Related papers: Reducing Spatial and Temporal Dimensionality in th…
In this paper we propose and study a new complexity model for approximation algorithms. The main motivation are practical problems over large data sets that need to be solved many times for different scenarios, e.g., many multicast trees…
We consider the problem of robustifying high-dimensional structured estimation. Robust techniques are key in real-world applications which often involve outliers and data corruption. We focus on trimmed versions of structurally regularized…
This work aims to construct an efficient and highly accurate numerical method to address the time singularity at $t=0$ involved in a class of time-fractional parabolic integro-partial differential equations in one and two dimensions. The…
A low-dimensional model (LDM) for turbulent Rayleigh-Benard convection in a Cartesian cell with square domain, based on the Galerkin projection of the Boussinesq equations onto a finite set of empirical eigenfunctions, is presented. The…
We present local discriminative Gaussian (LDG) dimensionality reduction, a supervised dimensionality reduction technique for classification. The LDG objective function is an approximation to the leave-one-out training error of a local…
High-dimensional simulation optimization is notoriously challenging. We propose a new sampling algorithm that converges to a global optimal solution and suffers minimally from the curse of dimensionality. The algorithm consists of two…
The classical vector autoregressive model is a fundamental tool for multivariate time series analysis. However, it involves too many parameters when the number of time series and lag order are even moderately large. This paper proposes to…
Now a days many algorithms are invented or being inventing to find the solution for Euclidean Minimum Spanning Tree, EMST, problem, as its applicability is increasing in much wide range of fields containing spatial or spatio temporal data…
Scientific computer simulations cannot represent all scales in realistic applications. To bridge this model-data gap, parameters are injected into models and constrained with noisy data using Bayesian inversion. To reduce the number of…
The two-dimensional layout optimization problem reinforced by the efficient space utilization demand has a wide spectrum of practical applications. Formulating the problem as a nonlinear minimization problem under planar equality and/or…
This paper addresses the structurally-constrained sparse decomposition of multi-dimensional signals onto overcomplete families of vectors, called dictionaries. The contribution of the paper is threefold. Firstly, a generic spatio-temporal…
Diffusion approximation provides weak approximation for stochastic gradient descent algorithms in a finite time horizon. In this paper, we introduce new tools motivated by the backward error analysis of numerical stochastic differential…
We present a framework leveraging a novel variant of the model-based diffusion algorithm to minimize the time required for a redundant dual-arm robot configuration to follow a desired relative Cartesian path. Our prior work proposed a…
We introduce a new method to jointly reduce the dimension of the input and output space of a function between high-dimensional spaces. Choosing a reduced input subspace influences which output subspace is relevant and vice versa.…
High-dimensional multivariate time series are challenging due to the dependent and high-dimensional nature of the data, but in many applications there is additional structure that can be exploited to reduce computing time along with…
The variational determination of the two-fermion reduced density matrix is described for harmonically trapped, ultracold few-fermion systems in one dimension with equal spin populations. This is accomplished by formulating the problem as a…
We provide a general method for efficiently simulating time-dependent Hamiltonian dynamics on a circuit-model based quantum computer. Our approach is based on approximating the truncated Dyson series of the evolution operator, extending the…
In this work, we explore the application of multilinear algebra in reducing the order of multidimentional linear time-invariant (MLTI) systems. We use tensor Krylov subspace methods as key tools, which involve approximating the system…
We propose a multifidelity dimension reduction method to identify a low-dimensional structure present in many engineering models. The structure of interest arises when functions vary primarily on a low-dimensional subspace of the…
Gaussian processes are employed for non-parametric regression in a Bayesian setting. They generalize linear regression, embedding the inputs in a latent manifold inside an infinite-dimensional reproducing kernel Hilbert space. We can…