Related papers: Bayesian bandwidth estimation for a nonparametric …
In this paper several related estimation problems are addressed from a Bayesian point of view and optimal estimators are obtained for each of them when some natural loss functions are considered. Namely, we are interested in estimating a…
The problem of nonparametric functional data classification and bandwidth selection is considered when the response variable, also called the class label, might be missing but not at random (MNAR). This setup is broadly acknowledged to be…
We introduce semiparametric Bayesian networks that combine parametric and nonparametric conditional probability distributions. Their aim is to incorporate the advantages of both components: the bounded complexity of parametric models and…
Non-conservative uncertainty bounds are key for both assessing an estimation algorithm's accuracy and in view of downstream tasks, such as its deployment in safety-critical contexts. In this paper, we derive a tight, non-asymptotic…
We study the Bayesian density estimation of data living in the offset of an unknown submanifold of the Euclidean space. In this perspective, we introduce a new notion of anisotropic H\"older for the underlying density and obtain posterior…
There is increasing interest in the problem of nonparametric regression with high-dimensional predictors. When the number of predictors $D$ is large, one encounters a daunting problem in attempting to estimate a $D$-dimensional surface…
Providing non-conservative uncertainty quantification for function estimates derived from noisy observations remains a fundamental challenge in statistical machine learning, particularly for applications in safety-critical domains. In this…
Dyadic data is often encountered when quantities of interest are associated with the edges of a network. As such it plays an important role in statistics, econometrics and many other data science disciplines. We consider the problem of…
Kernel Estimation is one of the most widely used estimation methods in non-parametric Statistics, having a wide-range of applications, including spot volatility estimation of stochastic processes. The selection of bandwidth and kernel…
We consider a sparse linear regression model with unknown symmetric error under the high-dimensional setting. The true error distribution is assumed to belong to the locally $\beta$-H\"{o}lder class with an exponentially decreasing tail,…
This paper introduces the kernel mixture network, a new method for nonparametric estimation of conditional probability densities using neural networks. We model arbitrarily complex conditional densities as linear combinations of a family of…
This paper concerns the estimation of the regression function at a given point in nonparametric heteroscedastic models with Gaussian noise or with noise having unknown distribution. In the two cases an asymptotically efficient kernel…
We are interested in the nonparametric estimation of the probability density of price returns, using the kernel approach. The output of the method heavily relies on the selection of a bandwidth parameter. Many selection methods have been…
Deep learning methods continue to have a decided impact on machine learning, both in theory and in practice. Statistical theoretical developments have been mostly concerned with approximability or rates of estimation when recovering…
While deep neural networks are highly performant and successful in a wide range of real-world problems, estimating their predictive uncertainty remains a challenging task. To address this challenge, we propose and implement a loss function…
Consistent weighted least square estimators are proposed for a wide class of nonparametric regression models with random regression function, where this real-valued random function of $k$ arguments is assumed to be continuous with…
Most machine learning methods require tuning of hyper-parameters. For kernel ridge regression with the Gaussian kernel, the hyper-parameter is the bandwidth. The bandwidth specifies the length scale of the kernel and has to be carefully…
Tensor regression methods have been widely used to predict a scalar response from covariates in the form of a multiway array. In many applications, the regions of tensor covariates used for prediction are often spatially connected with…
We present a new Bayesian approach to model-robust linear regression that leads to uncertainty estimates with the same robustness properties as the Huber--White sandwich estimator. The sandwich estimator is known to provide asymptotically…
Nonlinear function estimation is core to modern machine learning applications. In this paper, to perform nonlinear function estimation, we reduce a nonlinear inverse problem to a linear one using a polynomial kernel expansion. These kernels…