17 accepted papers
A rigid motion in $\mathbb{R}^d$ consists of a proper rotation and a translation, and it can be represented as a matrix in $\mathbb{R}^{(d+1)\times (d+1)}$. The problem of rigid motion synchronization aims to estimate a collection of rigid motions $G^*_1, \dots, G^*_n$ from noisy observations of the…
This paper introduces Probabilistic Multi-Variable Branching (PMVB), a simple and effective technique for accelerating mixed-integer optimization using data-driven machine learning models. At its core, PMVB employs a multi-variable branching procedure that partitions the feasible region via data-dri…
Quantum computation offers the potential for a significant constant-factor speedup for the Ordered Search Problem (OSP). A classical construction is the $k$-query quantum ordered search algorithm, which can exactly search an $N$-element ordered list and achieves a query complexity improvement of a f…
We design a class of additive noise mechanisms that satisfy $(\varepsilon, \delta)$-differential privacy (DP) for scalar, real-valued query functions with known sensitivities, with a particular focus on moderate and low-privacy regimes. These mechanisms, which we call *mixture mechanisms*, are const…
The maximal coding rate reduction (MCR$^2$) objective for learning structured and compact deep representations is drawing increasing attention, especially after its recent usage in the derivation of fully explainable and highly effective deep network architectures. However, it lacks a complete theor…
Time-varying graphical LASSO (TVGL) aims to infer a sequence of graphs from time series data and has been widely used in many statistical inference problems. The existing algorithms usually suffer from high computational cost when solving large-scale TVGL problems. In this paper, we develop an effic…
We study the problem of symmetric positive semi-definite low-rank matrix completion (MC) with deterministic entry-dependent sampling. In particular, we consider rectified linear unit (ReLU) sampling, where only positive entries are observed, as well as a generalization to threshold-based sampling. W…
Decentralized optimization aims to cooperatively solve a global finite-sum loss function, where each agent only possesses knowledge of its own local function. Real-world applications introduce challenges such as unstable channels and differential privacy concerns, necessitating the development of mo…
In this work, we present the Bregman Alternating Projected Gradient (BAPG) method, a single-loop algorithm that offers an approximate solution to the Gromov-Wasserstein (GW) distance. We introduce a novel relaxation technique that balances accuracy and computational efficiency, albeit with some com…
In this paper we develop a simple scheme for a coupled matrix factorization problem arising in the topic of hyperspectral super-resolution (HSR). HSR considers the problem of recovering a super-resolution image from a multispectral image and a hyperspectral image, which have lower spectral and spati…
This work presents ReSync, a Riemannian subgradient-based algorithm for solving the robust rotation synchronization problem, which arises in various engineering applications. ReSync solves a least-unsquared minimization formulation over the rotation group, which is nonsmooth and nonconvex, and aims…
The K-subspaces (KSS) method is a generalization of the K-means method for subspace clustering. In this work, we present local convergence analysis and a recovery guarantee for KSS, assuming data are generated by the semi-random union of subspaces model, where $N$ points are randomly sampled from $K…
In this paper, we study the problem of exact community recovery in the symmetric stochastic block model, where a graph of $n$ vertices is randomly generated by partitioning the vertices into $K \ge 2$ equal-sized communities and then connecting each pair of vertices with probability that depends on…
This paper describes a novel small-scale turtle-inspired Amphibious Spherical Robot (ASRobot) to accomplish exploration tasks in the restricted environment, such as amphibious areas and narrow underwater cave. A Legged, Multi-Vectored Water-Jet Composite Propulsion Mechanism (LMVWCPM) is designed wi…
In this paper, we consider the large-scale case of the robust beamforming problem with interference temperature constraints. Previous semidefinite relaxation (SDR) method becomes impracticable because of its expensive computational cost. Even successive convex approximation (SCA) method, the state-o…
In this paper, we consider a ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -PCA problem under the large-scale data sample scenario, which has extensive applications in science and engineering. Previous algorithms for the problem either are n…
A fundamental class of matrix optimization problems that arise in many areas of science and engineering is that of quadratic optimization with orthogonality constraints. Such problems can be solved using line-search methods on the Stiefel manifold, which are known to converge globally under mild con…