Related papers: Varying-Coefficient Fr\'echet Regression
We reexamine the classical linear regression model when the model is subject to two types of uncertainty: (i) some of covariates are either missing or completely inaccessible, and (ii) the variance of the measurement error is undetermined…
The semivarying coefficient models are widely used in the application of finance, economics, medical science and many other areas. The functional coefficients are commonly estimated by local smoothing methods, e.g. local linear estimator.…
Many scientific and industrial processes produce data that is best analysed as vectors of relative values, often called compositions or proportions. The Dirichlet distribution is a natural distribution to use for composition or proportion…
Variational inference is an alternative estimation technique for Bayesian models. Recent work shows that variational methods provide consistent estimation via efficient, deterministic algorithms. Other tools, such as model selection using…
We present a generative modeling approach based on the variational inference framework for likelihood-free simulation-based inference. The method leverages latent variables within variational autoencoders to efficiently estimate complex…
This paper presents a new variable selection approach integrated with Gaussian process (GP) regression. We consider a sparse projection of input variables and a general stationary covariance model that depends on the Euclidean distance…
A new approach of obtaining stratified random samples from statistically dependent random variables is described. The proposed method can be used to obtain samples from the input space of a computer forward model in estimating expectations…
For many important problems the quantity of interest is an unknown function of the parameters, which is a random vector with known statistics. Since the dependence of the output on this random vector is unknown, the challenge is to identify…
We propose a new method for multivariate response regression and covariance estimation when elements of the response vector are of mixed types, for example some continuous and some discrete. Our method is based on a model which assumes the…
Variational autoencoders often assume isotropic Gaussian priors and mean-field posteriors, hence do not exploit structure in scenarios where we may expect similarity or consistency across latent variables. Gaussian process variational…
We study the parameter estimation problem for a varying index coefficient model in high dimensions. Unlike the most existing works that iteratively estimate the parameters and link functions, based on the generalized Stein's identity, we…
Bayesian nonparametric regression under a rescaled Gaussian process prior offers smoothness-adaptive function estimation with near minimax-optimal error rates. Hierarchical extensions of this approach, equipped with stochastic variable…
Conformalized Quantile Regression (CQR) is a recently proposed method for constructing prediction intervals for a response $Y$ given covariates $X$, without making distributional assumptions. However, existing constructions of CQR can be…
With the wide adoption of machine learning techniques, requirements have evolved beyond sheer high performance, often requiring models to be trustworthy. A common approach to increase the trustworthiness of such systems is to allow them to…
This paper proposes a method for the automatic creation of variables (in the case of regression) that complement the information contained in the initial input vector. The method works as a pre-processing step in which the continuous values…
Flexible regression methods where interest centres on the way that the whole distribution of a response vector changes with covariates are very useful in some applications. A recently developed technique in this regard uses the…
This paper considers the quantile regression approach for partially linear spatial autoregressive models with possibly varying coefficients. B-spline is employed for the approximation of varying coefficients. The instrumental variable…
Model selection strategies have been routinely employed to determine a model for data analysis in statistics, and further study and inference then often proceed as though the selected model were the true model that were known a priori. This…
We study the problem of estimating time-varying coefficients in ordinary differential equations. Current theory only applies to the case when the associated state variables are observed without measurement errors as presented in…
In various applications with large spatial regions, the relationship between the response variable and the covariates is expected to exhibit complex spatial patterns. We propose a spatially clustered varying coefficient model, where the…