High-throughput sequencing can detect tens of thousands of genes in parallel, providing opportunities for improving the diagnostic accuracy of multiple diseases including sepsis, which is an aggressive inflammatory response to infection that can cause organ failure and death. Early screening of sepsis is essential in clinic, but no effective diagnostic biomarkers are available yet. Here, we present a novel method, Recurrent Logistic Regression, to identify diagnostic biomarkers for sepsis from the blood transcriptome data. A panel including five immune-related genes, LRRN3, IL2RB, FCER1A, TLR5, and S100A12, are determined as diagnostic biomarkers (LIFTS) for sepsis. LIFTS discriminates patients with sepsis from normal controls in high accuracy (AUROC = 0.9959 on average; IC = [0.9722-1.0]) on nine validation cohorts across three independent platforms, which outperforms existing markers. Our analysis determined an accurate prediction model and reproducible transcriptome biomarkers that can lay a foundation for clinical diagnostic tests and biological mechanistic studies.

Thompson sampling (TS) has attracted a lot of interest in the bandit area. It was introduced in the 1930s but has not been theoretically proven until recent years. All of its analysis in the combinatorial multi-armed bandit (CMAB) setting requires an exact oracle to provide optimal solutions with any input. However, such an oracle is usually not feasible since many combinatorial optimization problems are NP-hard and only approximation oracles are available. An example \cite{WangC18} has shown the failure of TS to learn with an approximation oracle. However, this oracle is uncommon and is designed only for a specific problem instance. It is still an open question whether the convergence analysis of TS can be extended beyond the exact oracle in CMAB. In this paper, we study this question under the greedy oracle, which is a common (approximation) oracle with theoretical guarantees to solve many (offline) combinatorial optimization problems. We provide a problem-dependent regret lower bound of order $\Omega(\log T/\Delta^2)$ to quantify the hardness of TS to solve CMAB problems with greedy oracle, where $T$ is the time horizon and $\Delta$ is some reward gap. We also provide an almost matching regret upper bound. These are the first theoretical results for TS to solve CMAB with a common approximation oracle and break the misconception that TS cannot work with approximation oracles.