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Properly estimating correlations between objects at different spatial scales necessitates $\mathcal{O}(n^2)$ distance calculations. For this reason, most widely adopted packages for estimating correlations use clustering algorithms to…
Precise probabilistic forecasts are fundamental for energy risk management, and there is a wide range of both statistical and machine learning models for this purpose. Inherent to these probabilistic models is some form of uncertainty…
The paper deals with the density estimation on Rd under sup- norm loss. We provide with fully data-driven estimation procedure and establish for it so called sup-norm oracle inequality. The pro- posed estimator allows to take into account…
Coarse-scale surrogate models in the context of numerical homogenization of linear elliptic problems with arbitrary rough diffusion coefficients rely on the efficient solution of fine-scale sub-problems on local subdomains whose solutions…
We present a probabilistic deep learning methodology that enables the construction of predictive data-driven surrogates for stochastic systems. Leveraging recent advances in variational inference with implicit distributions, we put forth a…
Uncertainty estimation is important for deploying LLMs in high-stakes applications such as healthcare and finance, where hallucinations can appear fluent and plausible while being factually incorrect, making it difficult for users to judge…
Consider the problem when $X_1,X_2,..., X_n$ are distributed on a circle following an unknown distribution $F$ on $S^1$. In this article we have consider the absolute general set-up where the density can have local features such as…
In ultrasound shear wave elasticity (SWE) imaging, a number of algorithms exist for estimating the shear wave speed (SWS) from spatiotemporal displacement data. However, no method provides a well-calibrated and practical uncertainty metric,…
Parametric density estimation, for example as Gaussian distribution, is the base of the field of statistics. Machine learning requires inexpensive estimation of much more complex densities, and the basic approach is relatively costly…
Machine learning classification techniques have been used widely to recognize the feasible design domain and discover hidden patterns in engineering design. An accurate classification model needs a large dataset; however, generating a large…
Traditional nonparametric estimation methods often lead to a slow convergence rate in large dimensions and require unrealistically enormous sizes of datasets for reliable conclusions. We develop an approach based on partial derivatives,…
We present results of the investigations of the statistical properties of a joint density and velocity divergence probability distribution function (PDF) in the mildly non-linear regime. For that purpose we use both perturbation theory…
Given $iid$ observations from an unknown absolute continuous distribution defined on some domain $\Omega$, we propose a nonparametric method to learn a piecewise constant function to approximate the underlying probability density function.…
Numerical solutions of partial differential equations (PDEs) require expensive simulations, limiting their application in design optimization, model-based control, and large-scale inverse problems. Surrogate modeling techniques seek to…
Due to the growing adoption of deep neural networks in many fields of science and engineering, modeling and estimating their uncertainties has become of primary importance. Despite the growing literature about uncertainty quantification in…
This paper describes novel algorithms for the identification of (almost-)resonant behavior in scattering problems. Our methods, relying on rational approximation, aim at building surrogate models of what we call "field amplification",…
Uncertainty quantification is an important and challenging problem in deep learning. Previous methods rely on dropout layers which are not present in modern deep architectures or batch normalization which is sensitive to batch sizes. In…
The emphasis of this paper is to investigate the high-order approximation of a class of SPDEs with cubic nonlinearity driven by multiplicative noise with the help of the amplitude equations. The highlight of our work is that we improve the…
Most of the existing methods for estimating the local intrinsic dimension of a data distribution do not scale well to high-dimensional data. Many of them rely on a non-parametric nearest neighbors approach which suffers from the curse of…
In this paper, we develop convergence analysis of a modified line search method for objective functions whose value is computed with noise and whose gradient estimates are inexact and possibly random. The noise is assumed to be bounded in…