相关论文: Improved Algorithm and Bounds for Successive Proje…
This paper presents a new extension of the classical Heron problem, termed the generalized $(k,m)$-Heron problem, which seeks an optimal configuration among $k$ feasible and $m$ target non-empty closed convex sets in $\mathbb{R}^n$. The…
This paper presents a proposal of a faster Wasserstein $k$-means algorithm for histogram data by reducing Wasserstein distance computations and exploiting sparse simplex projection. We shrink data samples, centroids, and the ground cost…
This work addresses the challenge of sub-pixel accuracy in detecting 2D local features, a cornerstone problem in computer vision. Despite the advancements brought by neural network-based methods like SuperPoint and ALIKED, these modern…
We study stochastic convex optimization under infinite noise variance. Specifically, when the stochastic gradient is unbiased and has uniformly bounded $(1+\kappa)$-th moment, for some $\kappa \in (0,1]$, we quantify the convergence rate of…
Singular value decomposition (SVD) based principal component analysis (PCA) breaks down in the high-dimensional and limited sample size regime below a certain critical eigen-SNR that depends on the dimensionality of the system and the…
Approximating the permanent of a complex-valued matrix is a fundamental problem with applications in Boson sampling and probabilistic inference. In this paper, we extend factor-graph-based methods for approximating the permanent of…
Many differentially private and classical non-private graph algorithms rely crucially on determining whether some property of each vertex meets a threshold. For example, for the $k$-core decomposition problem, the classic peeling algorithm…
We introduce a new method for sparse principal component analysis, based on the aggregation of eigenvector information from carefully-selected axis-aligned random projections of the sample covariance matrix. Unlike most alternative…
Precise object boundary detection for automatic image segmentation is critical for image analysis, including that used in computer-aided diagnosis. However, such detection traditionally uses active contour or snake models requiring accurate…
The proximal point algorithm plays a central role in non-smooth convex programming. The Augmented Lagrangian Method, one of the most famous optimization algorithms, has been found to be closely related to the proximal point algorithm. Due…
Dense self-supervised learning (SSL) methods showed its effectiveness in enhancing the fine-grained semantic understandings of vision models. However, existing approaches often rely on parametric assumptions or complex post-processing…
Pseudospectra and structured pseudospectra are important tools for the analysis of matrices. Their computation, however, can be very demanding for all but small matrices. A new approach to compute approximations of pseudospectra and…
Random projection, a dimensionality reduction technique, has been found useful in recent years for reducing the size of optimization problems. In this paper, we explore the use of sparse sub-gaussian random projections to approximate…
In many real-world problems, we are dealing with collections of high-dimensional data, such as images, videos, text and web documents, DNA microarray data, and more. Often, high-dimensional data lie close to low-dimensional structures…
The generation of a sky model for calibration of Square Kilometre Array observations requires a fast method of automatic point source detection and characterisation. In recent years, point source detection in two-dimensional images has been…
Sparse Subspace Clustering (SSC) has been used extensively for subspace identification tasks due to its theoretical guarantees and relative ease of implementation. However SSC has quadratic computation and memory requirements with respect…
We consider the problem of recovering off-the-grid spikes from linear measurements. The state of the art Over-Parametrized Continuous Orthogonal Matching Pursuit (OP-COMP) with Projected Gradient Descent (PGD) successfully recovers those…
We study differentially private (DP) optimization algorithms for stochastic and empirical objectives which are neither smooth nor convex, and propose methods that return a Goldstein-stationary point with sample complexity bounds that…
In this paper we study a broad class of structured nonlinear programming (SNLP) problems. In particular, we first establish the first-order optimality conditions for them. Then we propose sequential convex programming (SCP) methods for…
We study robust PCA for the fully observed setting, which is about separating a low rank matrix $\boldsymbol{L}$ and a sparse matrix $\boldsymbol{S}$ from their sum $\boldsymbol{D}=\boldsymbol{L}+\boldsymbol{S}$. In this paper, a new…