  (2024-09-07T06:37:23Z)
• Linearized Wasserstein dimensionality reduction with approximation guarantees [65.16758672591365]
  LOT Wassmap is a computationally feasible algorithm to uncover low-dimensional structures in the Wasserstein space. We show that LOT Wassmap attains correct embeddings and that the quality improves with increased sample size. We also show how LOT Wassmap significantly reduces the computational cost when compared to algorithms that depend on pairwise distance computations.
  arXiv  Detail & Related papers  (2023-02-14T22:12:16Z)
• Optimal Algorithms for the Inhomogeneous Spiked Wigner Model [89.1371983413931]
  We derive an approximate message-passing algorithm (AMP) for the inhomogeneous problem. We identify in particular the existence of a statistical-to-computational gap where known algorithms require a signal-to-noise ratio bigger than the information-theoretic threshold to perform better than random.
  arXiv  Detail & Related papers  (2023-02-13T19:57:17Z)
• Alternating Mahalanobis Distance Minimization for Stable and Accurate CP Decomposition [4.847980206213335]
  We introduce a new formulation for deriving singular values and vectors of a tensor by considering the critical points of a function different from what is used in the previous work. We show that a subsweep of this algorithm can achieve a superlinear convergence rate for exact CPD with known rank. We then view the algorithm as optimizing a Mahalanobis distance with respect to each factor with ground metric dependent on the other factors.
  arXiv  Detail & Related papers  (2022-04-14T19:56:36Z)
• Learning Sparse Graphs via Majorization-Minimization for Smooth Node Signals [8.140698535149042]
  We propose an algorithm for learning a sparse weighted graph by estimating its adjacency matrix. We show that the proposed algorithm converges faster, in terms of the average number of iterations, than several existing methods in the literature.
  arXiv  Detail & Related papers  (2022-02-06T17:06:13Z)
• Nearly Linear Row Sampling Algorithm for Quantile Regression [54.75919082407094]
  We give a row sampling algorithm for the quantile loss function with sample complexity nearly linear in the dimensionality of the data. Based upon our row sampling algorithm, we give the fastest known algorithm for quantile regression and a graph sparsification algorithm for balanced directed graphs.
  arXiv  Detail & Related papers  (2020-06-15T13:40:07Z)
• Effective Dimension Adaptive Sketching Methods for Faster Regularized Least-Squares Optimization [56.05635751529922]
  We propose a new randomized algorithm for solving L2-regularized least-squares problems based on sketching. We consider two of the most popular random embeddings, namely, Gaussian embeddings and the Subsampled Randomized Hadamard Transform (SRHT)
  arXiv  Detail & Related papers  (2020-06-10T15:00:09Z)
• Optimal Randomized First-Order Methods for Least-Squares Problems [56.05635751529922]
  This class of algorithms encompasses several randomized methods among the fastest solvers for least-squares problems. We focus on two classical embeddings, namely, Gaussian projections and subsampled Hadamard transforms. Our resulting algorithm yields the best complexity known for solving least-squares problems with no condition number dependence.
  arXiv  Detail & Related papers  (2020-02-21T17:45:32Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.