Related papers: Local Function Complexity for Active Learning via …
Frequency response function (FRF) estimation is a classical subject in system identification. In the past two decades, there have been remarkable advances in developing local methods for this subject, e.g., the local polynomial method,…
Locally weighted regression was created as a nonparametric learning method that is computationally efficient, can learn from very large amounts of data and add data incrementally. An interesting feature of locally weighted regression is…
In recent years, many types of machine learning potentials (MLPs) have been introduced, which are able to represent high-dimensional potential-energy surfaces (PES) with close to first-principles accuracy. Most current MLPs rely on atomic…
Hierarchical computational methods for multiscale mechanics such as the FE$^2$ and FE-FFT methods are generally accompanied by high computational costs. Data-driven approaches are able to speed the process up significantly by enabling to…
We consider the problem of learning causal structures in sparse high-dimensional settings that may be subject to the presence of (potentially many) unmeasured confounders, as well as selection bias. Based on the structure found in common…
Gaussian process regression (GPR) is a fundamental model used in machine learning. Owing to its accurate prediction with uncertainty and versatility in handling various data structures via kernels, GPR has been successfully used in various…
We study active learning (AL) based on Gaussian Processes (GPs) for efficiently enumerating all of the local minimum solutions of a black-box function. This problem is challenging due to the fact that local solutions are characterized by…
In modeling multivariate time series, it is important to allow time-varying smoothness in the mean and covariance process. In particular, there may be certain time intervals exhibiting rapid changes and others in which changes are slow. If…
Local Polynomial Regression (LPR) is a widely used nonparametric method for modeling complex relationships due to its flexibility and simplicity. It estimates a regression function by fitting low-degree polynomials to localized subsets of…
In a global numerical weather prediction (NWP) modeling framework we study the implementation of Gaussian uncertainty of individual particles into the assimilation step of a localized adaptive particle filter (LAPF). We obtain a local…
A method to reconstruct fields, source strengths and physical parameters based on Gaussian process regression is presented for the case where data are known to fulfill a given linear differential equation with localized sources. The…
Digital technologies can be used to gather accurate information about the behavior of structural components for improving systems design, as well as for enabling advanced Structural Health Monitoring strategies. New avenues for achieving…
We introduce a family of local inhomogeneous mark-weighted summary statistics, of order two and higher, for general marked point processes. Depending on how the involved weight function is specified, these summary statistics capture…
The analysis of complex computer simulations, often involving functional data, presents unique statistical challenges. Conventional regression methods, such as function-on-function regression, typically associate functional outcomes with…
High-dimensional, heterogeneous data with complex feature interactions pose significant challenges for traditional predictive modeling approaches. While Projection to Latent Structures (PLS) remains a popular technique, it struggles to…
In this study, we focus on a generalized nonparametric scalar-on-function regression model for heterogeneously distributed and strongly mixing data. We provide almost complete convergence rates for the local linear estimator of the…
Constructing a classical potential suited to simulate a given atomic system is a remarkably difficult task. This chapter presents a framework under which this problem can be tackled, based on the Bayesian construction of nonparametric force…
The increased demand for online prediction and the growing availability of large data sets drives the need for computationally efficient models. While exact Gaussian process regression shows various favorable theoretical properties…
Gaussian processes are flexible function approximators, with inductive biases controlled by a covariance kernel. Learning the kernel is the key to representation learning and strong predictive performance. In this paper, we develop…
This paper introduces a new approach to inferring the second order properties of a multivariate log Gaussian Cox process (LGCP) with a complex intensity function. We assume a semi-parametric model for the multivariate intensity function…