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The problem of statistical inference in its various forms has been the subject of decades-long extensive research. Most of the effort has been focused on characterizing the behavior as a function of the number of available samples, with far…
The problem of finding a solution to the linear system $Ax = b$ with certain minimization properties arises in numerous scientific and engineering areas. In the era of big data, the stochastic optimization algorithms become increasingly…
We propose a general framework for reduced-rank modeling of matrix-valued data. By applying a generalized nuclear norm penalty we can directly model low-dimensional latent variables associated with rows and columns. Our framework flexibly…
Earth observation resources are becoming increasingly indispensable in disaster relief, damage assessment and related domains. Many unpredicted factors, such as the change of observation task requirements, to the occurring of bad weather…
We consider the task of minimizing the sum of convex functions stored in a decentralized manner across the nodes of a communication network. This problem is relatively well-studied in the scenario when the objective functions are smooth, or…
Existing large-scale optimization schemes are challenged by both scalability and cyber-security. With the favorable scalability, adaptability, and flexibility, decentralized and distributed optimization paradigms are widely adopted in…
Low-rank matrix estimation plays a central role in various applications across science and engineering. Recently, nonconvex formulations based on matrix factorization are provably solved by simple gradient descent algorithms with strong…
Decentralized optimization is a powerful paradigm that finds applications in engineering and learning design. This work studies decentralized composite optimization problems with non-smooth regularization terms. Most existing gradient-based…
We study the convergence of a variant of distributed gradient descent (DGD) on a distributed low-rank matrix approximation problem wherein some optimization variables are used for consensus (as in classical DGD) and some optimization…
In modern decentralized applications, ensuring communication efficiency and privacy for the users are the key challenges. In order to train machine-learning models, the algorithm has to communicate to the data center and sample data for its…
Low-rank approximation of a matrix by means of structured random sampling has been consistently efficient in its extensive empirical studies around the globe, but adequate formal support for this empirical phenomenon has been missing so…
Spatial classification with limited feature observations has been a challenging problem in machine learning. The problem exists in applications where only a subset of sensors are deployed at certain spots or partial responses are collected…
Fitting statistical models is computationally challenging when the sample size or the dimension of the dataset is huge. An attractive approach for down-scaling the problem size is to first partition the dataset into subsets and then fit…
In this paper, we propose and analyze a trust-region model-based algorithm for solving unconstrained stochastic optimization problems. Our framework utilizes random models of an objective function $f(x)$, obtained from stochastic…
Unsupervised learning aims at the discovery of hidden structure that drives the observations in the real world. It is essential for success in modern machine learning. Latent variable models are versatile in unsupervised learning and have…
The goal of Feature Selection - comprising filter, wrapper, and embedded approaches - is to find the optimal feature subset for designated downstream tasks. Nevertheless, current feature selection methods are limited by: 1) the selection…
Dimension reduction is often the first step in statistical modeling or prediction of multivariate spatial data. However, most existing dimension reduction techniques do not account for the spatial correlation between observations and do not…
Most decentralized optimization algorithms are handcrafted. While endowed with strong theoretical guarantees, these algorithms generally target a broad class of problems, thereby not being adaptive or customized to specific problem…
In this paper, we consider the optimization problem of minimizing a continuously differentiable function subject to both convex constraints and sparsity constraints. By exploiting a mixed-integer reformulation from the literature, we define…
This study aims to optimize the evaluation metric of multimodal multi-objective optimization problems using a Regionalized Metric Framework, which provides a certain boost to research in this field. Existing evaluation metrics usually use…