Related papers: Optimal block designs for experiments with respons…
Clinical trials are an instrument for making informed decisions based on evidence from well-designed experiments. Here we consider adaptive designs mainly from the perspective of multi-arm Phase II clinical trials, in which one or more…
In optimal experimental design, the objective is to select a limited set of experiments that maximizes information about unknown model parameters based on factor levels. This work addresses the generalized D-optimal design problem, allowing…
The Poisson-Boltzmann equation is a widely used model to study the electrostatics in molecular solvation. Its numerical solution using a boundary integral formulation requires a mesh on the molecular surface only, yielding accurate…
In this paper, we investigate the randomized algorithms for block matrix multiplication from random sampling perspective. Based on the A-optimal design criterion, the optimal sampling probabilities and sampling block sizes are obtained. To…
Bayesian hierarchical Poisson models are an essential tool for analyzing count data. However, designing efficient algorithms to sample from the posterior distribution of the target parameters remains a challenging task for this class of…
Group testing techniques are widely used in resource-constrained settings, such as infectious-disease screening, blood safety, DNA library screening, and industrial inspection, where the efficient use of limited testing resources depends…
In experimental design, we are given $n$ vectors in $d$ dimensions, and our goal is to select $k\ll n$ of them to perform expensive measurements, e.g., to obtain labels/responses, for a linear regression task. Many statistical criteria have…
In an order-of-addition experiment, each treatment is a permutation of m components. It is often unaffordable to test all the m! treatments, and the design problem arises. We consider a model that incorporates the order of each pair of…
We obtain new explicit pseudorandom generators for several computational models involving groups. Our main results are as follows: 1. We consider read-once group-products over a finite group $G$, i.e., tests of the form $\prod_{i=1}^n…
Optimal two-treatment, $p$ period crossover designs for binary responses are determined. The optimal designs are obtained by minimizing the variance of the treatment contrast estimator over all possible allocations of $n$ subjects to $2^p$…
We construct optimal designs for group testing experiments where the goal is to estimate the prevalence of a trait by using a test with uncertain sensitivity and specificity. Using optimal design theory for approximate designs, we show that…
In this work we consider data-driven optimization problems where one must maximize a function given only queries at a fixed set of points. This problem setting emerges in many domains where function evaluation is a complex and expensive…
Sparse regularized regression methods are now widely used in genome-wide association studies (GWAS) to address the multiple testing burden that limits discovery of potentially important predictors. Linear mixed models (LMMs) have become an…
Estimation of generalized linear mixed models (GLMMs) with non-nested random effects structures requires approximation of high-dimensional integrals. Many existing methods are tailored to the low-dimensional integrals produced by nested…
Crossover designs randomly assign each unit to receive a sequence of treatments. By comparing outcomes within the same unit, these designs can effectively eliminate between-unit variation and facilitate the identification of both…
Real-world experiments involve batched & delayed feedback, non-stationarity, multiple objectives & constraints, and (often some) personalization. Tailoring adaptive methods to address these challenges on a per-problem basis is infeasible,…
We propose a new "Poisson flow" generative model (PFGM) that maps a uniform distribution on a high-dimensional hemisphere into any data distribution. We interpret the data points as electrical charges on the $z=0$ hyperplane in a space…
We propose a scalable algorithmic framework for exact Bayesian variable selection and model averaging in linear models under the assumption that the Gram matrix is block-diagonal, and as a heuristic for exploring the model space for general…
Let $P = \{p(i)\}$ be a measure of strictly positive probabilities on the set of nonnegative integers. Although the countable number of inputs prevents usage of the Huffman algorithm, there are nontrivial $P$ for which known methods find a…
We develop a novel iterative algorithm for locally optimal experimental design under constraints, like budget or performance constraints. It is an adaptive discretization algorithm. In every iteration, a discretized version of the…