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Group equivariant neural networks are growing in importance owing to their ability to generalise well in applications where the data has known underlying symmetries. Recent characterisations of a class of these networks that use high-order…
The alternating minimization (AM) method is a fundamental method for minimizing convex functions whose variable consists of two blocks. How to efficiently solve each subproblems when applying the AM method is the most concerned task. In…
The alternating direction method of multipliers (ADMM) algorithm is a powerful and flexible tool for complex optimization problems of the form $\min\{f(x)+g(y) : Ax+By=c\}$. ADMM exhibits robust empirical performance across a range of…
We propose a new unsupervised learning method for clustering a large number of time series based on a latent factor structure. Each cluster is characterized by its own cluster-specific factors in addition to some common factors which impact…
Consider a set of N agents seeking to solve distributively the minimization problem $\inf_{x} \sum_{n = 1}^N f_n(x)$ where the convex functions $f_n$ are local to the agents. The popular Alternating Direction Method of Multipliers has the…
Douglas-Rachford splitting and its equivalent dual formulation ADMM are widely used iterative methods in composite optimization problems arising in control and machine learning applications. The performance of these algorithms depends on…
We provide a new proof of the linear convergence of the alternating direction method of multipliers (ADMM) when one of the objective terms is strongly convex. Our proof is based on a framework for analyzing optimization algorithms…
We propose a new bundle-based augmented Lagrangian framework for solving constrained convex problems. Unlike the classical (inexact) augmented Lagrangian method (ALM) that has a nested double-loop structure, our framework features a…
The alternating direction method of multipliers (ADMM) is a powerful splitting algorithm for linearly constrained convex optimization problems. In view of its popularity and applicability, a growing attention is drawn towards the ADMM in…
Sparse covariance matrices play crucial roles by encoding the interdependencies between variables in numerous fields such as genetics and neuroscience. Despite substantial studies on sparse covariance matrices, existing methods face several…
Panel vector auto-regressive (VAR) models are widely used to capture the dynamics of multivariate time series across different subpopulations, where each subpopulation shares a common set of variables. In this work, we propose a panel VAR…
This paper aims to investigate the effectiveness of the recently proposed Boosted Difference of Convex functions Algorithm (BDCA) when applied to clustering with constraints and set clustering with constraints problems. This is the first…
This paper presents two new techniques relating to inexact solution of subproblems in augmented Lagrangian methods for convex programming. The first involves combining a relative error criterion for solution of the subproblems with over- or…
Change point analysis has applications in a wide variety of fields. The general problem concerns the inference of a change in distribution for a set of time-ordered observations. Sequential detection is an online version in which new data…
The success of deep learning hinges on enormous data and large models, which require labor-intensive annotations and heavy computation costs. Subset selection is a fundamental problem that can play a key role in identifying smaller portions…
This paper addresses the problem of efficiently classifying high-dimensional data over decentralized networks. Penalized support vector machines (SVMs) are widely used for high-dimensional classification tasks. However, the double…
Recent work has focused on the problem of conducting linear regression when the number of covariates is very large, potentially greater than the sample size. To facilitate this, one useful tool is to assume that the model can be well…
In this paper, we investigate community detection in networks in the presence of node covariates. In many instances, covariates and networks individually only give a partial view of the cluster structure. One needs to jointly infer the full…
This article investigates the problem of noisy low-rank matrix completion with a shared factor structure, leveraging the auxiliary information from the missing indicator matrix to enhance prediction accuracy. Despite decades of development…
Panel data allows for the modeling of unobserved heterogeneity, significantly raising the number of nuisance parameters and making high dimensionality a practical issue. Meanwhile, temporal and cross-sectional dependence in panel data…