Related papers: Improvement of random LHD for high dimensions
Although Hadamard matrices have been investigated since the nineteenth century, relatively little is known about their higher-dimensional analogues. In this paper, we introduce two constructions of Hadamard hypercubes. The first…
The rapid growth of Large Language Models (LLMs) has been a driving force in transforming various domains, reshaping the artificial general intelligence landscape. However, the increasing computational and memory demands of these models…
In this paper we use counting arguments to prove that the expected percentage coverage of a $d$ dimensional parameter space of size $n$ when performing $k$ trials with either Latin Hypercube sampling or Orthogonal sampling (when $n=p^d$) is…
In the Bayesian community, an ongoing imperative is to develop efficient algorithms. An appealing approach is to form a hybrid algorithm by combining ideas from competing existing techniques. This paper addresses issues in designing hybrid…
Stratified sampling is a fast and simple method to generate point sets with uniform distribution in hypercubes. However, for the most common paraxial stratfication it has the prominent drawback that the number of sampled points in n…
Large Language Models (LLMs) have revolutionized natural language processing by understanding and generating human-like text. However, the increasing demand for more sophisticated LLMs presents significant computational challenges due to…
Metaheuristics have gained great success in academia and practice because their search logic can be applied to any problem with available solution representation, solution quality evaluation, and certain notions of locality. Manually…
Latin squares and hypercubes are combinatorial designs with several applications in statistics, cryptography and coding theory. In this paper, we generalize a construction of Latin squares based on bipermutive cellular automata (CA) to the…
A common challenge in computer experiments and related fields is to efficiently explore the input space using a small number of samples, i.e., the experimental design problem. Much of the recent focus in the computer experiment literature,…
Experimental design has emerged as a powerful approach for improving the sample efficiency of A/B testing, yet existing designs rely critically on correctly specified models. We study robust sequential experimental design under model…
We study random designs that minimize the asymptotic variance of a de-biased lasso estimator when a large pool of unlabeled data is available but measuring the corresponding responses is costly. The optimal sampling distribution arises as…
Latent variable models are widely used in social and behavioural sciences, including education, psychology, and political science. With the increasing availability of large and complex datasets, high-dimensional latent variable models have…
The rapid development of large language models (LLMs) has significantly transformed the field of artificial intelligence, demonstrating remarkable capabilities in natural language processing and moving towards multi-modal functionality.…
Large collections of high-dimensional data have become nearly ubiquitous across many academic fields and application domains, ranging from biology to the humanities. Since working directly with high-dimensional data poses challenges, the…
Semi-Latin squares have been extensively studied. They can be interpreted as a special case of latinized block designs where the number of columns is equal to the number of replicates in the design. Latinized row-column designs are…
New algorithms are devised for finding the maxima of multidimensional point samples, one of the very first problems studied in computational geometry. The algorithms are very simple and easily coded and modified for practical needs. The…
In this paper, we present a significant improvement of Quick Hypervolume algorithm, one of the state-of-the-art algorithms for calculating exact hypervolume of the space dominated by a set of d-dimensional points. This value is often used…
We present a new efficient algortithm for construction of linear latent structure (LLS) models. This algorithm reduces a problem of estimation of model parameters to a sequence of problems of linear algebra, which assures a low…
Recent advancements in large language models (LLMs) have shown promise in feature engineering for tabular data, but concerns about their reliability persist, especially due to variability in generated outputs. We introduce a multi-level…
The development of tailored materials for specific applications is an active field of research in chemistry, material science and drug discovery. The number of possible molecules that can be obtained from a set of atomic species grow…