Related papers: Asymptotic Bayesian Generalization Error in Latent…

Supervised fine-tuning (SFT) is crucial for aligning Large Language Models (LLMs) with human instructions. The primary goal during SFT is to select a small yet representative subset of training data from the larger pool, such that…

Various regularized linear discriminant analysis (LDA) methods have been proposed to address the problems of the classic methods in high-dimensional settings. Asymptotic optimality has been established for some of these methods in high…

High-dimensional and sparse (HiDS) matrices are omnipresent in a variety of big data-related applications. Latent factor analysis (LFA) is a typical representation learning method that extracts useful yet latent knowledge from HiDS matrices…

The paper studies distributed Dictionary Learning (DL) problems where the learning task is distributed over a multi-agent network with time-varying (nonsymmetric) connectivity. This formulation is relevant, for instance, in big-data…

Laplacian regularized stratified models (LRSM) are models that utilize the explicit or implicit network structure of the sub-problems as defined by the categorical features called strata (e.g., age, region, time, forecast horizon, etc.),…

Latent Dirichlet Allocation (LDA) is a three-level hierarchical Bayesian model for topic inference. In spite of its great success, inferring the latent topic distribution with LDA is time-consuming. Motivated by the transfer learning…

In recent years, a number of methods have been developed for the dimension reduction and decomposition of multiple linked high-content data matrices. Typically these methods assume that just one dimension, rows or columns, is shared among…

A high-dimensional and incomplete (HDI) matrix can describe the complex interactions among numerous nodes in various big data-related applications. A stochastic gradient descent (SGD)-based latent factor analysis (LFA) model is remarkably…

We propose a geometric algorithm for topic learning and inference that is built on the convex geometry of topics arising from the Latent Dirichlet Allocation (LDA) model and its nonparametric extensions. To this end we study the…

We introduce supervised latent Dirichlet allocation (sLDA), a statistical model of labelled documents. The model accommodates a variety of response types. We derive an approximate maximum-likelihood procedure for parameter estimation, which…

Fine-tuning Large Language Models (LLMs) on specific datasets is a common practice to improve performance on target tasks. However, this performance gain often leads to overfitting, where the model becomes too specialized in either the task…

Community is a fundamental and critical characteristic of a Large-scale Undirected Network (LUN) like a social network, making community detection a vital yet thorny issue in LUN representation learning. Owing to its good scalability and…

Support vector machine (SVM) has been one of the most popular learning algorithms, with the central idea of maximizing the minimum margin, i.e., the smallest distance from the instances to the classification boundary. Recent theoretical…

This work provides test error bounds for iterative fixed point methods on linear predictors -- specifically, stochastic and batch mirror descent (MD), and stochastic temporal difference learning (TD) -- with two core contributions: (a) a…

Gaussian Mixture Models (GMMs) are a standard tool in data analysis. However, they face problems when applied to high-dimensional data (e.g., images) due to the size of the required full covariance matrices (CMs), whereas the use of…

The contribution of this paper is two-fold. First, we present Indexing by Latent Dirichlet Allocation (LDI), an automatic document indexing method. The probability distributions in LDI utilize those in Latent Dirichlet Allocation (LDA), a…

We begin by briefly surveying some results on the convergence of the Stochastic Gradient Descent (SGD) Method, proved in a companion paper by the present authors. These results are based on viewing SGD as a version of Stochastic…

Large language models (LLMs) have achieved remarkable progress, with post-training playing a crucial role in enhancing their reasoning capabilities. Among post-training paradigms, supervised fine-tuning (SFT) is widely used: it leverages…

First-order stochastic optimization methods are currently the most widely used class of methods for training deep neural networks. However, the choice of the optimizer has become an ad-hoc rule that can significantly affect the performance.…

Single Domain Generalization (SDG) aims to train models that maintain consistent performance across diverse scenarios using data from a single source. While latent diffusion models (LDMs) show promise for augmenting limited source data, our…