Related papers: Efficient Convex Algorithms for Universal Kernel L…
Best subset selection is considered the `gold standard' for many sparse learning problems. A variety of optimization techniques have been proposed to attack this non-convex and NP-hard problem. In this paper, we investigate the dual forms…
Randomly initialized first-order optimization algorithms are the method of choice for solving many high-dimensional nonconvex problems in machine learning, yet general theoretical guarantees cannot rule out convergence to critical points of…
Semidefinite programming is an indispensable tool in computer vision, but general-purpose solvers for semidefinite programs are often too slow and memory intensive for large-scale problems. We propose a general framework to approximately…
Acquiring labels are often costly, whereas unlabeled data are usually easy to obtain in modern machine learning applications. Semi-supervised learning provides a principled machine learning framework to address such situations, and has been…
Minimization of the nuclear norm is often used as a surrogate, convex relaxation, for finding the minimum rank completion (recovery) of a partial matrix. The minimum nuclear norm problem can be solved as a trace minimization semidefinite…
We develop a machine-learning framework to learn hyperparameter sequences for accelerated first-order methods (e.g., the step size and momentum sequences in accelerated gradient descent) to quickly solve parametric convex optimization…
Kernel means are frequently used to represent probability distributions in machine learning problems. In particular, the well known kernel density estimator and the kernel mean embedding both have the form of a kernel mean. Unfortunately,…
We present the viewpoint that optimization problems encountered in machine learning can often be interpreted as minimizing a convex functional over a function space, but with a non-convex constraint set introduced by model parameterization.…
In this work, we propose a new local optimization method to solve a class of nonconvex semidefinite programming (SDP) problems. The basic idea is to approximate the feasible set of the nonconvex SDP problem by inner positive semidefinite…
Data similarity is a key concept in many data-driven applications. Many algorithms are sensitive to similarity measures. To tackle this fundamental problem, automatically learning of similarity information from data via self-expression has…
Convex quadratic programs (QPs) constitute a fundamental computational primitive across diverse domains including financial optimization, control systems, and machine learning. The alternating direction method of multipliers (ADMM) has…
We propose the -- to the best of our knowledge -- first fully functional implementation of the ``Separation by a Convex Body'' (SCB) approach first outlined in Grzybowski et al. [1] for classification, separating two data sets using an…
Machine learning (ML) models, such as SVM, for tasks like classification and clustering of sequences, require a definition of distance/similarity between pairs of sequences. Several methods have been proposed to compute the similarity…
We give sublinear-time approximation algorithms for some optimization problems arising in machine learning, such as training linear classifiers and finding minimum enclosing balls. Our algorithms can be extended to some kernelized versions…
Semidefinite programs are convex optimisation problems involving a linear objective function and a domain of positive semidefinite matrices. Over the last two decades, they have become an indispensable tool in quantum information science.…
Recent work has shown a variety of ways in which machine learning can be used to accelerate the solution of constrained optimization problems. Increasing demand for real-time decision-making capabilities in applications such as artificial…
Support Vector Machines (SVMs) are a cornerstone of supervised learning, widely used for data classification. A central component of their success lies in kernel functions, which enable efficient computation of inner products in…
We consider the task of decentralized minimization of the sum of smooth strongly convex functions stored across the nodes of a network. For this problem, lower bounds on the number of gradient computations and the number of communication…
This paper presents a general framework to integrate prior knowledge in the form of logic constraints among a set of task functions into kernel machines. The logic propositions provide a partial representation of the environment, in which…
Global optimization of decision trees is a long-standing challenge in combinatorial optimization, yet such models play an important role in interpretable machine learning. Although the problem has been investigated for several decades, only…