Related papers: Importance sampling based active learning for para…
In this paper we propose and discuss variance reduction techniques for the estimation of quantiles of the output of a complex model with random input parameters. These techniques are based on the use of a reduced model, such as a metamodel…
Understanding output variance is critical in modeling nonlinear dynamic systems, as it reflects the system's sensitivity to input variations and feature interactions. This work presents a methodology for dynamically determining relevance…
Dependency functions of dependent variables are relevant for i) performing uncertainty quantification and sensitivity analysis in presence of dependent variables and/or correlated variables, and ii) simulating random dependent variables. In…
The estimation of the probability of rare events is an important task in reliability and risk assessment. We consider failure events that are expressed in terms of a limit state function, which depends on the solution of a partial…
We demonstrate an adaptive sampling approach for computing the probability of a rare event for a set of three-dimensional airplane geometries under various flight conditions. We develop a fully automated method to generate parameterized…
The topic of deep learning has seen a surge of interest in recent years both within and outside of the field of Statistics. Deep models leverage both nonlinearity and interaction effects to provide superior predictions in many cases when…
This paper is concerned with the robust tracking control of linear uncertain systems, whose unknown system parameters and disturbances are bounded within ellipsoidal sets. We propose an adaptive robust control that can actively learn the…
The paper deals with asymptotic properties of the adaptive procedure proposed in the author paper, 2007, for estimating a unknown nonparametric regression. We prove that this procedure is asymptotically efficient for a quadratic risk, i.e.…
Variational inference approximates the posterior distribution of a probabilistic model with a parameterized density by maximizing a lower bound for the model evidence. Modern solutions fit a flexible approximation with stochastic gradient…
We introduce an adaptive sampling method for the Deep Ritz method aimed at solving partial differential equations (PDEs). Two deep neural networks are used. One network is employed to approximate the solution of PDEs, while the other one is…
Machine learning optimization often depends on stochastic gradient descent, where the precision of gradient estimation is vital for model performance. Gradients are calculated from mini-batches formed by uniformly selecting data samples…
This paper improves upon existing data pruning methods for image classification by introducing a novel pruning metric and pruning procedure based on importance sampling. The proposed pruning metric explicitly accounts for data separability,…
Dynamic analysis of structures subjected to earthquake excitation is a time-consuming process, particularly in the case of extremely small time step required, or in the presence of high geometric and material nonlinearity. Performing…
Among various supervised deep metric learning methods proxy-based approaches have achieved high retrieval accuracies. Proxies, which are class-representative points in an embedding space, receive updates based on proxy-sample similarities…
Lower-dimensional subspaces that impact estimates of uncertainty are often described by Linear combinations of input variables, leading to active variables. This paper extends the derivative-based active subspace methods and…
During recent years, active learning has evolved into a popular paradigm for utilizing user's feedback to improve accuracy of learning algorithms. Active learning works by selecting the most informative sample among unlabeled data and…
Many cases exist in which a black-box function $f$ with high evaluation cost depends on two types of variables $\bm x$ and $\bm w$, where $\bm x$ is a controllable \emph{design} variable and $\bm w$ are uncontrollable \emph{environmental}…
In safety-critical deep learning applications, robustness measures the ability of neural models that handle imperceptible perturbations in input data, which may lead to potential safety hazards. Existing pre-deployment robustness assessment…
Supervised deep learning requires a large amount of training samples with annotations (e.g. label class for classification task, pixel- or voxel-wised label map for segmentation tasks), which are expensive and time-consuming to obtain.…
Importance sampling is a variance reduction technique for efficient estimation of rare-event probabilities by Monte Carlo. In standard importance sampling schemes, the system is simulated using an a priori fixed change of measure suggested…