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Optimization for Machine Learning with NumPy and SciPy

Gain insights into optimization for machine learning. Delve into gradients, convex optimization, and gradient descent. Explore constrained optimization and advanced methods using NumPy and SciPy to enhance your data science skills.

Intermediate

62 Lessons

Certificate of Completion

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Explanations

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Explanations

This course includes

1 Project

1 Assessment

43 Playgrounds

12 Challenges

6 Quizzes

Course Overview

What You'll Learn

Course Content

Course Overview

In this course, you will learn about optimization, one of the fundamental pillars of mathematics and machine learning. Machine learning depends heavily on optimization because it allows the model to learn from data and generate precise predictions. You will begin by introducing optimization. Then, you will learn about optimization basics, including gradients and integrals. Next, you will cover convex optimization. You will then learn how to compute gradient descent for non-convex optimization. Next, you’ll...Show More

TAKEAWAY SKILLS

Optimization

Machine Learning

Plotting

What You'll Learn

An understanding of how real-world problems can be framed as optimization problems

Working knowledge about the taxonomy of optimization problems and techniques

Familiarity with the fundamental concepts of optimization

Hands-on experience implementing popular optimization algorithms

The ability to solve popular machine learning problems using optimization

An understanding of how real-world problems can be framed as optimization problems

Course Content

Introduction to Optimization

8 Lessons

Get familiar with optimization techniques, algorithms, and their applications in machine learning.

What Is This Course About?

The Motivation for Optimization

Random Search Optimization

Grid Search Optimization

The Nelder-Mead Algorithm

Quiz Yourself on Optimization

Challenge: Grid Search

Solution: Grid Search

Vector Calculus

10 Lessons

Discover the logic behind differentiation, gradients, Hessian, Taylor series, and integrals in vector calculus.

Differentiation of the Univariate Functions

Partial Derivatives and Gradients

Gradients of the Vector-Valued Functions

Gradients of Matrices

Higher-Order Gradients: Hessian

Linearization and the Taylor Series

Integrals and the Trapezoidal Rule

Quiz Yourself on Vector Calculus

Challenge: The Taylor Series

Solution: The Taylor Series

Convex Optimization

14 Lessons

Examine convex optimization techniques, including gradient methods, ridge regression, and Fisher analysis.

Convex Sets and Functions

Gradient-Solving Approach

Solving Ridge Regression

Fisher Discriminant Analysis

Maximum Likelihood Estimation (MLE)

Maximum A Posteriori (MAP)

Alternating Least Squares Regression

Gradient Descent: Logistic Regression

Subgradient Descent—Lasso Regression

Steepest Descent

Coordinate Descent

Quiz Yourself on Convex Optimization

Challenge: Convex Optimization

Solution: Convex Optimization

Gradient Descent for Non-Convex Optimization

10 Lessons

Grasp the fundamentals of advanced gradient descent techniques for optimizing non-convex problems.

Limitations of Gradient Descent

Minibatch Gradient Descent

The Nesterov Momentum

Nesterov Accelerated Gradient (NAG)

Adaptive Gradient Descent

Root Mean Square Propagation (RMSProp)

Adaptive Moment Estimation (Adam)

Quiz Yourself on Non-Convex Optimization

Challenge: Non-Convex Optimization

Solution: Non-Convex Optimization

Constrained Optimization

10 Lessons

Explore constrained optimization using linear programming, simplex method, and Lagrange duality.

Linear Programming (LP): Formulation

The Simplex Tableau Method

Quadratic Programming (QP)

Lagrange Duality

The Dual of Linear Programming (LP)

The Dual of Quadratic Programing (QP)

Integer Linear Programming (ILP)

Quiz Yourself on Constrained Optimization

Challenge: Constrained Optimization

Solution: Constrained Optimization

Miscellaneous Methods

9 Lessons

Tackle diverse optimization techniques, including Newton's, Quasi-Newton, barrier methods, and SciPy utilities.

Newton’s Method

Quasi-Newton Methods

Conjugate Gradient Descent

The Log Barrier Method

SciPy Utilities

Interpolation and Curve Fitting

Quiz Yourself on Miscellaneous Methods

Challenge: The Log Barrier Method

Solution: The Log Barrier Method

Course Conclusion

1 Lessons

Build on essential optimization techniques for machine learning, enhancing models with advanced algorithms.

Conclusion

Test Your Concepts of Optimization

Assessment

Training Support Vector Machines (SVMs)

Project

Course Author

Puneet Mangla

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