Mathematical Methods in Machine Learning and Data Science

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Mathematics and Computer Science".

Deadline for manuscript submissions: 31 January 2025 | Viewed by 1661

Special Issue Editors


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Guest Editor
Faculty of Engineering, Canadian University Dubai, Dubai, United Arab Emirates
Interests: operator algebras; machine learning
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Guest Editor
College of Arts and Sciences, Department of Mathematics and Statistics, American University of Sharjah, Sharjah P.O. Box 26666, United Arab Emirates
Interests: statistics; probability and random processes; business mathematics; statistical modeling and data science

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Guest Editor
Department of Mathematics and Statistics, American University of Sharjah, Sharjah P.O. Box 26666, United Arab Emirates
Interests: generalized statistical distributions arising from the hazard function; statistical inference of probability models; characterization of distributions; bivariate and multivariate weighted distributions

Special Issue Information

Dear Colleagues,

This Special Issue is devoted to recent advances in the use of mathematical methods in data science and machine learning. It includes a range of topics of concern to scholars applying quantitative, optimization, combinatorial, logical, topological, geometrical, statistical, algebraic, and algorithmic methods to diverse areas of data science and machine learning. Novel methods, new applications, comparative analyses of models, case studies, and state-of-the-art review papers are particularly welcomed.

Mathematical methods have underlain every major advancement in data science and machine learning—from reproducing kernel Hilbert spaces and back-propagation in the beginning, to more recent methods such as random matrices and graph theory. Combined with the enormous amount of available data and computing power, mathematical methods have propelled machine learning to astonishing results, achieving near-human-level performance on many tasks. As a response to the recent advancements, the objective of this Special Issue is to present a collection of notable mathematical and statistical methods in data science and machine learning. We invite scholars from all around the world to contribute to developing a comprehensive collection of papers on this important theme.

Dr. Firuz Kamalov
Prof. Dr. Hana Sulieman
Dr. Ayman Alzaatreh
Guest Editors

Manuscript Submission Information

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Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • mathematical methods
  • machine learning
  • data science
  • optimization
  • mathematical statistics
  • algorithms
  • linear algebra
  • dimensionality reduction
  • topology
  • geometry
  • logic
  • combinatorics
  • fuzzy logic
  • time series
  • regression
  • classification
  • imbalanced data
  • feature selection

Published Papers (1 paper)

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Research

14 pages, 1461 KiB  
Article
Prompt Optimization in Large Language Models
by Antonio Sabbatella, Andrea Ponti, Ilaria Giordani, Antonio Candelieri and Francesco Archetti
Mathematics 2024, 12(6), 929; https://doi.org/10.3390/math12060929 - 21 Mar 2024
Viewed by 1113
Abstract
Prompt optimization is a crucial task for improving the performance of large language models for downstream tasks. In this paper, a prompt is a sequence of n-grams selected from a vocabulary. Consequently, the aim is to select the optimal prompt concerning a certain [...] Read more.
Prompt optimization is a crucial task for improving the performance of large language models for downstream tasks. In this paper, a prompt is a sequence of n-grams selected from a vocabulary. Consequently, the aim is to select the optimal prompt concerning a certain performance metric. Prompt optimization can be considered as a combinatorial optimization problem, with the number of possible prompts (i.e., the combinatorial search space) given by the size of the vocabulary (i.e., all the possible n-grams) raised to the power of the length of the prompt. Exhaustive search is impractical; thus, an efficient search strategy is needed. We propose a Bayesian Optimization method performed over a continuous relaxation of the combinatorial search space. Bayesian Optimization is the dominant approach in black-box optimization for its sample efficiency, along with its modular structure and versatility. We use BoTorch, a library for Bayesian Optimization research built on top of PyTorch. Specifically, we focus on Hard Prompt Tuning, which directly searches for an optimal prompt to be added to the text input without requiring access to the Large Language Model, using it as a black-box (such as for GPT-4 which is available as a Model as a Service). Albeit preliminary and based on “vanilla” Bayesian Optimization algorithms, our experiments with RoBERTa as a large language model, on six benchmark datasets, show good performances when compared against other state-of-the-art black-box prompt optimization methods and enable an analysis of the trade-off between the size of the search space, accuracy, and wall-clock time. Full article
(This article belongs to the Special Issue Mathematical Methods in Machine Learning and Data Science)
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