Related papers: Interpolation and linear prediction of data -- thr…
One way to investigate the precision of estimates likely to result from planned experiments and planned epidemiological studies is to simulate a large number of possible outcomes and analyse the sets of possible results. This appears to be…
Effective verification and validation techniques for modern scientific machine learning workflows are challenging to devise. Statistical methods are abundant and easily deployed, but often rely on speculative assumptions about the data and…
In the era of big data, we first need to manage the data, which requires us to find missing data or predict the trend, so we need operations including interpolation and data fitting. Interpolation is a process to discover deducing new data…
Video frame interpolation task has recently become more and more prevalent in the computer vision field. At present, a number of researches based on deep learning have achieved great success. Most of them are either based on optical flow…
Ice cores record crucial information about past climate. However, before ice core data can have scientific value, the chronology must be inferred by estimating the age as a function of depth. Under certain conditions, chemicals locked in…
Computing the expectation of kernel functions is a ubiquitous task in machine learning, with applications from classical support vector machines to exploiting kernel embeddings of distributions in probabilistic modeling, statistical…
Kernel-based methods offer a powerful and flexible mathematical framework for addressing histopolation problems. In histopolation, the available input data does not consist of pointwise function samples but of averages taken over intervals…
This article advocates the use of conformal prediction (CP) methods for Gaussian process (GP) interpolation to enhance the calibration of prediction intervals. We begin by illustrating that using a GP model with parameters selected by…
The use of regression analysis for processing experimental data is fraught with certain difficulties, which, when models are constructed, are associated with assumptions, and there is a normal law of error distribution and variables are…
Ray tracing is increasingly utilized in wireless system simulations to estimate channel paths. In large-scale simulations with complex environments, ray tracing at high resolution can be computationally demanding. To reduce the computation,…
Machine learning models can represent climate processes that are nonlocal in horizontal space, height, and time, often by combining information across these dimensions in highly nonlinear ways. While this can improve predictive skill, it…
In applications of climate information, coarse-resolution climate projections commonly need to be downscaled to a finer grid. One challenge of this requirement is the modeling of sub-grid variability and the spatial and temporal dependence…
Collecting time series data spatially distributed in many locations is often important for analyzing climate change and its impacts on ecosystems. However, comprehensive spatial data collection is not always feasible, requiring us to…
Many dynamical systems, from quantum many-body systems to evolving populations to financial markets, are described by stochastic processes. Parameters characterizing such processes can often be inferred using information integrated over…
When providing the boundary conditions for hydrological flood models and estimating the associated risk, interpolating precipitation at very high temporal resolutions (e.g. 5 minutes) is essential not to miss the cause of flooding in local…
Temporal interpolation often plays a crucial role to learn meaningful representations in dynamic scenes. In this paper, we propose a novel method to train spatiotemporal neural radiance fields of dynamic scenes based on temporal…
Gaussian processes (GP) and Kriging are widely used in traditional spatio-temporal mod-elling and prediction. These techniques typically presuppose that the data are observed from a stationary GP with parametric covariance structure.…
A fundamental building block for supporting better utilization of radio spectrum involves predicting the impact that an emitter will have at different geographic locations. To this end, fixed sensors can be deployed to spatially sample the…
In this paper we investigate the approximation properties of kernel interpolants on manifolds. The kernels we consider will be obtained by the restriction of positive definite kernels on $\R^d$, such as radial basis functions (RBFs), to a…
Many machine/deep learning artificial neural networks are trained to simply be interpolation functions that map input variables to output values interpolated from the training data in a linear/nonlinear fashion. Even when the input/output…