Related papers: Approximating Metric Magnitude of Point Sets

The incremental aggregated gradient algorithm is popular in network optimization and machine learning research. However, the current convergence results require the objective function to be strongly convex. And the existing convergence…

In this work, we address unconstrained finite-sum optimization problems, with particular focus on instances originating in large scale deep learning scenarios. Our main interest lies in the exploration of the relationship between recent…

This paper considers the decentralized convex optimization problem, which has a wide range of applications in large-scale machine learning, sensor networks, and control theory. We propose novel algorithms that achieve optimal computation…

Within the current sphere of deep learning research, despite the extensive application of optimization algorithms such as Stochastic Gradient Descent (SGD) and Adaptive Moment Estimation (Adam), there remains a pronounced inadequacy in…

As deep learning models and datasets rapidly scale up, network training is extremely time-consuming and resource-costly. Instead of training on the entire dataset, learning with a small synthetic dataset becomes an efficient solution.…

We investigate three related and important problems connected to machine learning: approximating a submodular function everywhere, learning a submodular function (in a PAC-like setting [53]), and constrained minimization of submodular…

Skeletonization is a powerful tool for shape analysis, rooted in the inherent instinct to understand an object's morphology. It has found applications across various domains, including robotics. Although skeletonization algorithms have been…

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…

We study a class of nonconvex nonsmooth optimization problems in which the objective is a sum of two functions: One function is the average of a large number of differentiable functions, while the other function is proper, lower…

A subgradient method is presented for solving general convex optimization problems, the main requirement being that a strictly-feasible point is known. A feasible sequence of iterates is generated, which converges to within user-specified…

Point cloud completion is the task of predicting complete geometry from partial observations using a point set representation for a 3D shape. Previous approaches propose neural networks to directly estimate the whole point cloud through…

Machine learning develops rapidly, which has made many theoretical breakthroughs and is widely applied in various fields. Optimization, as an important part of machine learning, has attracted much attention of researchers. With the…

In training neural networks, it is common practice to use partial gradients computed over batches, mostly very small subsets of the training set. This approach is motivated by the argument that such a partial gradient is close to the true…

Typically, the sequence of points generated by an optimization algorithm may have multiple limit points. Under convexity assumptions, however, (sub)gradient methods are known to generate a convergent sequence of points. In this paper, we…

Clustering approaches that utilize convex loss functions have recently attracted growing interest in the formation of compact data clusters. Although classical methods like k-means and its wide family of variants are still widely used, all…

This survey reviews a clustering method based on solving a convex optimization problem. Despite the plethora of existing clustering methods, convex clustering has several uncommon features that distinguish it from prior art. The…

We propose a definition of magnitude for a length space with a Borel measure, which involves integrals over the set of geodesics. This quantity agrees with the magnitude of finite metric spaces, up to re-scaling the metric to ensure the…

We address the problem of minimizing a convex function over the space of large matrices with low rank. While this optimization problem is hard in general, we propose an efficient greedy algorithm and derive its formal approximation…

Most complex machine learning and modelling techniques are prone to over-fitting and may subsequently generalise poorly to future data. Artificial neural networks are no different in this regard and, despite having a level of implicit…

We are interested in reconstructing the mesh representation of object surfaces from point clouds. Surface reconstruction is a prerequisite for downstream applications such as rendering, collision avoidance for planning, animation, etc.…