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The Rasch model has been widely used to analyse item response data in psychometrics and educational assessments. When the number of individuals and items are large, it may be impractical to provide all possible responses. It is desirable to…
We study the maximum likelihood estimation (MLE) in the multivariate deviated model where the data are generated from the density function $(1-\lambda^{\ast})h_{0}(x)+\lambda^{\ast}f(x|\mu^{\ast}, \Sigma^{\ast})$ in which $h_{0}$ is a known…
We investigate the usage of Large Language Model (LLM) in collecting high-quality data to warm-start Reinforcement Learning (RL) algorithms for learning in some classical Markov Decision Process (MDP) environments. In this work, we focus on…
Recent advancements in large language models (LLMs) have significantly improved code generation and program comprehension, accelerating the evolution of software engineering. Current methods primarily enhance model performance by leveraging…
The scaling law, a cornerstone of Large Language Model (LLM) development, predicts improvements in model performance with increasing computational resources. Yet, while empirically validated, its theoretical underpinnings remain poorly…
In this paper, a nonparametric maximum likelihood (ML) estimator for band-limited (BL) probability density functions (pdfs) is proposed. The BLML estimator is consistent and computationally efficient. To compute the BLML estimator, three…
This work considers Maximum Likelihood Estimation (MLE) of a Toeplitz structured covariance matrix. In this regard, an equivalent reformulation of the MLE problem is introduced and two iterative algorithms are proposed for the optimization…
Structured Latent Attribute Models (SLAMs) are a family of discrete latent variable models widely used in education, psychology, and epidemiology to model multivariate categorical data. A SLAM assumes that multiple discrete latent…
Kernel density estimators (KDEs) are ubiquitous tools for nonparametric estimation of probability density functions (PDFs), when data are obtained from unknown data generating processes. The KDEs that are typically available in software…
To address the needs of modeling uncertainty in sensitive machine learning applications, the setup of distributionally robust optimization (DRO) seeks good performance uniformly across a variety of tasks. The recent multi-distribution…
General log-linear models specified by non-negative integer design matrices have a potentially wide range of applications, although using models without the genuine overall effect, that is, ones which cannot be reparameterized to include a…
The use of machine learning methods helps to improve decision making in different fields. In particular, the idea of bridging predictions (machine learning models) and prescriptions (optimization problems) is gaining attention within the…
Linear birth-and-death processes (LBDPs) are foundational stochastic models in population dynamics, evolutionary biology, and hematopoiesis. Estimating parameters from discretely observed data is computationally demanding due to irregular…
How to efficiently identify multiple-input multiple-output (MIMO) linear parameter-varying (LPV) discrete-time state-space (SS) models with affine dependence on the scheduling variable still remains an open question, as identification…
Continuous-time reinforcement learning (CTRL) provides a natural framework for sequential decision-making in dynamic environments where interactions evolve continuously over time. While CTRL has shown growing empirical success, its ability…
Power law cumulative frequency $(P)$ vs. event size $(l)$ distributions $P(\geq l)\sim l^{-\alpha}$ are frequently cited as evidence for complexity and serve as a starting point for linking theoretical models and mechanisms with observed…
We study the problem of computing the maximum likelihood estimator (MLE) of multivariate log-concave densities. Our main result is the first computationally efficient algorithm for this problem. In more detail, we give an algorithm that, on…
A Maximum Likelihood recursive state estimator is derived for non-linear and non-Gaussian state-space models. The estimator combines a particle filter to generate the conditional density and the Expectation Maximization algorithm to compute…
In recent decades, multilevel regression and poststratification (MRP) has surged in popularity for population inference. However, the validity of the estimates can depend on details of the model, and there is currently little research on…
Off-policy evaluation and learning (OPE/L) use offline observational data to make better decisions, which is crucial in applications where online experimentation is limited. However, depending entirely on logged data, OPE/L is sensitive to…