Related papers: Random Sampling High Dimensional Model Representat…
Sparse identification of differential equations aims to compute the analytic expressions from the observed data explicitly. However, there exist two primary challenges. Firstly, it exhibits sensitivity to the noise in the observed data,…
Dimensionality reduction (DR) is an important technique for data exploration and knowledge discovery. However, most of the main DR methods are either linear (e.g., PCA), do not provide an explicit mapping between the original data and its…
Gaussian processes (GP) are a widely used model for regression problems in supervised machine learning. Implementation of GP regression typically requires $O(n^3)$ logic gates. We show that the quantum linear systems algorithm [Harrow et…
Single-image super-resolution (SISR) typically focuses on restoring various degraded low-resolution (LR) images to a single high-resolution (HR) image. However, during SISR tasks, it is often challenging for models to simultaneously…
Making an accurate prediction of an unknown system only from a short-term time series is difficult due to the lack of sufficient information, especially in a multi-step-ahead manner. However, a high-dimensional short-term time series…
Three-Dimensional Gaussian Splatting (3DGS) has shown substantial promise in the field of computer vision, but remains unexplored in the field of magnetic resonance imaging (MRI). This study explores its potential for the reconstruction of…
Prediction and explanation are key objects in supervised machine learning, where predictive models are known as black boxes and explanatory models are known as glass boxes. Explanation provides the necessary and sufficient information to…
Gaussian processes (GPs) provide a probabilistic nonparametric representation of functions in regression, classification, and other problems. Unfortunately, exact learning with GPs is intractable for large datasets. A variety of approximate…
We present a new method for estimating multivariate, second-order stationary Gaussian Random Field (GRF) models based on the Sparse Precision matrix Selection (SPS) algorithm, proposed by Davanloo et al. (2015) for estimating scalar GRF…
Gaussian process regression is a machine learning approach which has been shown its power for estimation of unknown functions. However, Gaussian processes suffer from high computational complexity, as in a basic form they scale cubically…
Despite the widespread utilization of Gaussian process models for versatile nonparametric modeling, they exhibit limitations in effectively capturing abrupt changes in function smoothness and accommodating relationships with heteroscedastic…
A practical approach to evaluate performance of a Gaussian process regression models (GPR) for irregularly sampled sparse time-series is introduced. The approach entails construction of a secondary autoregressive model using the fine scale…
High-dimensional linear regression model is the most popular statistical model for high-dimensional data, but it is quite a challenging task to achieve a sparse set of regression coefficients. In this paper, we propose a simple heuristic…
The extraction of parton distribution functions (PDFs) from experimental or lattice QCD data is an ill-posed inverse problem, where regularization strongly impacts both systematic uncertainties and the reliability of the results. We study a…
Gaussian process (GP) models form a core part of probabilistic machine learning. Considerable research effort has been made into attacking three issues with GP models: how to compute efficiently when the number of data is large; how to…
We implemented a geometry optimizer based on Gaussian process regression (GPR) to find minimum structures on potential energy surfaces. We tested both a two times differentiable form of the Mat\'{e}rn kernel and the squared exponential…
Lost circulation remains a major and costly challenge in drilling operations, often resulting in wellbore instability, stuck pipe, and extended non-productive time. Accurate prediction of fluid loss is therefore essential for improving…
Accurate human motion prediction with well-calibrated uncertainty is critical for safe human-robot collaboration (HRC), where robots must anticipate and react to human movements in real time. We propose a structured multitask variational…
Gaussian processes are probabilistic models that are commonly used as functional priors in machine learning. Due to their probabilistic nature, they can be used to capture the prior information on the statistics of noise, smoothness of the…
Unsupervised real world super resolution (USR) aims to restore high-resolution (HR) images given low-resolution (LR) inputs, and its difficulty stems from the absence of paired dataset. One of the most common approaches is synthesizing…