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In aligning large language models (LLMs), reward models have played an important role, but are standardly trained as discriminative models and rely only on labeled human preference data. In this paper, we explore methods that train reward…

Large language models (LLMs) have exhibited expert-level capabilities across various domains. However, their abilities to solve problems in Operations Research (OR) -- the analysis and optimization of mathematical models derived from…

Sequential data collection has emerged as a widely adopted technique for enhancing the efficiency of data gathering processes. Despite its advantages, such data collection mechanism often introduces complexities to the statistical inference…

Logistic regression models are a popular and effective method to predict the probability of categorical response data. However inference for these models can become computationally prohibitive for large datasets. Here we adapt ideas from…

The scalability of Generalized Linear Models (GLMs) for large-scale, high-dimensional data often forces a trade-off between computational feasibility and statistical accuracy, particularly for inference on pre-specified parameters. While…

The ultimate goal of regression analysis is to obtain information about the conditional distribution of a response given a set of explanatory variables. This goal is, however, seldom achieved because most established regression models only…

Large Language Model (LLM) has demonstrated significant ability in various Natural Language Processing tasks. However, their effectiveness is highly dependent on the phrasing of the task prompt, leading to research on automatic prompt…

The development and use of dimension reduction methods is prevalent in modern statistical literature. This paper reviews a class of dimension reduction techniques which aim to simultaneously select relevant predictors and find clusters…

The use of the Preconditioned Conjugate Gradient (PCG) method for computing the Generalized Least Squares (GLS) estimator of the General Linear Model (GLM) is considered. The GLS estimator is expressed in terms of the solution of an…

In this work, we conduct an assessment of the optimization capabilities of LLMs across various tasks and data sizes. Each of these tasks corresponds to unique optimization domains, and LLMs are required to execute these tasks with…

Bivariate ordered logistic models (BOLMs) are appealing to jointly model the marginal distribution of two ordered responses and their association, given a set of covariates. When the number of categories of the responses increases, the…

The generalized outcome-adaptive lasso (GOAL) is a variable selection for high-dimensional causal inference proposed by Bald\'e et al. [2023, {\em Biometrics} {\bfseries 79(1)}, 514--520]. When the dimension is high, it is now well…

Accurate load forecasting is crucial for maintaining the power balance between generators and consumers,particularly with the increasing integration of renewable energy sources, which introduce significant intermittent volatility. With the…

We introduce a new computational framework for estimating parameters in generalized generalized linear models (GGLM), a class of models that extends the popular generalized linear models (GLM) to account for dependencies among observations…

Optimization methods have been broadly applied to two classes of objects viz. (i) modeling and description of data and (ii) the determination of the stationary points of functions. Here, a theoretical basis is developed that optimizes an…

Many applications of generalised linear models (GLMs) can be improved by applying constraints that impose assumptions on the associations or improve consistency of the estimators. Yet, there are still barriers to the implementation and…

In many areas of engineering, nonlinear numerical analysis is playing an increasingly important role in supporting the design and monitoring of structures. Whilst increasing computer resources have made such formerly prohibitive analyses…

Linear model prediction with a large number of potential predictors is both statistically and computationally challenging. The traditional approaches are largely based on shrinkage selection/estimation methods, which are applicable even…

We propose a learning framework for calibrating predictive models to make loss-controlling prediction for exchangeable data, which extends our recently proposed conformal loss-controlling prediction for more general cases. By comparison,…

We show that large language models (LLMs) are remarkably good at working with interpretable models that decompose complex outcomes into univariate graph-represented components. By adopting a hierarchical approach to reasoning, LLMs can…