Related papers: More efficient approximation of smoothing splines …
A significant hurdle for analyzing large sample data is the lack of effective statistical computing and inference methods. An emerging powerful approach for analyzing large sample data is subsampling, by which one takes a random subsample…
We present a static analysis for discovering differentiable or more generally smooth parts of a given probabilistic program, and show how the analysis can be used to improve the pathwise gradient estimator, one of the most popular methods…
We study the computational complexity of approximately computing the partition function of a spin system. Techniques based on standard counting-to-sampling reductions yield $\tilde{O}(n^2)$-time algorithms, where $n$ is the size of the…
In this paper, we focus on the variable selection techniques for a class of semiparametric spatial regression models which allow one to study the effects of explanatory variables in the presence of the spatial information. The spatial…
We consider methods for finding high-precision approximations to simple zeros of smooth functions. As an application, we give fast methods for evaluating the elementary functions log(x), exp(x), sin(x) etc. to high precision. For example,…
Currently, the high-precision estimation of nonlinear parameters such as Gini indices, low-income proportions or other measures of inequality is particularly crucial. In the present paper, we propose a general class of estimators for such…
In countries where population census data are limited, generating accurate subnational estimates of health and demographic indicators is challenging. Existing model-based geostatistical methods leverage covariate information and spatial…
We present a dimension-incremental algorithm for the nonlinear approximation of high-dimensional functions in an arbitrary bounded orthonormal product basis. Our goal is to detect a suitable truncation of the basis expansion of the…
Model-assisted estimation with complex survey data is an important practical problem in survey sampling. When there are many auxiliary variables, selecting significant variables associated with the study variable would be necessary to…
We propose to smooth the entire objective function, rather than only the check function, in a linear quantile regression context. Not only does the resulting smoothed quantile regression estimator yield a lower mean squared error and a more…
In Astronomy, Survival Analysis and Epidemiology, among many other fields, doubly truncated data often appear. Double truncation generally induces a sampling bias, so ordinary estimators may be inconsistent. In this paper, smoothing spline…
Estimating effects of spatially structured exposures is complicated by unmeasured spatial confounders, which undermine identifiability in spatial linear regression models unless structural assumptions are imposed. We develop a general…
A new efficient orthogonalization of the B-spline basis is proposed and contrasted with some previous orthogonalized methods. The resulting orthogonal basis of splines is best visualized as a net of functions rather than a sequence of them.…
A variance reduction technique in nonparametric smoothing is proposed: at each point of estimation, form a linear combination of a preliminary estimator evaluated at nearby points with the coefficients specified so that the asymptotic bias…
We consider stochastic optimization problems which use observed data to estimate essential characteristics of the random quantities involved. Sample average approximation (SAA) or empirical (plug-in) estimation are very popular ways to use…
We present a framework to train a structured prediction model by performing smoothing on the inference algorithm it builds upon. Smoothing overcomes the non-smoothness inherent to the maximum margin structured prediction objective, and…
In this paper, we explore statistical versus computational trade-off to address a basic question in the application of a distributed algorithm: what is the minimal computational cost in obtaining statistical optimality? In smoothing spline…
In this paper, we analyze several methods for approximating gradients of noisy functions using only function values. These methods include finite differences, linear interpolation, Gaussian smoothing and smoothing on a sphere. The methods…
In implementations of the functional data methods, the effect of the initial choice of an orthonormal basis has not gained much attention in the past. Typically, several standard bases such as Fourier, wavelets, splines, etc. are considered…
This paper demonstrates that the space of piecewise smooth functions can be well approximated by the space of functions defined by a set of simple (non-linear) operations on smooth uniform splines. The examples include bivariate functions…