Mathematical Techniques in Machine Learning and Data Science

Authors

Dr. Anurag Singh

Abstract

Mathematical techniques form the foundational framework upon which machine learning (ML) and data science are built, providing essential tools for understanding, modelling, and forecasting from data. This essay explores key mathematical techniques critical to these fields, highlighting their practical applications and profound impact on intelligent systems. Linear algebra enables efficient data representation and transformation, crucial for tasks like dimensionality reduction and pattern recognition. Calculus plays a pivotal role in optimizing models through gradient-based methods, enhancing predictive accuracy by minimizing error functions. Probability and statistics quantify uncertainty and validate models, essential for robust decision-making in diverse applications. Optimization techniques like gradient descent refine model parameters, ensuring convergence to optimal solutions in complex parameter spaces. Algebraic structures and graph theory provide insights into complex data relationships, enhancing analysis and algorithmic efficiency. Information theory guides data compression and feature selection, optimizing data representation and enhancing model interpretability. Together, these mathematical underpinnings empower ML algorithms to leverage vast datasets effectively, driving innovation across industries.

Keywords

Machine Learning, Data Science, Mathematical Techniques, Linear Algebra.

Mathematical Techniques in Machine Learning and Data Science. Dr. Anurag Singh. 2019. IJIRCT, Volume 5, Issue 4. Pages 1-5. https://www.ijirct.org/viewPaper.php?paperId=2407043