Related papers: Asymptotic Bayesian Generalization Error in Latent…
This paper provides a framework to analyze stochastic gradient algorithms in a mean squared error (MSE) sense using the asymptotic normality result of the stochastic gradient descent (SGD) iterates. We perform this analysis by taking the…
Self-supervised learning (SSL) excels at finding general-purpose latent representations from complex data, yet lacks a unifying theoretical framework that explains the diverse existing methods and guides the design of new ones. We cast SSL…
Dual averaging and gradient descent with their stochastic variants stand as the two canonical recipe books for first-order optimization: Every modern variant can be viewed as a descendant of one or the other. In the convex regime, these…
Symmetric positive definite (SPD) matrix has been demonstrated to be an effective feature descriptor in many scientific areas, as it can encode spatiotemporal statistics of the data adequately on a curved Riemannian manifold, i.e., SPD…
Adapting large language models (LLMs) to specific domains often faces a critical bottleneck: the scarcity of high-quality, human-curated data. While large volumes of unchecked data are readily available, indiscriminately using them for…
Standard statistical learning theory predicts that Large Language Models (LLMs) should overfit because their parameter counts vastly exceed the number of training tokens. Yet, in practice, they generalize robustly. We propose that the…
AI-generated text (AIGT) detection evasion aims to reduce the detection probability of AIGT, helping to identify weaknesses in detectors and enhance their effectiveness and reliability in practical applications. Although existing evasion…
The linearized-Laplace approximation (LLA) has been shown to be effective and efficient in constructing Bayesian neural networks. It is theoretically compelling since it can be seen as a Gaussian process posterior with the mean function…
Community is a fundamental and critical characteristic of an undirected social network, making community detection be a vital yet thorny issue in network representation learning. A symmetric and non-negative matrix factorization (SNMF)…
We study generalised linear regression and classification for a synthetically generated dataset encompassing different problems of interest, such as learning with random features, neural networks in the lazy training regime, and the hidden…
The adaptation of large-scale Vision-Language Models (VLMs) through post-training reveals a pronounced generalization gap: models fine-tuned with Reinforcement Learning (RL) consistently achieve superior out-of-distribution (OOD)…
In many social, economical, biological and medical studies, one objective is to classify a subject into one of several classes based on a set of variables observed from the subject. Because the probability distribution of the variables is…
Understanding the algorithmic bias of \emph{stochastic gradient descent} (SGD) is one of the key challenges in modern machine learning and deep learning theory. Most of the existing works, however, focus on \emph{very small or even…
Assessing the quality of LLM-generated text remains a fundamental challenge in natural language processing. Current evaluation approaches often rely on isolated metrics or simplistic aggregations that fail to capture the nuanced trade-offs…
This paper proposes a nonparametric Bayesian method for exploratory data analysis and feature construction in continuous time series. Our method focuses on understanding shared features in a set of time series that exhibit significant…
Fisher discriminant analysis (FDA) is a widely used method for classification and dimensionality reduction. When the number of predictor variables greatly exceeds the number of observations, one of the alternatives for conventional FDA is…
Symmetric Nonnegative Matrix Factorization (SNMF) models arise naturally as simple reformulations of many standard clustering algorithms including the popular spectral clustering method. Recent work has demonstrated that an elementary…
This paper concerns message passing based approaches to sparse Bayesian learning (SBL) with a linear model corrupted by additive white Gaussian noise with unknown variance. With the conventional factor graph, mean field (MF) message passing…
Prior research shows that large language models (LLMs) exhibit systematic extrapolation bias when forming predictions from both experimental and real-world data, and that prompt-based approaches appear limited in alleviating this bias. We…
Nonnegative matrix factorization (NMF) is a powerful technique for dimension reduction, extracting latent factors and learning part-based representation. For large datasets, NMF performance depends on some major issues: fast algorithms,…