Math 0-1: Matrix Calculus in Data Science & Machine Learning
Cosa imparerai
- Derive matrix and vector derivatives for linear and quadratic forms
- Solve common optimization problems (least squares, Gaussian, financial portfolio)
- Understand and implement Gradient Descent and Newton's method
- Learn to use the Matrix Cookbook
Requisiti
- Competence with Calculus and Linear Algebra
- Optional: Familiarity with Python, Numpy, and Matplotlib to implement optimization techniques
Descrizione
Welcome to the exciting world of Matrix Calculus, a fundamental tool for understanding and solving problems in machine learning and data science. In this course, we will dive into the powerful mathematics that underpin many of the algorithms and techniques used in these fields. By the end of this course, you'll have the knowledge and skills to navigate the complex landscape of derivatives, gradients, and optimizations involving matrices.
Course Objectives:
Understand the basics of matrix calculus, linear and quadratic forms, and their derivatives.
Learn how to utilize the famous Matrix Cookbook for a wide range of matrix calculus operations.
Gain proficiency in optimization techniques like gradient descent and Newton's method in one and multiple dimensions.
Apply the concepts learned to real-world problems in machine learning and data science, with hands-on exercises and Python code examples.
Why Matrix Calculus? Matrix calculus is the language of machine learning and data science. In these fields, we often work with high-dimensional data, making matrices and their derivatives a natural representation for our problems. Understanding matrix calculus is crucial for developing and analyzing algorithms, building predictive models, and making sense of the vast amounts of data at our disposal.
Section 1: Linear and Quadratic Forms In the first part of the course, we'll explore the basics of linear and quadratic forms, and their derivatives. The linear form appears in all of the most fundamental and popular machine learning models, including linear regression, logistic regression, support vector machine (SVM), and deep neural networks. We will also dive into quadratic forms, which are fundamental to understanding optimization problems, which appear in regression, portfolio optimization in finance, signal processing, and control theory.
The Matrix Cookbook is a valuable resource that compiles a wide range of matrix derivative formulas in one place. You'll learn how to use this reference effectively, saving you time and ensuring the accuracy of your derivations.
Section 2: Optimization Techniques Optimization lies at the heart of many machine learning and data science tasks. In this section, we will explore two crucial optimization methods: gradient descent and Newton's method. You'll learn how to optimize not only in one dimension but also in high-dimensional spaces, which is essential for training complex models. We'll provide Python code examples to help you grasp the practical implementation of these techniques.
Course Structure:
Each lecture will include a theoretical introduction to the topic.
We will work through relevant mathematical derivations and provide intuitive explanations.
Hands-on exercises will allow you to apply what you've learned to real-world problems.
Python code examples will help you implement and experiment with the concepts.
There will be opportunities for questions and discussions to deepen your understanding.
Prerequisites:
Basic knowledge of linear algebra, calculus, and Python programming is recommended.
A strong desire to learn and explore the fascinating world of matrix calculus.
Conclusion: Matrix calculus is an indispensable tool in the fields of machine learning and data science. It empowers you to understand, create, and optimize algorithms that drive innovation and decision-making in today's data-driven world. This course will equip you with the knowledge and skills to navigate the intricate world of matrix calculus, setting you on a path to become a proficient data scientist or machine learning engineer. So, let's dive in, embrace the world of matrices, and unlock the secrets of data science and machine learning together!
A chi è rivolto questo corso:
- Students and professionals interested in the math behind AI, data science and machine learning
Insegnanti
- Valutazione dell'insegnante: 4,7
- 198.463 recensioni
- 621.599 studenti
- 44 corsi
The Lazy Programmer is a seasoned online educator with an unwavering passion for sharing knowledge. With over 10 years of experience, he has revolutionized the field of data science and machine learning by captivating audiences worldwide through his comprehensive courses and tutorials.
Equipped with a multidisciplinary background, the Lazy Programmer holds a remarkable duo of master's degrees. His first foray into academia led him to pursue computer engineering, with a specialized focus on machine learning and pattern recognition. Undeterred by boundaries, he then ventured into the realm of statistics, exploring its applications in financial engineering.
Recognized as a trailblazer in his field, the Lazy Programmer quickly embraced the power of deep learning when it was still in its infancy. As one of the pioneers, he fearlessly embarked on instructing one of the first-ever online courses on deep learning, catapulting him to the forefront of the industry.
Beyond the realm of education, the Lazy Programmer possesses invaluable hands-on experience that has shaped his expertise. His ventures into online advertising and digital media have yielded astounding results, propelling click-through rates and conversion rates to new heights and boosting revenues by millions of dollars at the companies he's worked for. As a full-stack software engineer, he boasts intimate familiarity with an array of backend and web technologies, including Python, Ruby on Rails, C++, Scala, PHP, Javascript, SQL, big data, Spark, and Redis.
While his achievements in the field of data science and machine learning are awe-inspiring, the Lazy Programmer's intellectual curiosity extends far beyond these domains. His fervor for knowledge leads him to explore diverse fields such as drug discovery, bioinformatics, and algorithmic trading. Embracing the challenges and intricacies of these subjects, he strives to unravel their potential and contribute to their development.
With an unwavering commitment to his students and a penchant for simplifying complex concepts, the Lazy Programmer stands as an influential figure in the realm of online education. Through his courses in data science, machine learning, deep learning, and artificial intelligence, he empowers aspiring learners to navigate the intricate landscapes of these disciplines with confidence.
As an author, mentor, and innovator, the Lazy Programmer leaves an indelible mark on the world of data science, machine learning, and beyond. With his ability to demystify the most intricate concepts, he continues to shape the next generation of data scientists and inspires countless individuals to embark on their own intellectual journeys.
- Valutazione dell'insegnante: 4,7
- 198.463 recensioni
- 620.869 studenti
- 44 corsi
The Lazy Programmer is a seasoned online educator with an unwavering passion for sharing knowledge. With over 10 years of experience, he has revolutionized the field of data science and machine learning by captivating audiences worldwide through his comprehensive courses and tutorials.
Equipped with a multidisciplinary background, the Lazy Programmer holds a remarkable duo of master's degrees. His first foray into academia led him to pursue computer engineering, with a specialized focus on machine learning and pattern recognition. Undeterred by boundaries, he then ventured into the realm of statistics, exploring its applications in financial engineering.
Recognized as a trailblazer in his field, the Lazy Programmer quickly embraced the power of deep learning when it was still in its infancy. As one of the pioneers, he fearlessly embarked on instructing one of the first-ever online courses on deep learning, catapulting him to the forefront of the industry.
Beyond the realm of education, the Lazy Programmer possesses invaluable hands-on experience that has shaped his expertise. His ventures into online advertising and digital media have yielded astounding results, propelling click-through rates and conversion rates to new heights and boosting revenues by millions of dollars at the companies he's worked for. As a full-stack software engineer, he boasts intimate familiarity with an array of backend and web technologies, including Python, Ruby on Rails, C++, Scala, PHP, Javascript, SQL, big data, Spark, and Redis.
While his achievements in the field of data science and machine learning are awe-inspiring, the Lazy Programmer's intellectual curiosity extends far beyond these domains. His fervor for knowledge leads him to explore diverse fields such as drug discovery, bioinformatics, and algorithmic trading. Embracing the challenges and intricacies of these subjects, he strives to unravel their potential and contribute to their development.
With an unwavering commitment to his students and a penchant for simplifying complex concepts, the Lazy Programmer stands as an influential figure in the realm of online education. Through his courses in data science, machine learning, deep learning, and artificial intelligence, he empowers aspiring learners to navigate the intricate landscapes of these disciplines with confidence.
As an author, mentor, and innovator, the Lazy Programmer leaves an indelible mark on the world of data science, machine learning, and beyond. With his ability to demystify the most intricate concepts, he continues to shape the next generation of data scientists and inspires countless individuals to embark on their own intellectual journeys.