Large Language Models (LLMs) have become essential in advancing natural language processing (NLP) tasks, but their sequential token generation limits inference speed.Multi-Draft Speculative Decoding (MDSD) offers a promising solution by using a smaller draft model to generate multiple token sequences, which the target LLM verifies in parallel.However, current heuristic approaches, such as Recursive Rejection Sampling (RRS), suffer from low acceptance rates in subsequent drafts, limiting the advantages of using multiple drafts.Meanwhile, Optimal Transport with Membership Cost (OTM) can theoretically improve acceptance rates, but its computational cost is too high for real-time use.We present SpecHub, a novel, efficient samplingverification method for MDSD that improves acceptance rates with only linear computational overhead.By simplifying the OTM problem into a compact Linear Programming model, SpecHub significantly reduces computational complexity.It further accelerates sampling by leveraging a sparse joint distribution, focusing computation on high-probability token sequences.In extensive experiments, Spechub consistently generates 0.05-0.27and 0.02-0.16more tokens per step than RRS and RRS without replacement.We attach our code at https://github.com/MasterGodzilla/ Speculative_decoding_OT.

MOTIVATION: Cancer genomics studies frequently aim to identify genes that are differentially expressed between clinically distinct patient subgroups, generally by testing single genes one at a time. However, the results of any individual transcriptomic study are often not fully reproducible. A particular challenge impeding statistical analysis is the difficulty of distinguishing between differential expression comprising part of the genomic disease etiology and that induced by downstream effects. More robust analytical approaches that are well-powered to detect potentially causative genes, are less prone to discovering spurious associations, and can deliver reproducible findings across different studies are needed. RESULTS: We propose a set-based procedure for testing of differential expression and show that this set-based approach can produce more robust results by aggregating information across multiple, correlated genomic markers. Specifically, we adapt the Generalized Berk-Jones statistic to test for the transcription factors that may contribute to the progression of estrogen receptor positive breast cancer. We demonstrate the ability of our method to produce reproducible findings by applying the same analysis to 21 publicly available datasets, producing a similar list of significant transcription factors across most studies. Our Generalized Berk-Jones approach produces results that show improved consistency over three set-based testing algorithms: Generalized Higher Criticism, Gene Set Analysis and Gene Set Enrichment Analysis. AVAILABILITY AND IMPLEMENTATION: Data are in the MetaGxBreast R package. Code is available at github.com/ryanrsun/gaynor_sun_GBJ_breast_cancer. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.