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The expectation-maximization (EM) algorithm is a powerful computational technique for finding the maximum likelihood estimates for parametric models when the data are not fully observed. The EM is best suited for situations where the…
As an effective nonparametric method, empirical likelihood (EL) is appealing in combining estimating equations flexibly and adaptively for incorporating data information. To select important variables and estimating equations in the sparse…
This paper develops a quantitative framework for analyzing the mean-square exponential stabilization of stochastic linear systems with multiplicative noise, focusing specifically on the optimal stabilizing rate, which characterizes the…
This article presents the first systematic review of unsupervised and semi-supervised computational text-based ideal point estimation (CT-IPE) algorithms, methods designed to infer latent political positions from textual data. These…
The current work on reinforcement learning (RL) from demonstrations often assumes the demonstrations are samples from an optimal policy, an unrealistic assumption in practice. When demonstrations are generated by sub-optimal policies or…
Medical imaging systems are commonly assessed and optimized by use of objective measures of image quality (IQ). The Ideal Observer (IO) performance has been advocated to provide a figure-of-merit for use in assessing and optimizing imaging…
One aim of representation learning is to recover the original latent code that generated the data, a task which requires additional information or inductive biases. A recently proposed approach termed Independent Mechanism Analysis (IMA)…
While Reinforcement Learning (RL) has advanced LLM reasoning, applying it to long-context scenarios is hindered by sparsity of outcome rewards. This limitation fails to penalize ungrounded "lucky guesses," leaving the critical process of…
In this work, we investigate the regularized solutions and their finite element solutions to the inverse source problems governed by partial differential equations, and establish the stochastic convergence and optimal finite element…
Estimating the values of unknown parameters from corrupted measured data faces a lot of challenges in ill-posed problems. In such problems, many fundamental estimation methods fail to provide a meaningful stabilized solution. In this work,…
A deterministic attitude estimation problem for a rigid body in a potential field, with bounded attitude and angular velocity measurement errors is considered. An attitude estimation algorithm that globally minimizes the attitude estimation…
Feature subset selection arises in many high-dimensional applications of statistics, such as compressed sensing and genomics. The $\ell_0$ penalty is ideal for this task, the caveat being it requires the NP-hard combinatorial evaluation of…
Model-based reinforcement learning (RL) algorithms allow us to combine model-generated data with those collected from interaction with the real system in order to alleviate the data efficiency problem in RL. However, designing such…
Existing approaches to estimating politicians' latent positions along specific dimensions often fail when relevant data is limited. We leverage the embedded knowledge in generative large language models (LLMs) to address this challenge and…
We establish an equivalence between the $\ell_2$-regularized solution path for a convex loss function, and the solution of an ordinary differentiable equation (ODE). Importantly, this equivalence reveals that the solution path can be viewed…
Robust waypoint prediction is crucial for mobile robots operating in open-world, safety-critical settings. While Imitation Learning (IL) methods have demonstrated great success in practice, they are susceptible to distribution shifts: the…
Linear inverse problems are ubiquitous. Often the measurements do not follow a Gaussian distribution. Additionally, a model matrix with a large condition number can complicate the problem further by making it ill-posed. In this case, the…
This paper deals with parameter estimation when the data are randomly right censored. The maximum likelihood estimates from censored samples are obtained by using the expectation-maximization (EM) and Monte Carlo EM (MCEM) algorithms. We…
We explore past and recent developments in rare-event probability estimation with a particular focus on a novel Monte Carlo technique Empirical Likelihood Maximization (ELM). This is a versatile method that involves sampling from a sequence…
Machine learning models now influence decisions that directly affect people's lives, making it important to understand not only their predictions, but also how individuals could act to obtain better results. Algorithmic recourse provides…