How to get started with machine learning in general mathematics

秋天不回来

How to get started with machine learning in general mathematics [Copy link]

 

How to get started with machine learning in general mathematics

采菊东篱下

You probably already have some basic math skills, which will serve you well in learning machine learning. Here are some steps you can take to get started with the math for machine learning:

1. Linear Algebra :

   • Linear algebra is one of the most basic mathematical concepts in machine learning. Learn concepts such as vectors, matrices, linear transformations, eigenvalues, and understand their applications in machine learning, such as feature transformation, dimensionality reduction, and matrix decomposition.

2. calculus :

   • Understand the basic concepts of calculus, including derivatives, partial derivatives, integrals, etc. These concepts have important applications in optimization algorithms, solving loss functions, etc.

3. Probability and Statistics :

   • Understand statistical concepts such as probability distribution, expectation, variance, hypothesis testing, parameter estimation, etc. This knowledge is very important in understanding the probabilistic basis of machine learning models, model evaluation and inference, etc.

4. Optimization :

   • Learn about optimization algorithms like Gradient Descent, Stochastic Gradient Descent, Newton's Method, etc. These algorithms play a vital role in the training process of machine learning models.

5. Information Theory :

   • Understand the basic concepts of information theory such as information entropy and mutual information. These concepts have important applications in algorithms such as decision trees and information gain.

6. Learning Resources :

   • Find some high-quality learning resources, such as textbooks, online courses, video tutorials, etc. Books such as "Linear Algebra and Its Applications", "Statistical Learning Methods", and "Probability Theory and Mathematical Statistics" are all good learning materials.

7. Practical projects :

   • Try to apply the mathematical knowledge you have learned through practical projects, such as implementing some simple machine learning algorithms using Python or other programming languages, and conducting experiments and verification on real data sets.

Through the above steps, you can build the mathematical foundation required for machine learning and gradually gain a deeper understanding of the application of mathematics in machine learning. I wish you good luck in your study!

王元元

If you want to get started with machine learning, a mathematical foundation is very important. Machine learning involves a lot of mathematical knowledge, including linear algebra, calculus, probability theory, and statistics. Here are some systematic suggestions to help you lay a solid mathematical foundation and gradually enter the field of machine learning.

1. Linear Algebra

Linear algebra is very important in machine learning because many algorithms rely on matrix operations. You need to understand the following concepts:

• Matrices and Vectors : Understand the basic operations of matrices and vectors, such as addition, multiplication, transposition, etc.
• Determinant and inverse matrix : Master the calculation of determinant and the method of finding inverse matrix.
• Eigenvalues and Eigenvectors : Understand the concepts of eigenvalues and eigenvectors and their applications in matrix decomposition.
• Singular Value Decomposition (SVD) : This is a matrix decomposition method commonly used in machine learning.

Recommended textbooks:

• Linear Algebra and Its Applications by Gilbert Strang
• "Introduction to Linear Algebra" by Gilbert Strang

2. Calculus

Calculus is crucial in optimization algorithms and analysis of continuous functions. You need to understand the following:

• Derivatives and Integrals : Understand the basic concepts of derivatives and integrals, and be able to perform simple differential and integral calculations.
• Multivariable Calculus : Learn the basic concepts of multivariable calculus such as partial derivatives, gradients, divergences, and curl.
• Chain Rule and Taylor Series : Understand the application of the chain rule to differentiation of composite functions and Taylor series expansion.

Recommended textbooks:

• Calculus by James Stewart
• "Thomas' Calculus" by George B. Thomas

3. Probability Theory and Statistics

Probability theory and statistics are used in machine learning for data analysis, model evaluation, and algorithm design. You will need to master the following:

• Basic probability concepts : events, sample space, probability distribution, conditional probability and independence.
• Random variables : Discrete and continuous random variables and their probability distributions, such as binomial distribution, normal distribution, etc.
• Expectation and Variance : Understand the concepts and calculations of expected value, variance, and covariance.
• Bayes’ Theorem : Master Bayes’ Theorem and its applications in machine learning.
• Statistical Inference : Understand the basic principles of point estimation, interval estimation, and hypothesis testing.

Recommended textbooks:

• Probability Theory and Mathematical Statistics by Higher Education Press
• "Introduction to Probability and Statistics for Engineers and Scientists" by Sheldon M. Ross

4. Practical Application

It is more effective to learn mathematical theory while practicing with actual machine learning projects. Here are some recommended online courses and resources:

• Coursera : Andrew Ng's "Machine Learning" course, which not only explains machine learning algorithms, but also introduces the mathematical principles behind them.
• edX : MIT's "Introduction to Computational Thinking and Data Science", which covers the foundations of data analysis and statistical inference.
• Khan Academy : Offers free and detailed courses in linear algebra, calculus, and probability theory.

5. Tools and Programming

Mastering some tools and programming languages, such as Python and its scientific computing libraries (NumPy, SciPy, Pandas), as well as machine learning libraries (Scikit-Learn, TensorFlow, PyTorch), will help you better understand and apply mathematical knowledge in practice.

6. Reference Books

• Machine Learning in Action by Peter Harrington
• Deep Learning by Ian Goodfellow, Yoshua Bengio, Aaron Courville

By systematically studying the above mathematical knowledge and practicing it with actual projects, you will be able to firmly grasp the mathematical foundations required for machine learning, thereby better understanding and applying various machine learning algorithms.

Amybaby

Getting started with machine learning requires some basic math knowledge as a prerequisite. Here are the steps you can follow:

1. Linear Algebra : Linear Algebra is one of the most fundamental mathematical concepts in machine learning. You need to understand concepts such as vectors, matrices, determinants, eigenvalues, and eigenvectors. This knowledge is very important for understanding models and algorithms in machine learning.

2. Calculus : Calculus is another fundamental mathematical concept in machine learning. You need to understand concepts such as derivatives, partial derivatives, gradients, and Taylor series. This knowledge is essential to understand the optimization algorithms and model training process in machine learning.

3. Probability and Statistics : Probability and statistics are one of the cornerstones of machine learning. You need to understand concepts such as probability distribution, expectation, variance, hypothesis testing, confidence intervals, etc. This knowledge is very important for understanding probabilistic models and statistical inference in machine learning.

4. Optimization theory : Optimization theory is one of the key concepts in machine learning. You need to understand concepts such as convex optimization, non-convex optimization, gradient descent, etc. This knowledge is essential to understand the optimization algorithms and model training process in machine learning.

5. Deep Learning Theory : If you are interested in going deeper into the field of machine learning, you can learn more advanced mathematical concepts such as graph theory, information theory, functional analysis, etc. This knowledge is very helpful for understanding advanced machine learning algorithms such as deep learning.

You can learn this math by self-study or by taking a course. Some excellent online courses, such as Coursera's "Machine Learning Basics" or "Deep Learning Specialization", provide great learning resources. In addition, you can also read relevant textbooks or academic papers to deepen your understanding of the mathematical foundations of machine learning. Good luck with your studies!