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Numerical Linear Algebra and Optimization in Machine Learning and Deep Learning

Professor Biswa Nath Datta
Date & Time
14 Jun 2024 (Fri) | 04:00 PM - 05:00 PM
Y5-302, Yeung Kin Man Academic Building


Machine Learning (ML) is a scientific study of numerical algorithms and statistical models that computer systems use to effectively predict a specific task without using specific human instructions.  It is an emerging area of study and research, and has found applications in solutions of a variety of real-life problems, arising, for instance, in computer vision, handwritten recognition, image and speech recognitions, medical diagnosis, health care, social media, manufacturing, and many more.

Most machine learning problems fall into one of two categories: Supervised or Unsupervised.  The purpose of supervised learning is to make a meaningful prediction given a set of input and output data. Two statistical techniques, Regression and Classification, are used for this purpose,

Regression is used to predict the output that is quantitative, such as blood pressure or blood sugar of a person, and the price of a stock.  On the other hand, Classification is used to predict the output that is qualitative in nature, such as the type of an email (spam or not), color of an eye, or diagnosis of disease of a person: heart attack or stroke or any other disease.

Implementations of regression and classification techniques give rise to unconstrained and constrained optimization problems which in turn require sophisticated techniques of numerical linear algebra for their solutions,

In contrast with supervised learning, in unsupervised learning the machine learns from the data without any human supervision. Here the data is not labeled, the machine learns from the hidden pattern and by discovering the insights from the data.

Unsupervised learning algorithms, such as, the K-Means algorithm and Principal Component Analysis also require numerical linear algebra and optimization techniques for their solutions.

Deep Learning (DL) is a type of powerful Machine Learning based on Artificial Neural Network (ANN) , which is a collection of connected nodes that mimic the neurons of human brains. It enables the process of unstructured data, such as, images, texts and documents. Deep Learning algorithms are nowadays routinely used in industries and elsewhere to perform complex tasks, such as, Image Recognition, arising, for example, in Automated Driving, Medical Imaging, Facial Recognition, Speech Recognition, Emotional Identification, Document Classification, Language Translation, Hand written Recognition, Mobile Banking Applications, and many more. A special type of Neural Network, called, Convolution Neural Network (CNN), is used for achieving many of these tasks. The training of CNN is rather a complicated task and gives rise to difficult nonlinear optimization problems which need to be solved using sophisticated numerical algorithms.

This talk is intended to give a brief overview of the subjects of Machine Learning (ML) and Deep Learning (DL) and show what roles do numerical linear algebra and optimization techniques play in implementations of the associated learning algorithms.

The talk will be of interests to a wide variety of students and researchers in mathematics, computer science, engineering, business, economics, health sciences, and many other disciplines.