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The local volatility model is a widely used for pricing and hedging financial derivatives. While its main appeal is its capability of reproducing any given surface of observed option prices---it provides a perfect fit---the essential…

We propose an extension of the non-homogeneous Gaussian regression (NGR) model by Gneiting et al. (2005) that yields locally calibrated probabilistic forecasts of tem- perature, based on the output of an ensemble prediction system (EPS).…

Folding uncertainty in theoretical models into Bayesian parameter estimation is necessary in order to make reliable inferences. A general means of achieving this is by marginalizing over model uncertainty using a prior distribution…

In this work we introduce a generalized flavor, in the sense of generalized Kohn-Sham density functional theory (gKS-DFT), of the recently derived local potential functional embedding theory (LPFET) [J. Chem. Theory Comput. 2025, 21, 20,…

Local polynomial regression struggles with several challenges when dealing with sparse data. The difficulty in capturing local features of the underlying function can lead to a potential misrepresentation of the true relationship.…

We study the problem of estimating the spectral density of a centered stationary Gaussian time series under local differential privacy constraints. Specifically, we propose new interactive privacy mechanisms for three tasks: recovering a…

Non-parametric reconstruction methods, such as Gaussian process (GP) regression, provide a model-independent way of estimating an underlying function and its uncertainty from noisy data. We demonstrate how GP-reconstruction can be used as a…

We present an extension of reverse engineered Kohn-Sham potentials from a density matrix renormalization group calculation towards the construction of a density functional theory functional via deep learning. Instead of applying machine…

To infer a function value on a specific point $x$, it is essential to assign higher weights to the points closer to $x$, which is called local polynomial / multivariable regression. In many practical cases, a limited sample size may ruin…

Machine learning (ML) techniques have recently gained significant attention for solving compliance minimization (CM) problems. However, these methods typically provide poor feature boundaries, are very expensive, and lack a systematic…

Spatial-temporal Gaussian process regression is a popular method for spatial-temporal data modeling. Its state-of-art implementation is based on the state-space model realization of the spatial-temporal Gaussian process and its…

Development of the electronic kinetic-energy density functional is a subject of major interest in theoretical physics and chemistry. In this work, the nonlocal kinetic-energy functional is developed in terms of the response function for the…

Machine learning (ML) of kinetic energy functionals (KEF) for orbital-free density functional theory (OF-DFT) holds the promise of addressing an important bottleneck in large-scale ab initio materials modeling where sufficiently accurate…

Understanding sub-cellular protein localisation is an essential component to analyse context specific protein function. Recent advances in quantitative mass-spectrometry (MS) have led to high resolution mapping of thousands of proteins to…

We present a Gaussian regression method for time series with missing data and stationary residuals of unknown power spectral density (PSD). The missing data are efficiently estimated by their conditional expectation as in universal Kriging,…

Subspace-valued functions arise in a wide range of problems, including parametric reduced order modeling (PROM). In PROM, each parameter point can be associated with a subspace, which is used for Petrov-Galerkin projections of large system…

Density functional theory (DFT) can run into serious difficulties with localized states in elements such as transition metals with occupied-d states and oxygen. In contrast, Hartree-Fock (HF) method can be a better approach for such…

The Gaussian process state-space model (GPSSM) has garnered considerable attention over the past decade. However, the standard GP with a preliminary kernel, such as the squared exponential kernel or Mat\'{e}rn kernel, that is commonly used…

The Gaussian Process with a deep kernel is an extension of the classic GP regression model and this extended model usually constructs a new kernel function by deploying deep learning techniques like long short-term memory networks. A…

Despite a large corpus of recent work on scaling up Gaussian processes, a stubborn trade-off between computational speed, prediction and uncertainty quantification accuracy, and customizability persists. This is because the vast majority of…