Related papers: On adaptive estimation of linear functionals
In this paper we consider the approximation of a function by its interpolating multilinear spline and the approximation of its derivatives by the derivatives of the corresponding spline. We derive formulas for the uniform approximation…
We consider high-dimensional estimation problems where the number of parameters diverges with the sample size. General conditions are established for consistency, uniqueness, and asymptotic normality in both unpenalized and penalized…
In this paper we will consider the estimation of a monotone regression (or density) function in a fixed point by the least squares (Grenander) estimator. We will show that this estimator is fully adaptive, in the sense that the attained…
In this article, we extend predictor envelope models to settings with multivariate outcomes and multiple, functional predictors. We propose a two-step estimation strategy, which first projects the function onto a finite-dimensional…
How can one meaningfully make a measurement, if the meter does not conform to any standard and its scale expands or shrinks depending on what is measured? In the present work it is argued that current evaluation practices for…
Big data is ubiquitous in practices, and it has also led to heavy computation burden. To reduce the calculation cost and ensure the effectiveness of parameter estimators, an optimal subset sampling method is proposed to estimate the…
This paper explores learning emulators for parameter estimation with uncertainty estimation of high-dimensional dynamical systems. We assume access to a computationally complex simulator that inputs a candidate parameter and outputs a…
Model complexity is an important factor to consider when selecting among graphical models. When all variables are observed, the complexity of a model can be measured by its standard dimension, i.e. the number of independent parameters. When…
When predicting scalar responses in the situation where the explanatory variables are functions, it is sometimes the case that some functional variables are related to responses linearly while other variables have more complicated…
Motivated by a recently proposed error estimator for the transfer function of the reduced-order model of a given linear dynamical system, we further develop more theoretical results in this work. Furthermore, we propose several variants of…
We consider a general nonparametric regression model called the compound model. It includes, as special cases, sparse additive regression and nonparametric (or linear) regression with many covariates but possibly a small number of relevant…
A goodness-of-fit test for the fitting of a parametric model to data obtained from a detector with finite resolution and limited acceptance is proposed. The parameters of the model are found by minimization of a statistic that is used for…
Model complexity is a fundamental problem in deep learning. In this paper we conduct a systematic overview of the latest studies on model complexity in deep learning. Model complexity of deep learning can be categorized into expressive…
In the need for low assumption inferential methods in infinite-dimensional settings, Bayesian adaptive estimation via a prior distribution that does not depend on the regularity of the function to be estimated nor on the sample size is…
We consider two classes of computations which admit taking linear combinations of execution runs: probabilistic sampling and generalized animation. We argue that the task of program learning should be more tractable for these architectures…
We investigate three related and important problems connected to machine learning: approximating a submodular function everywhere, learning a submodular function (in a PAC-like setting [53]), and constrained minimization of submodular…
We provide a unified approach to MM-estimation with auxiliary scale for balanced linear models with structured covariance matrices. This approach leads to estimators that are highly robust against outliers and highly efficient for normal…
We propose a framework for computing, optimizing and integrating with respect to a smooth marginal likelihood in statistical models that involve high-dimensional parameters/latent variables and continuous low-dimensional hyperparameters.…
We present a general framework for studying regularized estimators; such estimators are pervasive in estimation problems wherein "plug-in" type estimators are either ill-defined or ill-behaved. Within this framework, we derive, under…
We obtain approximation results for general positive linear operators satisfying mild conditions, when acting on discontinuous functions and absolutely continuous functions having discontinuous derivatives. The upper bounds, given in terms…