Related papers: Sobol Tensor Trains for Global Sensitivity Analysi…
Variance-based Sobol' sensitivity is one of the most well-known measures in global sensitivity analysis (GSA). However, uncertainties with certain distributions, such as highly skewed distributions or those with a heavy tail, cannot be…
We propose new algorithms for singular value decomposition (SVD) of very large-scale matrices based on a low-rank tensor approximation technique called the tensor train (TT) format. The proposed algorithms can compute several dominant…
The tensor-train (TT) format is a data-sparse tensor representation commonly used in high dimensional data approximations. In order to represent data with interpretability in data science, researchers develop data-centric skeletonized low…
Given-data methods for variance-based sensitivity analysis have significantly advanced the feasibility of Sobol' index computation for computationally expensive models and models with many inputs. However, the limitations of existing…
Bayesian Additive Regression Trees (BART) are non-parametric models that can capture complex exogenous variable effects. In any regression problem, it is often of interest to learn which variables are most active. Variable activity in BART…
The estimation of variance-based importance measures (called Sobol' indices) of the input variables of a numerical model can require a large number of model evaluations. It turns to be unacceptable for high-dimensional model involving a…
One-dimensional Poincare inequalities are used in Global Sensitivity Analysis (GSA) to provide derivative-based upper bounds and approximations of Sobol indices. We add new perspectives by investigating weighted Poincare inequalities. Our…
The variance-based method of global sensitivity indices based on Sobol sensitivity indices became very popular among practitioners due to its easiness of interpretation. For complex practical problems computation of Sobol indices generally…
The hierarchically orthogonal functional decomposition of any measurable function f of a random vector X=(X_1,...,X_p) consists in decomposing f(X) into a sum of increasing dimension functions depending only on a subvector of X. Even when…
We investigate the application of tensor-train (TT) algorithms to multigroup thermal radiation transport (i.e., photon radiation transport). The TT framework enables simulations at discretizations that might otherwise be computationally…
This paper addresses sensitivity analysis for dynamic models, linking dependent inputs to observed outputs. The usual method to estimate Sobol indices are based on the independence of input variables. We present a method to overpass this…
The era of exascale computing opens new venues for innovations and discoveries in many scientific, engineering, and commercial fields. However, with the exaflops also come the extra-large high-dimensional data generated by high-performance…
Tensor networks have in recent years emerged as the powerful tools for solving the large-scale optimization problems. One of the most popular tensor network is tensor train (TT) decomposition that acts as the building blocks for the…
In the context of sensitivity analysis of complex phenomena in presence of uncertainty, we motivate and precise the idea of orienting the analysis towards a critical domain of the studied phenomenon. We make a brief history of related…
In recent years, the application of tensors has become more widespread in fields that involve data analytics and numerical computation. Due to the explosive growth of data, low-rank tensor decompositions have become a powerful tool to…
Global sensitivity analysis aims at quantifying respective effects of input random variables (or combinations thereof) onto variance of a physical or mathematical model response. Among the abundant literature on sensitivity measures, Sobol'…
Recently, a tensor-on-tensor (ToT) regression model has been proposed to generalize tensor recovery, encompassing scenarios like scalar-on-tensor regression and tensor-on-vector regression. However, the exponential growth in tensor…
The tensor train (TT) rank has received increasing attention in tensor completion due to its ability to capture the global correlation of high-order tensors ($\textrm{order} >3$). For third order visual data, direct TT rank minimization has…
The tensor-train (TT) decomposition is widely used to compress large tensors into a more compact form by exploiting their inherent data structures. A fundamental approach for constructing the TT format is the well-known TT-SVD method, which…
The tensor-train (TT) format is a data-sparse tensor representation commonly used in high dimensional function approximations arising from computational and data sciences. Various sequential and parallel TT decomposition algorithms have…