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There are many opinions on the relationship between mathematics and machine learning.

The purpose of writing this paper is to try to solve the perplexity of mathematics to machine learning.

Now mathematics puzzles us mainly in these aspects:

1. Is the mathematical knowledge required for machine learning so difficult that you can’t understand the formulas on the Internet?

2, a lot of people say that after work is to adjust, switch, do not need to use mathematics?

3, zero basis on earth how to self-study mathematics, learn which degree?

View:

1. Math is a must.

Mathematics is a necessary foundation for machine learning. Mathematics is internal work. You need to understand the internal logic of an algorithm. In the future, when you’re running an algorithm, you might just tune and switch, without using math. But when you find it doesn’t work, it’s hard to optimize if you don’t know the math, which is your ceiling on machine learning.

2. Math is not too difficult.

But is math really hard? To be honest, for the average person, it is a little threshold, but not as difficult as you think. Assuming you’ve taken a college math class, you’ve got the math threshold for machine learning, and you can get down with a bit of math. If you have not taken college mathematics, EMMM, it is very difficult, which means that you have to pay more college mathematics in addition to the same effort as others.

3. Practical project ability is more important than mathematics.

That’s true, but most people are locked out of the actual project before they even get to it. A lot of people who are engaged in machine learning, if you ask them math, they may not understand it very well, but what can you do? That’s what they’re going to ask you when they interview you, and they’re going to ask you what you know about algorithms, and you’re not going to pass the interview.

Learning is boring, but there are ways to alleviate it.

When we’re learning an algorithm, we see a lot of derivation, we get scared, we lose interest, and here’s a way to do that. There’s a book in my previous series called Machine Learning in action, and it’s very easy to follow the code above, and you’ll see it in real life, and it’s very rewarding.

5, the study of mathematics can be “clever”

What I mean by cheat is that there’s a track record for learning math, because that’s what entry-level math actually requires, just list it out and do it yourself. The way to learn algorithms is not to wait until you’ve learned all the math. It’s that when you’re learning an algorithm, it’s most efficient to see what you’re missing in math and fill it in. Of course, you can read through the basics of math before that, which is probably better for learning.

Essential Knowledge of Mathematics

1. Linear algebra

Scalars, vectors, matrices and tensors; Matrix vector operation; Identity matrix and inverse matrix; The determinant; Variance, standard deviation, covariance matrix; Norm; Special types of matrices and vectors; Feature decomposition and its significance; Singular value decomposition and its significance

Moore – Penrose pseudo inverse; Trace operation

2. Probability and statistics

Probability school and Bayes school; What are random variables and what are probability distributions? Conditional probability, joint probability and total probability formulas; Edge probability; Independence and conditional independence; Expectation, variance, covariance and correlation coefficient; Common probability distribution; Bayes and its application; Central limit theorem; Maximum likelihood estimation; Independent isodistributions in probability theory

3, optimize

Computational complexity and NP problem; Overflow and underflow; Derivative, partial derivative and two special matrices; Directional derivatives and gradients; Gradient descent method; Newton’s method. Affine set, convex set and convex cone; Hyperplane, half space and convex set separation theorem; Operations that do not change convexity; Convex function and convex optimization; Unconstrained optimization, equality constrained optimization, inequality constrained optimization; Duality theory in linear programming; Lagrange duality theory

4. Information and others

The information entropy; Conditional entropy; Relative entropy (KL divergence); Mutual information; Several commonly used distance measures; Graph theory; The theory of tree

That’s basically all the math we have to learn, so it’s kind of scary, right? Don’t panic, it’s not that difficult, just a little bit down.

Recommended information:

Data 1: Machine learning ace course CS229, supporting mathematics, specifically supporting machine learning.

Link: https://pan.baidu.com/s/1Fh__7N7rqGEgjsyb4YpNSg password: 48 n4 interchange

Data 2: Yoshua Bengio’s book deep Learning, which is published on the Internet, has a part of special explanation on mathematics in the front, which is very basic and comprehensive.

Link: https://pan.baidu.com/s/1A9mcO8_ORQmTJ-V7z9bLdw password: HWJN

Information three: zhihu answer the Lord’s excellent answer, very detailed, suitable for beginners

Line generation column: https://zhuanlan.zhihu.com/p/30191876

Probability and statistics: https://zhuanlan.zhihu.com/p/30314229

Optimization (top) : https://zhuanlan.zhihu.com/p/30383127

Optimization (under) : https://zhuanlan.zhihu.com/p/30486793

Information about other: https://zhuanlan.zhihu.com/p/30383356

I’ve read a lot of math materials, and the top three are the best I’ve come up with and must see. But everyone’s basis is different, maybe after watching the above three, there is still a need to see others.

What if math is too weak?

If you are struggling with the above three materials, or if your math is not up to college level. That’s a question of basic mathematics. In view of this situation, I feel that I can only take out the relevant university mathematics books to look over, to understand the basic concepts, what is matrix, derivative and so on, can not steal lazy.

Mathematical analysis and Probability Theory

Department of Mathematics, Tongji University, Higher Mathematics, Higher Education Press, 1996

Wang songgui, Cheng Weihu, gao Luduan, Probability Theory and Mathematical Statistics, Science Press, 2000

Matrix and linear algebra

Department of Mathematics, Tongji University, Ed., Linear Algebra of Engineering Mathematics (5th edition), Higher Education Press, 2007

If you forget the basic concepts of these three math books, you can choose to read the corresponding chapters.

To reiterate:

The best way to learn math is to learn while supplementing. There is no need to understand 100% of the derivation process of math. It is enough to understand 70% at the primary stage. Online often see hundreds of dollars of math courses, I hope you will not be cut IQ tax.

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