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he learning of the introductory machine is required for Mathematics
he learning of the introductory machine is required for Mathematics
Over the past few months, I have been communicating with some people who have started to cut into the field of data science and actively use ML technology to explore statistical rules, or to build perfect data driven products. However, I find that the reasons for the unsatisfactory results of statistical analysis are the lack of necessary mathematical intuition and knowledge framework. That's the main reason why I decided to write this blog.
It
Recently, many easy to use machine learning and deep learning device packages, such as scikit-learn, Weka, tensorflow, r-caret and so on, have been developed. Machine learning theory is related to statistics, probability, computer science and algorithm, and can be used to build intelligent applications. Although machines and deep learning have unlimited prospects, a thorough mathematical understanding of these techniques is necessary to control internal operations and achieve better results.
Why do we need to emphasize mathematics?
There is no doubt that mathematics is important in machine learning, for example, you need:
1. select the appropriate algorithm, including thinking accuracy, exercise time, model complexity, parameters and quantitative characteristics.
2. choice of parameter setting and textual research strategy;
3. through the understanding bias bias trade-off to identify the lack of fitting and over fitting;
4. estimate the correct confidence interval and uncertainty.
Demand has the root of Mathematics:
How many mathematical skills do we need to understand the technology of machine learning? There is no uniform answer to this question, but usually it varies from person to person. The mathematical formulas and theoretical discussions of machine learning are being stopped, and the researchers are developing more advanced technology, so it is not easy to answer this question. Next, I will discuss the minimum math level and the importance of each mathematical concept I believe to be the machine learning scientist / engineer from the following aspects.
1. Linear Algebra: in ML, linear algebra is everywhere. Principal component analysis (PCA), singular value synthesis (SVD), characteristic synthesis of matrices, LU synthesis, QR synthesis / factorial synthesis, symmetric matrices, orthogonalization and orthogonalization, matrix operations, projection, eigenvalues and eigenvectors, vector spaces and standards are all necessary for understanding machine learning and optimization. Surprisingly, linear algebra has many online resources. I keep saying that traditional classrooms are dying because there are lots of resources on the Internet. My favorite linear algebra course is MIT (Gilbert Strang) course.
2. probability theory and Statistics: machine learning and statistics have many similar centers. In practice, someone has recently defined machine learning as "statistical data on Mac". Machine learning needs the comprehensive knowledge of basic statistics and probability theory, such as probability rules and axioms, Bias's theorem, random variable, variance and hope, condition and combination spread, standard dispersion (Bernoulli, binomial, polynomial, mean and Gauss), moment generation function, maximum likelihood estimation (MLE), prior and after. Test, maximum a posteriori (MAP) and sampling method.
3. multivariate calculus: the main categories include calculus, partial derivative, vector value function, gradient direction, Hessian matrix, Jacobi matrix, Laplasse and Lagrange dispersion.
4. algorithm and complexity Optimization: These are important in evaluating the efficiency and scalability of computation, or when applying dense matrices. Requirement learning includes data structures (two forked trees, hash, heap, stack, etc.), dynamic programming, random and linear algorithms, graphics, gradient / random landing and primal duality.
5. others: including other mathematical topics not covered in the four main areas mentioned above. They include real and complex analysis (confluence and sequence, topology, metric space, single value and continuous function, restriction, Cauchy kernel, Fu Liye transform), information theory (entropy, information gain), function space and Manifolds manifold.
Some machine learning enthusiasts are beginners in mathematics. For beginners, you don't need to control many mathematical knowledge to start machine learning.
Such
It
Recently, many easy to use machine learning and deep learning device packages, such as scikit-learn, Weka, tensorflow, r-caret and so on, have been developed. Machine learning theory is related to statistics, probability, computer science and algorithm, and can be used to build intelligent applications. Although machines and deep learning have unlimited prospects, a thorough mathematical understanding of these techniques is necessary to control internal operations and achieve better results.
Why do we need to emphasize mathematics?
There is no doubt that mathematics is important in machine learning, for example, you need:
1. select the appropriate algorithm, including thinking accuracy, exercise time, model complexity, parameters and quantitative characteristics.
2. choice of parameter setting and textual research strategy;
3. through the understanding bias bias trade-off to identify the lack of fitting and over fitting;
4. estimate the correct confidence interval and uncertainty.
Demand has the root of Mathematics:
How many mathematical skills do we need to understand the technology of machine learning? There is no uniform answer to this question, but usually it varies from person to person. The mathematical formulas and theoretical discussions of machine learning are being stopped, and the researchers are developing more advanced technology, so it is not easy to answer this question. Next, I will discuss the minimum math level and the importance of each mathematical concept I believe to be the machine learning scientist / engineer from the following aspects.
1. Linear Algebra: in ML, linear algebra is everywhere. Principal component analysis (PCA), singular value synthesis (SVD), characteristic synthesis of matrices, LU synthesis, QR synthesis / factorial synthesis, symmetric matrices, orthogonalization and orthogonalization, matrix operations, projection, eigenvalues and eigenvectors, vector spaces and standards are all necessary for understanding machine learning and optimization. Surprisingly, linear algebra has many online resources. I keep saying that traditional classrooms are dying because there are lots of resources on the Internet. My favorite linear algebra course is MIT (Gilbert Strang) course.
2. probability theory and Statistics: machine learning and statistics have many similar centers. In practice, someone has recently defined machine learning as "statistical data on Mac". Machine learning needs the comprehensive knowledge of basic statistics and probability theory, such as probability rules and axioms, Bias's theorem, random variable, variance and hope, condition and combination spread, standard dispersion (Bernoulli, binomial, polynomial, mean and Gauss), moment generation function, maximum likelihood estimation (MLE), prior and after. Test, maximum a posteriori (MAP) and sampling method.
3. multivariate calculus: the main categories include calculus, partial derivative, vector value function, gradient direction, Hessian matrix, Jacobi matrix, Laplasse and Lagrange dispersion.
4. algorithm and complexity Optimization: These are important in evaluating the efficiency and scalability of computation, or when applying dense matrices. Requirement learning includes data structures (two forked trees, hash, heap, stack, etc.), dynamic programming, random and linear algorithms, graphics, gradient / random landing and primal duality.
5. others: including other mathematical topics not covered in the four main areas mentioned above. They include real and complex analysis (confluence and sequence, topology, metric space, single value and continuous function, restriction, Cauchy kernel, Fu Liye transform), information theory (entropy, information gain), function space and Manifolds manifold.
Some machine learning enthusiasts are beginners in mathematics. For beginners, you don't need to control many mathematical knowledge to start machine learning.
Such