In this paper, we address the robustness, in the sense of l 2-stability, of the set-membership normalized least-mean-square (SM-NLMS) and the set-membership affine projection (SM-AP) algorithms. For the SM-NLMS algorithm, we demonstrate that it is robust regardless of the choice of its parameters and that the SM-NLMS enhances the parameter estimation in most of the iterations in which an update occurs, two advantages over the classical NLMS algorithm. Moreover, we also prove that if the noise bound is known, then we can set the SM-NLMS so that it never degrades the estimate. As for the SM-AP algorithm, we demonstrate that its robustness depends on a judicious choice of one of its parameters: the constraint vector (CV). We prove the existence of CVs satisfying the robustness condition, but practical choices remain unknown. We also demonstrate that both the SM-AP and SM-NLMS algorithms do not diverge, even when their parameters are selected naively, provided the additional noise is bounded. Numerical results that corroborate our analyses are presented.

Credit risk analysis is a process that involves a wide range of complex cognitive abilities. Automating the credit risk analysis process using Large Language Models can bring transformative changes to the finance industry, but not without appropriate measures to ensure trustworthy responses. In this work, we propose a novel prompt-engineering method that enhances the ability of Large Language Models to generate reliable credit risk reports - Labeled Guide Prompting (LGP). LGP consists of: (1) providing annotated few-shot examples to the LLM that denote sets of tokens in an exemplary prompt that are of greater importance when generating sets of tokens in the exemplary response and (2) providing text in the prompt that describes the direction, pathways and interactions between variables from a Bayesian network used for credit risk assessment, thus promoting abductive reasoning. Using data from 100 credit applications, we demonstrate that LGP enables LLMs to generate credit risk reports that are preferred by human credit analysts (in 60-90% of cases) over alternative credit risk reports created by their peers in a blind review. Additionally, we found a statistically significant improvement (p-value < 10− 10) in the insightfulness of the responses generated using LGP when compared to identical prompts without LGP components. We conclude that Labeled Guide Prompting can enhance LLM performance in complex problem-solving tasks, achieving a level of competency comparable to or exceeding human experts.

This brief introduces new data-selective adaptive filtering algorithms for trinion and quaternion spaces T and H. The work advances the set-membership trinionand quaternion-valued normalized least mean square (SMTNLMS and SMQNLMS) and the set-membership trinionand quaternion-valued affine projection (SMTAP and SMQAP) algorithms. We derive set-membership trinion algorithms and then, as special cases, obtain trinion algorithms not employing the set-membership strategy. Prediction simulations based on recorded wind data are provided, showing the improved performance of the proposed algorithms in terms of reduced computational complexity. Then, the quaternion-based SMQAP and SMQNLMS algorithms are derived, and their improved performances are verified in an adaptive beamforming problem.

In this paper, the localization of an emitter based on Time Difference of Arrival (TDoA) has been investigated. The classical least-squares (LS) algorithm, with a limited number of TDoA measurements, has been utilized for obtaining a closed-form solution to the source localization problem. Recently, an extension of the classical LS algorithm has been employed in an attempt to improve the precision of the localization technique by using a larger set of TDoA estimates. However, considering all TDoA values can eventually degrade the accuracy of the localization method due to the presence of heavily noisy measurements. In this work, by employing a data-selective approach, we have proposed a closed-form LS solution that disregards bad measurements. To this end, we have used two distinct objective functions, one to obtain a solution and a second one to test that particular solution among all possible ones within a subset of measurements. Simulation results indicate the superior performance of the proposed algorithm in the source localization problem.

We have been witnessed a growing research activity to advance new strategies to detect and exploit underlying sparsity in the parameters of physical models. In many cases, the sparsity is not explicit in the relations among the parameter coefficients requiring some suitable tools to reveal the potential sparsity. This work proposes a family of adaptive filtering algorithms, aimed at exposing some hidden features of the unknown parameters. Although the basic idea applies to any algorithm, we will concentrate the work in the LMS-type algorithms, giving rise to a family collectively named as Feature LMS (F-LMS) algorithms. These algorithms increase the convergence speed and reduce the steady-state mean-squared error, in comparison with the classical LMS solution. The main idea is to apply linear transformations, through the so-called feature matrices, to reveal the sparsity hidden in the coefficient vector, followed by a sparsity-promoting penalty function to exploit the exposed sparsity. For illustration, a few F-LMS algorithms for lowpass, bandpass, and highpass systems are introduced by using simple feature matrices that require either only simple operations or can learn the features. Simulations and real-life experiments demonstrate that the F-LMS algorithms bring about several performance improvements whenever the unknown sparsity of parameters is exposed.