Related papers: Large and Small Deviations for Statistical Sequenc…

Contrastive representation learning (CRL) underpins many modern foundation models. Despite recent theoretical progress, existing analyses suffer from several key limitations: (i) the statistical consistency of CRL remains poorly understood;…

Generalized Linear Models (GLMs) have been used extensively in statistical models of spike train data. However, the maximum likelihood estimates of the model parameters and their uncertainty, can be challenging to compute in situations…

While large language models (LLMs) have made considerable advancements in understanding and generating unstructured text, their application in structured data remains underexplored. Particularly, using LLMs for complex reasoning tasks on…

Various applications in different fields, such as gene expression analysis or computer vision, suffer from data sets with high-dimensional low-sample-size (HDLSS), which has posed significant challenges for standard statistical and modern…

We develop a systematic, omnibus approach to goodness-of-fit testing for parametric distributional models when the variable of interest is only partially observed due to censoring and/or truncation. In many such designs, tests based on the…

Using a sensitive statistical test we determine whether or not one can detect the breakdown of linear response given observations of deterministic dynamical systems. A goodness-of-fit statistics is developed for a linear statistical model…

Signal-agnostic data exploration based on machine learning could unveil very subtle statistical deviations of collider data from the expected Standard Model of particle physics. The beneficial impact of a large training sample on machine…

Sampling is a promising bottom-up method for exposing what generative models have learned about language, but it remains unclear how to generate representative samples from popular masked language models (MLMs) like BERT. The MLM objective…

Background With microarray technology becoming mature and popular, the selection and use of a small number of relevant genes for accurate classification of samples is a hot topic in the circles of biostatistics and bioinformatics. However,…

In this work, we investigate Gaussian Mixture Models ({\it abbrv} GMM) and the related problem of non parametric maximum likelihood estimation ({\it abbrv} NPMLE) from the perspective of statistical mechanics. In particular, we establish…

Large Language Models (LLMs) such as GPT-4.0 have shown significant promise in addressing the semantic complexities of regulatory documents, particularly in detecting inconsistencies and contradictions. This study evaluates GPT-4.0's…

Evaluating whether large language models (LLMs) capture the structure of natural language beyond local fluency remains an open challenge. Existing evaluation methods, largely based on task performance or short-context behavior, provide…

We propose a novel approach for domain generalisation (DG) leveraging risk distributions to characterise domains, thereby achieving domain invariance. In our findings, risk distributions effectively highlight differences between training…

This paper studies the problem of sequential Gaussian shift-in-mean hypothesis testing in a distributed multi-agent network. A sequential probability ratio test (SPRT) type algorithm in a distributed framework of the…

Just like the previous generation of task-tuned models, large language models (LLMs) that are adapted to tasks via prompt-based methods like in-context-learning (ICL) perform well in some setups but not in others. This lack of consistency…

Large random matrices appear in different fields of mathematics and physics such as combinatorics, probability theory, statistics, operator theory, number theory, quantum field theory, string theory etc... In the last ten years, they…

We consider the problem of identifying tandem scattered subsequences within a string. Our algorithm identifies a longest subsequence which occurs twice without overlap in a string. This algorithm is based on the Hunt-Szymanski algorithm,…

Large Language Models (LLMs) have shown remarkable capabilities in processing both natural and programming languages, which have enabled various applications in software engineering, such as requirement engineering, code generation, and…

Generalized Chinese Remainder Theorem (CRT) has been shown to be a powerful approach to solve the ambiguity resolution problem. However, with its close relationship to number theory, study in this area is mainly from a coding theory…

We study the common continual learning setup where an overparameterized model is sequentially fitted to a set of jointly realizable tasks. We analyze forgetting, defined as the loss on previously seen tasks, after $k$ iterations. For…