Related papers: LR-GLM: High-Dimensional Bayesian Inference Using …

This article investigates uncertainty quantification of the generalized linear lasso~(GLL), a popular variable selection method in high-dimensional regression settings. In many fields of study, researchers use data-driven methods to select…

A full parametric and linear specification may be insufficient to capture complicated patterns in studies exploring complex features, such as those investigating age-related changes in brain functional abilities. Alternatively, a partially…

The evolving capabilities of large language models are accompanied by growing sizes and deployment costs, necessitating effective inference optimisation techniques. We propose a novel pruning method utilising centrality measures from graph…

Generalized linear model or GLM constitutes a large class of models and essentially extends the ordinary linear regression by connecting the mean of the response variable with the covariate through appropriate link functions. On the other…

Generalized linear models (GLMs) form one of the most popular classes of models in statistics. The gamma variant is used, for instance, in actuarial science for the modelling of claim amounts in insurance. A flaw of GLMs is that they are…

Latent factor models that integrate data from multiple sources/studies or modalities have garnered considerable attention across various disciplines. However, existing methods predominantly focus either on multi-study integration or…

Large Language Models (LLMs) have transformed artificial intelligence by excelling in complex natural language processing tasks. Their ability to generate human-like text has opened new possibilities for market research, particularly in…

The analytic characterization of the high-dimensional behavior of optimization for Generalized Linear Models (GLMs) with Gaussian data has been a central focus in statistics and probability in recent years. While convex cases, such as the…

Projection predictive inference is a decision theoretic Bayesian approach that decouples model estimation from decision making. Given a reference model previously built including all variables present in the data, projection predictive…

In practice, there often exist unobserved variables, also termed hidden variables, associated with both the response and covariates. Existing works in the literature mostly focus on linear regression with hidden variables. However, when the…

Traditional time series analysis has long relied on pattern recognition, trained on static and well-established benchmarks. However, in real-world settings -- where policies shift, human behavior adapts, and unexpected events unfold --…

Large language models are often assumed to acquire increasingly structured, generalizable internal representations simply by scaling data and parameters. We interrogate this assumption by introducing a Clinical Trial Natural Language…

Technological advances have led to a proliferation of structured big data that have matrix-valued covariates. We are specifically motivated to build predictive models for multi-subject neuroimaging data based on each subject's brain imaging…

Interpretability is crucial for machine learning in many scenarios such as quantitative finance, banking, healthcare, etc. Symbolic regression (SR) is a classic interpretable machine learning method by bridging X and Y using mathematical…

Real-time nonlinear Bayesian filtering algorithms are overwhelmed by data volume, velocity and increasing complexity of computational models. In this paper, we propose a novel ensemble based nonlinear Bayesian filtering approach which only…

Multi-task regression attempts to exploit the task similarity in order to achieve knowledge transfer across related tasks for performance improvement. The application of Gaussian process (GP) in this scenario yields the non-parametric yet…

The vast quantity of information brought by big data as well as the evolving computer hardware encourages success stories in the machine learning community. In the meanwhile, it poses challenges for the Gaussian process (GP) regression, a…

Bayesian inference on non-Gaussian data is often non-analytic and requires computationally expensive approximations such as sampling or variational inference. We propose an approximate inference framework primarily designed to be…

The efficient solution of large-scale multiterm linear matrix equations is a challenging task in numerical linear algebra, and it is a largely open problem. We propose a new iterative scheme for symmetric and positive definite operators,…

In Bayesian inference, making deductions about a parameter of interest requires one to sample from or compute an integral against a posterior distribution. A popular method to make these computations cheaper in high-dimensional settings is…