Related papers: Optimal Subsampling Design for Polynomial Regressi…
In a seminal paper \cite{studden1968} characterized $c$-optimal designs in regression models, where the regression functions form a Chebyshev system. He used these results to determine the optimal design for estimating the individual…
This paper studies optimal designs for linear regression models with correlated effects for single responses. We introduce the concept of rhombic design to reduce the computational complexity and find a semi-algebraic description for the…
We propose a method called ideal regression for approximating an arbitrary system of polynomial equations by a system of a particular type. Using techniques from approximate computational algebraic geometry, we show how we can solve ideal…
As a powerful tool for longitudinal data analysis, the generalized estimating equations have been widely studied in the academic community. However, in large-scale settings, this approach faces pronounced computational and storage…
We present large sample results for partitioning-based least squares nonparametric regression, a popular method for approximating conditional expectation functions in statistics, econometrics, and machine learning. First, we obtain a…
In linear regression we wish to estimate the optimum linear least squares predictor for a distribution over $d$-dimensional input points and real-valued responses, based on a small sample. Under standard random design analysis, where the…
We consider the problem of constructing optimal designs for population pharmacokinetics which use random effect models. It is common practice in the design of experiments in such studies to assume uncorrelated errors for each subject. In…
Data augmentation is commonly used to encode invariances in learning methods. However, this process is often performed in an inefficient manner, as artificial examples are created by applying a number of transformations to all points in the…
If the assumed model does not accurately capture the underlying structure of the data, a statistical method is likely to yield sub-optimal results, and so model selection is crucial in order to conduct any statistical analysis. However, in…
In this short paper, we describe an efficient numerical solver for the optimal sampling problem considered in "Designing Sampling Schemes for Multi-Dimensional Data". An implementation may be found on…
A major challenge for building statistical models in the big data era is that the available data volume far exceeds the computational capability. A common approach for solving this problem is to employ a subsampled dataset that can be…
This paper proposes a new deterministic sampling strategy for constructing polynomial chaos approximations for expensive physics simulation models. The proposed approach, effectively subsampled quadratures involves sparsely subsampling an…
It is common practice to incorporate additional covariates in empirical economics. In the context of Regression Discontinuity (RD) designs, covariate adjustment plays multiple roles, making it essential to understand its impact on analysis…
Extraordinary amounts of data are being produced in many branches of science. Proven statistical methods are no longer applicable with extraordinary large data sets due to computational limitations. A critical step in big data analysis is…
We study (constrained) least-squares regression as well as multiple response least-squares regression and ask the question of whether a subset of the data, a coreset, suffices to compute a good approximate solution to the regression. We…
We consider the problem of determining the optimal block (or subsample) size for a spatial subsampling method for spatial processes observed on regular grids. We derive expansions for the mean square error of the subsampling variance…
With appropriately chosen sampling probabilities, sampling-based random projection can be used to implement large-scale statistical methods, substantially reducing computational cost while maintaining low statistical error. However,…
The Cox proportional hazards model is widely used in survival analysis to model time-to-event data. However, it faces significant computational challenges in the era of large-scale data, particularly when dealing with time-dependent…
Covariate-adaptive randomization is widely employed to balance baseline covariates in interventional studies such as clinical trials and experiments in development economics. Recent years have witnessed substantial progress in inference…
In the big data era researchers face a series of problems. Even standard approaches/methodologies, like linear regression, can be difficult or problematic with huge volumes of data. Traditional approaches for regression in big datasets may…