42 accepted papers
Synchronization over the special Euclidean group $\mathrm{SE}(3)$ aims to recover absolute poses from noisy pairwise relative transformations and is a core primitive in robotics and 3D vision. Standard approaches often require multi-step heuristic procedures to recover valid poses, which are difficu…
Learning the graph topology of a complex network is challenging due to limited data availability and imprecise data models. A common remedy in existing works is to incorporate priors such as sparsity or modularity which highlight on the structural property of graph topology. We depart from these app…
Language models (LMs) can produce texts that appear accurate and coherent but contain untruthful or toxic content. Inference-time interventions that edit the hidden activations have shown promising results in steering the LMs towards desirable generations. Existing activation intervention methods of…
Solving bilevel optimization (BLO) problems to global optimality is generally intractable. A common surrogate is to compute a hyper-stationary point—a stationary point of the hyper-objective function obtained by minimizing or maximizing the upper-level objective over the lower-level solution set. Ex…
Nonconvex-concave (NC-C) finite-sum minimax problems have broad applications in decentralized optimization and various machine learning tasks. However, the nonsmooth nature of NC-C problems makes it challenging to design effective variance reduction techniques. Existing vanilla stochastic algorithms…
Fair principal component analysis (FPCA), a ubiquitous dimensionality reduction technique in signal processing and machine learning, aims to find a low-dimensional representation for a high-dimensional dataset in view of fairness. The FPCA problem involves optimizing a non-convex and non-smooth func…
Hyperparameter tuning is an important task of machine learning, which can be formulated as a bilevel program (BLP). However, most existing algorithms are not applicable for BLP with non-smooth lower-level problems. To address this, we propose a single-level reformulation of the BLP based on lower-le…
This paper proposes a Generalized Power Method (GPM) to simultaneously solve the joint problem of community detection and group synchronization in a direct non-convex manner, in contrast to the existing method of semidefinite programming (SDP). Under a natural extension of stochastic block model (SB…
Many machine learning tasks, such as principal component analysis and low-rank matrix completion, give rise to manifold optimization problems. Although there is a large body of work studying the design and analysis of algorithms for manifold optimization in the centralized setting, there are current…
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…
Graph learning from signals is a core task in graph signal processing (GSP). A significant subclass of graph signals called the stationary graph signals that broadens the concept of stationarity of data defined on regular domains to signals on graphs is gaining increasing popularity in the GSP commu…
Fine-tuning pre-trained models has been ubiquitously proven to be effective in a wide range of NLP tasks. However, fine-tuning the whole model is parameter inefficient as it always yields an entirely new model for each task. Currently, many research works propose to only fine-tune a small portion of…
Gromov-Wasserstein (GW) distance is a powerful tool for comparing and aligning probability distributions supported on different metric spaces. Recently, GW has become the main modeling technique for aligning heterogeneous data for a wide range of graph learning tasks. However, the GW distance is kno…
This paper investigates the problem of exact community recovery in the symmetric $d$-uniform $(d \geq 2)$ hypergraph stochastic block model ($d$-HSBM). In this model, a $d$-uniform hypergraph with $n$ nodes is generated by first partitioning the $n$ nodes into $K\geq 2$ equal-sized disjoint communit…
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…
Nonconvex-nonconcave minimax optimization has received intense attention over the last decade due to its broad applications in machine learning. Most existing algorithms rely on one-sided information, such as the convexity (resp. concavity) of the primal (resp. dual) functions, or other specific str…
This paper is concerned with the algorithmic aspects of sharper stationarity of a nonconvex, nonsmooth, Clarke irregular machine learning model. We study the SVM problem with a $\rho$-margin loss function, which is the margin theory generalization bound of SVM introduced in the learning theory textb…
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…
Signed graphs encode similarity and dissimilarity relationships among different entities with positive and negative edges. In this paper, we study the problem of community recovery over signed graphs generated by the signed stochastic block model (SSBM) with two equal-sized communities. Our approach…
We report a practical finite-time algorithmic scheme to compute approximately stationary points for nonconvex nonsmooth Lipschitz functions. In particular, we are interested in two kinds of approximate stationarity notions for nonconvex nonsmooth problems, i.e., Goldstein approximate stationarity (G…
In convex optimization, the problem of finding near-stationary points has not been adequately studied yet, unlike other optimality measures such as the function value. Even in the deterministic case, the optimal method (OGM-G, due to Kim and Fessler (2021)) has just been discovered recently. In this…
Text generation tasks, including translation, summarization, language models, and etc. see rapid growth during recent years. Despite the remarkable achievements, the repetition problem has been observed in nearly all text generation models undermining the generation performance extensively. To solve…
We consider the problem of identifying the graph topology from a set of smooth graph signals. A well-known approach to this problem is minimizing the Dirichlet energy accompanied with some Frobenius norm regularization. Recent works have incorporated the logarithmic barrier on the node degrees to im…
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…
In this paper, we study the cardinality constrained mean-variance-skewness-kurtosis (MVSKC) model for sparse high-order portfolio optimization. The MVSKC model is computationally challenging, as the objective function is non-convex and the cardinality constraint is discontinuous. Since the cardinali…
Graph learning is one of the most important tasks in machine learning, statistics and signal processing. In this paper, we focus on the problem of learning the generalized graph Lapla-cian (GGL) and propose an efficient algorithm to solve it. We first fully exploit the sparsity structure hidden in t…
Learning community structures in graphs that are randomly generated by stochastic block models (SBMs) has received much attention lately. In this paper, we focus on the problem of exactly recovering the communities in a binary symmetric SBM, where a graph of $n$ vertices is partitioned into two equa…
Variable selection is one of the most important tasks in statistics and machine learning. To incorporate more prior information about the regression coefficients, various constrained Lasso models have been proposed in the literature. Compared with the classic (unconstrained) Lasso model, the algorit…
We propose a new methodology to design first-order methods for unconstrained strongly convex problems. Specifically, instead of tackling the original objective directly, we construct a shifted objective function that has the same minimizer as the original objective and encodes both the smoothness an…
Wasserstein \textbf{D}istributionally \textbf{R}obust \textbf{O}ptimization (DRO) is concerned with finding decisions that perform well on data that are drawn from the worst probability distribution within a Wasserstein ball centered at a certain nominal distribution. In recent years, it has been sh…
Wasserstein distance-based distributionally robust optimization (DRO) has received much attention lately due to its ability to provide a robustness interpretation of various learning models. Moreover, many of the DRO problems that arise in the learning context admits exact convex reformulations and…
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…
We consider the problem of unknown emitter geolocation using the time difference of arrival (TDOA) of the path rays through the ionosphere by multiple coordinated distant receivers. We formulate the geolocation in the sense of maximum likelihood with the exact ray expressions for the quasi-parabolic…
We consider the degree distribution design of the low-density parity-check (LDPC) code ensembles for symmetric Gaussian multiple-access channels (GMAC). To characterize the probability density function (PDF) of the message passing in the process of joint decoding, we propose a new scheme to construc…
In this work, we consider the robust beamforming design for secondary downlink multicasting channels, where primary users are present with norm-bounded channel errors. In particular, the max-min-fair formulation is considered and the resulting design problem is a quadratically constrained quadratic…
Unlike dimensionality reduction (DR) tools for single-view data, e.g., principal component analysis (PCA), canonical correlation analysis (CCA) and generalized CCA (GCCA) are able to integrate information from multiple feature spaces of data. This is critical in multi-modal data fusion and analytics…
In this paper, we consider the robust beamforming design in a device-to-device (D2D) two-hop one-way relay network. Specifically, we study the amplify-and-forward (AF) scheme in the scenario where both the transmitter-to-relays link and relays-to-receiver link are subject to estimation errors. Assum…
We consider the problem of geolocating two unknown co-channel emitters by a cluster of formation-flying satellites using both time difference of arrival (TDOA) and frequency difference of arrival (FDOA) measurements. As the association between the TDOA/FDOA measurements obtained by each pair of sate…
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…
In this paper, we consider a cloud relay network (C-RN) which provides reliable communication between long-distance users. Specifically, we study the amplify-and-forward (AF) schemes in C-RNs. In our scenario setting, with the cloud processor units fully coordinating in the network, the C-RN can be…
Recently, \ell_1,p-regularization has been widely used to induce structured sparsity in the solutions to various optimization problems. Motivated by the desire to analyze the convergence rate of first-order methods, we show that for a large class of \ell_1,p-regularized problems, an error bound cond…