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Clustering multi-dimensional points is a fundamental task in many fields, and density-based clustering supports many applications as it can discover clusters of arbitrary shapes. This paper addresses the problem of Density-Peaks Clustering…
Artificial neural networks that learn to perform Principal Component Analysis (PCA) and related tasks using strictly local learning rules have been previously derived based on the principle of similarity matching: similar pairs of inputs…
We investigate a difference-of-convex (DC) formulation where the second term is allowed to be weakly convex. We examine the precise behavior of a single iteration of the difference-of-convex algorithm (DCA), providing a tight…
Due to the rapid growth of smart agents such as weakly connected computational nodes and sensors, developing decentralized algorithms that can perform computations on local agents becomes a major research direction. This paper considers the…
Deep neural networks (DNNs) often produce overconfident out-of-distribution predictions, motivating Bayesian uncertainty quantification. The Linearized Laplace Approximation (LLA) achieves this by linearizing the DNN and applying Laplace…
Context parallelism has emerged as a key technique to support long-context training, a growing trend in generative AI for modern large models. However, existing context parallel methods rely on static parallelization configurations that…
We consider a Susceptible-Infective-Recovered (SIR) model, where the mechanism for the renewal of susceptibles is demographic, on a ring with next nearest neighbour interactions, and a family of correlated pair approximations (CPA),…
The difference-of-convex algorithm (DCA) and its variants are the most popular methods to solve the difference-of-convex optimization problem. Each iteration of them is reduced to a convex optimization problem, which generally needs to be…
Dynamic inner principal component analysis (DiPCA) is a powerful method for the analysis of time-dependent multivariate data. DiPCA extracts dynamic latent variables that capture the most dominant temporal trends by solving a large-scale,…
Sparse Canonical Correlation Analysis (CCA) has received considerable attention in high-dimensional data analysis to study the relationship between two sets of random variables. However, there has been remarkably little theoretical…
Semantic segmentation of high-resolution remote sensing imagery (HRSI) suffers from the domain shift, resulting in poor performance of the model in another unseen domain. Unsupervised domain adaptive (UDA) semantic segmentation aims to…
This paper introduces AdaSDCA: an adaptive variant of stochastic dual coordinate ascent (SDCA) for solving the regularized empirical risk minimization problems. Our modification consists in allowing the method adaptively change the…
The Boosted Difference of Convex functions Algorithm (BDCA) has been recently introduced to accelerate the performance of the classical Difference of Convex functions Algorithm (DCA). This acceleration is achieved thanks to an extrapolation…
This paper develops a novel Continuous-time Accelerated Proximal Point Algorithm (CAPPA) for $\ell_1$-minimization problems with provable fixed-time convergence guarantees. The problem of $\ell_1$-minimization appears in several contexts,…
Unsupervised domain adaptive (UDA) image segmentation has recently gained increasing attention, aiming to improve the generalization capability for transferring knowledge from the source domain to the target domain. However, in high spatial…
Motivated by the recently shown connection between self-attention and (kernel) principal component analysis (PCA), we revisit the fundamentals of PCA. Using the difference-of-convex (DC) framework, we present several novel formulations and…
Sparse principal component analysis (PCA) and sparse canonical correlation analysis (CCA) are two essential techniques from high-dimensional statistics and machine learning for analyzing large-scale data. Both problems can be formulated as…
The difference-of-convex algorithm (DCA) is a well-established nonlinear programming technique that solves successive convex optimization problems. These sub-problems are obtained from the difference-of-convex~(DC) decompositions of the…
Decentralized optimization, particularly the class of decentralized composite convex optimization (DCCO) problems, has found many applications. Due to ubiquitous communication congestion and random dropouts in practice, it is highly…
This paper presents solutions to Density Classification Task (DCT) using a variant of Cellular Automata (CA) called Programmable Cellular Automata (PCA). The translation property as well as the density preserving property of fundamental CA…