Related papers: Designs for Generalized Linear Models
We develop adaptive discretization algorithms for locally optimal experimental design of nonlinear prediction models. With these algorithms, we refine and improve a pertinent state-of-the-art algorithm in various respects. We establish…
Structural reliability analysis is concerned with estimation of the probability of a critical event taking place, described by $P(g(\textbf{X}) \leq 0)$ for some $n$-dimensional random variable $\textbf{X}$ and some real-valued function…
Generalized models provide a framework for the study of evolution equations without specifying all functional forms. The generalized formulation of problems has been shown to facilitate the analytical investigation of local dynamics and has…
We study a statistical model for infinite dimensional Gaussian random variables with unknown parameters. For this model we derive linear estimators for the mean and the variance of the Gaussian distribution. Furthermore, we construct…
We consider the problem of how to assign treatment in a randomized experiment, in which the correlation among the outcomes is informed by a network available pre-intervention. Working within the potential outcome causal framework, we…
Optimal design of experiments for Bayesian inverse problems has recently gained wide popularity and attracted much attention, especially in the computational science and Bayesian inversion communities. An optimal design maximizes a…
We develop a new computational approach for "focused" optimal Bayesian experimental design with nonlinear models, with the goal of maximizing expected information gain in targeted subsets of model parameters. Our approach considers…
Linear mixed models (LMMs) are a powerful and established tool for studying genotype-phenotype relationships. A limiting assumption of LMMs is that the residuals are Gaussian distributed, a requirement that rarely holds in practice.…
A generic construction of linear codes over finite fields has recently received a lot of attention, and many one-weight, two-weight and three-weight codes with good error correcting capability have been produced with this generic approach.…
The paper is devoted to the relaxation and integral representation in the space of functions of bounded variation for an integral energy arising from optimal design problems. The presence of a perimeter penalization is also considered in…
We consider high-dimensional generalized linear models when the covariates are contaminated by measurement error. Estimates from errors-in-variables regression models are well-known to be biased in traditional low-dimensional settings if…
In this paper we show how nonlinear internal models can be effectively used in the design of output regulators for nonlinear systems. This result provides a significant enhancement of the non-equilibrium theory for output regulation, which…
Bayesian optimal experiments that maximize the information gained from collected data are critical to efficiently identify behavioral models. We extend a seminal method for designing Bayesian optimal experiments by introducing two…
At the heart of machine learning lies the question of generalizability of learned rules over previously unseen data. While over-parameterized models based on neural networks are now ubiquitous in machine learning applications, our…
We propose a computational approach to constructing exact designs on finite design spaces that are optimal for multiresponse regression experiments under a combination of the standard linear and specific 'sparsity' constraints. The linear…
In this article, we develop a distributed variable screening method for generalized linear models. This method is designed to handle situations where both the sample size and the number of covariates are large. Specifically, the proposed…
Fitting linear regression models can be computationally very expensive in large-scale data analysis tasks if the sample size and the number of variables are very large. Random projections are extensively used as a dimension reduction tool…
Generalized linear mixed-effects models (GLMMs) are widely used to analyze grouped and hierarchical data. In a GLMM, each response is assumed to follow an exponential-family distribution where the natural parameter is given by a linear…
This paper surveys the machine learning literature and presents in an optimization framework several commonly used machine learning approaches. Particularly, mathematical optimization models are presented for regression, classification,…
A simple yet efficient computational algorithm for computing the continuous optimal experimental design for linear models is proposed. An alternative proof the monotonic convergence for $D$-optimal criterion on continuous design spaces are…