Related papers: Shared active subspace for multivariate vector-val…

Shape constraints such as positive semi-definiteness (PSD) for matrices or convexity for functions play a central role in many applications in machine learning and sciences, including metric learning, optimal transport, and economics. Yet,…

Memristor crossbars enable vector-matrix multiplication (VMM), and are promising for low-power applications. However, it can be difficult to write the memristor conductance values exactly. To improve the accuracy of VMM, we propose a scheme…

We analyse a multilevel Monte Carlo method for the approximation of distribution functions of univariate random variables. Since, by assumption, the target distribution is not known explicitly, approximations have to be used. We provide an…

Recently there is a line of research work proposing to employ Spectral Clustering (SC) to segment (group){Throughout the paper, we use segmentation, clustering, and grouping, and their verb forms, interchangeably.} high-dimensional…

In recent years, considerable attention has been devoted to the regularization models due to the presence of high-dimensional data in scientific research. Sparse support vector machine (SVM) are useful tools in high-dimensional data…

We introduce a numerical method for reconstructing a multidimensional surface using the gradient of the surface measured at some values of the coordinates. The method consists of defining a multidimensional spline function and minimizing…

We develop a new method for multivariate scalar on multidimensional distribution regression. Traditional approaches typically analyze isolated univariate scalar outcomes or consider unidimensional distributional representations as…

We present Submatrix-wise Vector Embedding Learner (Swivel), a method for generating low-dimensional feature embeddings from a feature co-occurrence matrix. Swivel performs approximate factorization of the point-wise mutual information…

Vector-valued learning, where the output space admits a vector-valued structure, is an important problem that covers a broad family of important domains, e.g. multi-task learning and transfer learning. Using local Rademacher complexity and…

This paper explores variants of the subspace iteration algorithm for computing approximate invariant subspaces. The standard subspace iteration approach is revisited and new variants that exploit gradient-type techniques combined with a…

Support Vector Machines (SVM), a popular machine learning technique, has been applied to a wide range of domains such as science, finance, and social networks for supervised learning. Whether it is identifying high-risk patients by…

Singular Value Decomposition (SVD) is the basic body of many statistical algorithms and few users question whether SVD is properly handling its job. SVD aims at evaluating the decomposition that best approximates a data matrix, given some…

Since many real-world data can be described from multiple views, multi-view learning has attracted considerable attention. Various methods have been proposed and successfully applied to multi-view learning, typically based on matrix…

Algorithms for multi-agent systems to locate a source or to follow a desired level curve of spatially distributed scalar fields generally require sharing field measurements among the agents for gradient estimation. Yet, in this paper, we…

Shifted partial derivative (SPD) methods are a central algebraic tool for circuit lower bounds, measuring the dimension of spaces of shifted derivatives of a polynomial. We develop the Shifted Partial Derivative Polynomial (SPDP) framework,…

Modeling and predicting the dynamics of complex multiscale systems remains a significant challenge due to their inherent nonlinearities and sensitivity to initial conditions, as well as limitations of traditional machine learning methods…

Distributed optimization consists of multiple computation nodes working together to minimize a common objective function through local computation iterations and network-constrained communication steps. In the context of robotics,…

We propose randomized subspace gradient methods for high-dimensional constrained optimization. While there have been similarly purposed studies on unconstrained optimization problems, there have been few on constrained optimization problems…

We develop a framework for the distributed minimization of submodular functions. Submodular functions are a discrete analog of convex functions and are extensively used in large-scale combinatorial optimization problems. While there has…

Distributed machine learning has recently become a critical paradigm for training large models on vast datasets. We examine the stochastic optimization problem for deep learning within synchronous parallel computing environments under…