Trajectory inference (TI) or pseudotime analysis has dramatically extended the analytical framework of single-cell RNA-seq data, allowing regulatory genes contributing to cell differentiation and those involved in various dynamic cellular processes to be identified. However, most TI analysis procedures deal with individual genes independently while overlooking the regulatory relations between genes. Integrating information from gene regulatory networks (GRNs) at different pseudotime points may lead to more interpretable TI results. To this end, we introduce scInTime—an unsupervised machine learning framework coupling inferred trajectory with single-cell GRNs (scGRNs) to identify master regulatory genes. We validated the performance of our method by analyzing multiple scRNA-seq data sets. In each of the cases, top-ranking genes predicted by scInTime supported their functional relevance with corresponding signaling pathways, in line with the results of available functional studies. Overall results demonstrated that scInTime is a powerful tool to exploit pseudotime-series scGRNs, allowing for a clear interpretation of TI results toward more significant biological insights.

It is well known that the microbiome data are ridden with outliers and have heavy distribution tails, but the impact of outliers and heavy-tailedness has yet to be examined systematically. This paper investigates the impact of outliers and heavy-tailedness on differential abundance analysis (DAA) using the linear models for the differential abundance analysis (LinDA) method and proposes effective strategies to mitigate their influence. The presence of outliers and heavy-tailedness can significantly decrease the power of LinDA. We investigate various techniques to address outliers and heavy-tailedness, including generalizing LinDA into a more flexible framework that allows for the use of robust regression and winsorizing the data before applying LinDA. Our extensive numerical experiments and real-data analyses demonstrate that robust Huber regression has overall the best performance in addressing outliers and heavy-tailedness.

The rapid adoption of large language models (LLMs), such as GPT-4 and Claude 3.5, underscores the need to distinguish LLM-generated text from human-written content to mitigate the spread of misinformation and misuse in education. One promising approach to address this issue is the watermark technique, which embeds subtle statistical signals into LLM-generated text to enable reliable identification. In this paper, we first generalize the likelihood-based LLM detection method of a previous study by introducing a flexible weighted formulation, and further adapt this approach to the inverse transform sampling method. Moving beyond watermark detection, we extend this adaptive detection strategy to tackle the more challenging problem of segmenting a given text into watermarked and non-watermarked substrings. In contrast to the approach in a previous study, which relies on accurate estimation of next-token probabilities that are highly sensitive to prompt estimation, our proposed framework removes the need for precise prompt estimation. Extensive numerical experiments demonstrate that the proposed methodology is both effective and robust in accurately segmenting texts containing a mixture of watermarked and non-watermarked content.

Watermarking is a technique that involves embedding nearly unnoticeable statistical signals within generated content to help trace its source. This work focuses on a scenario where an untrusted third-party user sends prompts to a trusted language model (LLM) provider, who then generates a text from their LLM with a watermark. This setup makes it possible for a detector to later identify the source of the text if the user publishes it. The user can modify the generated text by substitutions, insertions, or deletions. Our objective is to develop a statistical method to detect if a published text is LLM-generated from the perspective of a detector. We further propose a methodology to segment the published text into watermarked and non-watermarked sub-strings. The proposed approach is built upon randomization tests and change point detection techniques. We demonstrate that our method ensures Type I and Type II error control and can accurately identify watermarked sub-strings by finding the corresponding change point locations. To validate our technique, we apply it to texts generated by several language models with prompts extracted from Google's C4 dataset and obtain encouraging numerical results. We release all code publicly at https://github.com/doccstat/llm-watermark-cpd.