Search Results for author:
Found 10 papers, 6 papers with code
Self-reinforced polynomial approximation methods for concentrated probability densities
We approximate the complicated target density by a composition of self-reinforced KR rearrangements, in which previously constructed KR rearrangements -- based on the same approximation ansatz -- are used to precondition the density approximation problem for building each new KR rearrangement.
A weighted subspace exponential kernel for support tensor machines
High-dimensional data in the form of tensors are challenging for kernel classification methods.
Deep importance sampling using tensor trains with application to a priori and a posteriori rare event estimation
We approximate the optimal importance distribution in a general importance sampling problem as the pushforward of a reference distribution under a composition of order-preserving transformations, in which each transformation is formed by a squared tensor-train decomposition.
Scalable conditional deep inverse Rosenblatt transports using tensor-trains and gradient-based dimension reduction
We present a novel offline-online method to mitigate the computational burden of the characterization of posterior random variables in statistical learning.
Deep composition of tensor-trains using squared inverse Rosenblatt transports
The recent surge of transport maps offers a mathematical foundation and new insights for tackling this challenge by coupling intractable random variables with tractable reference random variables.
Efficient Structure-preserving Support Tensor Train Machine
An increasing amount of collected data are high-dimensional multi-way arrays (tensors), and it is crucial for efficient learning algorithms to exploit this tensorial structure as much as possible.
Tensor Decomposition Methods for High-dimensional Hamilton-Jacobi-Bellman Equations
For nonlinear dynamics, the effectiveness of the high-dimensional control synthesis method is assessed in the optimal feedback stabilization of the Allen-Cahn and Fokker-Planck equations with a hundred of variables.
Optimization and Control Numerical Analysis Numerical Analysis
Kriging in Tensor Train data format
Combination of low-tensor rank techniques and the Fast Fourier transform (FFT) based methods had turned out to be prominent in accelerating various statistical operations such as Kriging, computing conditional covariance, geostatistical optimal design, and others.
Computation Numerical Analysis Methodology
Parallel cross interpolation for high-precision calculation of high-dimensional integrals
We propose a parallel version of the cross interpolation algorithm and apply it to calculate high-dimensional integrals motivated by Ising model in quantum physics.
Numerical Analysis 15A69, 15A23, 65D05, 65F99
Approximation and sampling of multivariate probability distributions in the tensor train decomposition
We find that the importance-weight corrected quasi-Monte Carlo quadrature performs best in all computed examples, and is orders-of-magnitude more efficient than DRAM across a wide range of approximation accuracies and sample sizes.
Numerical Analysis Probability Statistics Theory Statistics Theory 65D15, 65D32, 65C05, 65C40, 65C60, 62F15, 15A69, 15A23
