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Class imbalance and label noise are pervasive in large-scale datasets, yet much of machine learning research assumes well-labeled, balanced data, which rarely reflects real world conditions. Existing approaches typically address either…
Prompt sensitivity, referring to the phenomenon where paraphrasing (i.e., repeating something written or spoken using different words) leads to significant changes in large language model (LLM) performance, has been widely accepted as a…
We study data-driven stabilization of continuous-time systems in autoregressive form when only noisy input-output data are available. First, we provide an operator-based characterization of the set of systems consistent with the data. Next,…
Having a clean dataset has been the foundational assumption of most natural language processing (NLP) systems. However, properly written text is rarely found in real-world scenarios and hence, oftentimes invalidates the aforementioned…
In this paper we present a generic framework for the asymptotic performance analysis of subspace-based parameter estimation schemes. It is based on earlier results on an explicit first-order expansion of the estimation error in the signal…
Study samples often differ from the target populations of inference and policy decisions in non-random ways. Researchers typically believe that such departures from random sampling -- due to changes in the population over time and space, or…
We consider solutions to the Lam\'e system in two dimensions. By using systematic way, based on layer potential techniques and the field expansion (FE) method (formal derivation), we establish a rigorous asymptotic expansion for the…
We present an extension of Willems' Fundamental Lemma to the class of multi-input multi-output discrete-time feedback linearizable nonlinear systems, thus providing a data-based representation of their input-output trajectories. Two sources…
In this work we address the problem of approximating high-dimensional data with a low-dimensional representation. We make the following contributions. We propose an inverse regression method which exchanges the roles of input and response,…
The ensemble Kalman inversion is widely used in practice to estimate unknown parameters from noisy measurement data. Its low computational costs, straightforward implementation, and non-intrusive nature makes the method appealing in various…
Class imbalance and noisy labels are the norm rather than the exception in many large-scale classification datasets. Nevertheless, most works in machine learning typically assume balanced and clean data. There have been some recent attempts…
In this paper, we consider the problem of recovering a sparse signal from noisy linear measurements using the so called LASSO formulation. We assume a correlated Gaussian design matrix with additive Gaussian noise. We precisely analyze the…
Willems' fundamental lemma enables a trajectory-based characterization of linear systems through data-based Hankel matrices. However, in the presence of measurement noise, we ask: Is this noisy Hankel-based model expressive enough to…
The zero-shot capability of Large Language Models (LLMs) has enabled highly flexible, reference-free metrics for various tasks, making LLM evaluators common tools in NLP. However, the robustness of these LLM evaluators remains relatively…
We present a general framework for studying regularized estimators; such estimators are pervasive in estimation problems wherein "plug-in" type estimators are either ill-defined or ill-behaved. Within this framework, we derive, under…
In the current landscape of large language models (LLMs), the process of instruction tuning serves as an essential step. Considering the high computing power overhead, data-efficient instruction tuning was proposed to reduce the training…
When we are interested in high-dimensional system and focus on classification performance, the $\ell_{1}$-penalized logistic regression is becoming important and popular. However, the Lasso estimates could be problematic when penalties of…
We study the estimation capacity of the generalized Lasso, i.e., least squares minimization combined with a (convex) structural constraint. While Lasso-type estimators were originally designed for noisy linear regression problems, it has…
Data corruption, including missing and noisy data, poses significant challenges in real-world machine learning. This study investigates the effects of data corruption on model performance and explores strategies to mitigate these effects…
Large-scale empirical data, the sample size and the dimension are high, often exhibit various characteristics. For example, the noise term follows unknown distributions or the model is very sparse that the number of critical variables is…