Related papers: Interpolation error of misspecified Gaussian proce…
While extensive work has been done to correct for biases due to measurement error in scalar-valued covariates prone to errors in generalized linear regression models, limited work has been done to address biases associated with functional…
To compare different forecasting methods on demand series we require an error measure. Many error measures have been proposed, but when demand is intermittent some become inapplicable, some give counter-intuitive results, and there is no…
For pulsar projects it is often necessary to predict the pulse phase in advance, for example, when preparing for new observations. Interpolation of the pulse phase between existing measurements is also often required, for example, when…
We report a deep generative model for regression tasks in materials informatics. The model is introduced as a component of a data imputer, and predicts more than 20 diverse experimental properties of organic molecules. The imputer is…
Covariance matrix estimation concerns the problem of estimating the covariance matrix from a collection of samples, which is of extreme importance in many applications. Classical results have shown that $O(n)$ samples are sufficient to…
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 paper we consider interpolation problem connected with series by integer shifts of Gaussians. Known approaches for these problems met numerical difficulties. Due to it another method is considered based on finite-rank approximations…
For the quadratic Lagrange interpolation function, an algorithm is proposed to provide explicit and verified bound for the interpolation error constant that appears in the interpolation error estimation. The upper bound for the…
This paper investigates multistep prediction errors for non-stationary autoregressive processes with both model order and true parameters unknown. We give asymptotic expressions for the multistep mean squared prediction errors and…
In this work, we investigate Gaussian process regression used to recover a function based on noisy observations. We derive upper and lower error bounds for Gaussian process regression with possibly misspecified correlation functions. The…
In the 1990's exponential-type error bounds appeared in the theory of radial basis functions. This kind of error bounds is very powerful. However it only measures the difference between the approximant and approximand. Mathematicians and…
A multivariate errors-in-variables (EIV) model with an intercept term, and a polynomial EIV model are considered. Focus is made on a structural homoskedastic case, where vectors of covariates are i.i.d. and measurement errors are i.i.d. as…
In this work we consider a model problem of deep neural learning, namely the learning of a given function when it is assumed that we have access to its point values on a finite set of points. The deep neural network interpolant is the the…
In this paper, interpolation by scaled multi-integer translates of Gaussian kernels is studied. The main result establishes $L_p$ Sobolev error estimates and shows that the error is controlled by the $L_p$ multiplier norm of a Fourier…
This paper aims at analyzing the regularization effect that data augmentation induces on supervised regression methods in the proportional regime, where the number of covariates grows proportionally to the number of samples. We provide a…
Anomalous diffusion, process in which the mean-squared displacement of system states is a non-linear function of time, is usually identified in real stochastic processes by comparing experimental and theoretical displacements at relatively…
Standard interpolation techniques are implicitly based on the assumption that the signal lies on a homogeneous domain. In this letter, the proposed interpolation method instead exploits prior information about domain inhomogeneity,…
This paper presents an efficient variational inference framework for deriving a family of structured gaussian process regression network (SGPRN) models. The key idea is to incorporate auxiliary inducing variables in latent functions and…
Image interpolation is a special case of image super-resolution, where the low-resolution image is directly down-sampled from its high-resolution counterpart without blurring and noise. Therefore, assumptions adopted in super-resolution…
Large-scale Gaussian process inference has long faced practical challenges due to time and space complexity that is superlinear in dataset size. While sparse variational Gaussian process models are capable of learning from large-scale data,…