How high is the requirement of machine learning for mathematical skills?

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What kind of mathematical foundation is needed to learn machine learning?

From: Qiuzhen 2013-07-113: 44: 22.

I am a small master, and my research direction is machine learning. By reading some teaching materials of machine learning, it is found that machine learning needs a higher mathematical foundation.

Excuse me: What kind of mathematical foundation do you need for general learning machine learning?

Can basic mathematics courses such as advanced mathematics, linear algebra and probability theory be used in our university?

Skynet 2013-07-1215: 30: 26

Look at the direction, but no direction is enough. Make up for your own shortcomings. Mathematics is a pit, so is machine learning. People can't struggle in two pits at the same time.

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Skynet 2013-07-1215: 30: 26

Look at the direction, but no direction is enough. Make up for your own shortcomings. Mathematics is a pit, so is machine learning. People can't struggle in two pits at the same time.

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Seeking the truth 2013-07-1216: 07: 20

Look at the direction, but no direction is enough. Make up for your own shortcomings. Mathematics is a pit, so is machine learning. People can't be like people. ...

Uh-huh, okay.

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French franc 2065438

Well said. I like it.

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Opera 2014-06-0915: 43: 56

Advanced mathematics, linear algebra and probability theory are definitely important. There may be something else besides them.

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Mr. Wang (long life) 2014-06-09 20: 51:39

What about the application field?

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Paopaolong 2014-07-0317:16: 37

The concrete points should be calculus, probability theory, linear algebra, random distribution and convex optimization.

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Seeking truth +04-07-06 10: 46: 35

The concrete points should be calculus, probability theory, linear algebra, random distribution, convex optimization bubble dragon.

thank you

Zhihu's topic:

If machine learning only aims at application, how much mathematics … such as differential manifold, algebraic topology, functional, etc., do you understand?

"For application purposes only" is a bit vague. . At first glance, the topic seems to be used in the company, but later a large number of courses came out, which seems to be academic. . The feelings mentioned by previous scholars are more academic. Let me add some information about the industry.

Generally speaking, I prefer anonymous users' answers. If machine learning only aims at application, how much mathematics … such as differential manifold, algebraic topology, functional, etc., do you understand? -Answers from anonymous users

Before thinking about this problem, we must first find out what the company pays you for. My experience is that there are two situations. First, the company had no business before, and now it has to run some machine learning things (starting from scratch). Second, the company had a certain foundation when you took over, and now you need to adjust your performance (from poor to excellent). The former doesn't need any mathematics at all, and it is king to build a system with other people's modules/codes first. The latter depends on specific problems, and in most cases mathematics is not used.

Starting from scratch, for example, I used to do place deduplication on facebook, which probably means I have to die. There are too many places to stay, so it is necessary to judge which places are duplicate. Similar to Zhihu, there are many repetitive problems. How to identify and redirect these problems? This problem is not difficult from the perspective of machine learning, and there are many existing jobs. But the company is more concerned about how to build any system on fb tens of TB data. So most of our time is not spent evaluating which machine learning model is better, what is the essence of this manifold, and what is the lower limit of that system, but-Hadoop uses thousands of cores to extract features first. After the feature, the background classifier is randomly found by the mother. Will I talk nonsense? This situation has nothing to do with mathematics.

I also participated in this project from the best to the best tuning. The basic experience is-classifier, model, no matter how complex and exquisite the mathematical nature, the key is to look at the characteristics. Get an effective feature and the accuracy will go up. There is basically no difference between blindly changing JB and tuning for various classifiers. . (of course, except for the qualitative change in the mode of deep learning, but this has nothing to do with people who don't engage in scientific research. ) So you have to ask if mathematics is useful. I said yes, and you can put forward an effective model based on mathematics-but this special matrix is used by people who have been grinding their swords for ten years in academia. Put it in the company and use math arch KPI to be killed by nen in minutes. Wang next door got a lot of new function bonuses, and here you have to bite the functional products to death. .

Of course, it is still useful in some research places, such as some departments of Google X, but I think it is still academic.

Generally speaking, my advice is that if you want to go to the company, don't worry about anything too high. Learn linear algebra, statistics, convex optimization, and go out to play tricks. Saving the system experience and dirty tricks is king. Of course, I'm not saying that you shouldn't do math. Only if you go to the company, it is more cost-effective to spend the same time learning the computer system structure and systematic thinking method on the premise of learning the statistical convex optimization of line generation.

Edited on 20 15-04-09 35. Thank you.

This is an application of the 80-20 principle.

As long as 20% of machine learning knowledge, in fact, it can achieve satisfactory results in 80% of commercial applications.

But if it is a company that strives for perfection, or a company that focuses on machine learning algorithms, it may be necessary to invest exponential efforts to achieve performance improvement.

I came uninvited and switched from mathematics to data science, which is an application-oriented machine learning. During my nine years as a doctor, I have probably studied mathematics courses: mathematical analysis (calculus), linear algebra, probability theory, statistics, applied statistics, numerical analysis, ordinary differential equations, partial differential equations, numerical partial differential equations, operational research, discrete mathematics, random processes, random partial differential equations, abstract algebra, real variable functions, functional analysis, complex variable functions, mathematical modeling, and so on.

From my personal learning process, I think the mathematics disciplines that are helpful to the application of machine learning are (from high to low in importance):

1, Linear Algebra (or Higher Algebra): If necessary, all algorithms will be represented by vectorization in the end. If you are not familiar with linear algebra, the algorithm cannot be understood.

2. Calculus: This is the basis of all advanced mathematics, so I won't elaborate on it.

3. Statistics: This includes the theoretical basis of statistics and applied statistics (mainly linear models). The predecessor of many machine learning contents is statistics.

3.5, convex optimization: supplemented by @ Xu Wenhao, for reasons similar to 6.

The first three senses are necessary for learning machine learning well, and the latter is not necessary, but it is also very helpful after proper understanding:

4. Probability theory: Basic probability theory is enough, and advanced probability theory based on measurement is not helpful for machine learning.

5. Numerical analysis: A part of numerical analysis includes interpolation, fitting, numerical solution of various equations and numerical integration. Although these tips are not directly related to machine learning, they may work wonders in some small places when you deal with complex problems. Another big block of numerical analysis is numerical linear algebra, including how to find the inverse of matrix, various decomposition of matrix and singular value of matrix characteristic root. Many algorithms in it will be directly used by machine learning calligraphy. For example, principal component analysis directly calls SVD.

6. operational research: operational research is to do optimization. To put it bluntly, it is to express the problem as a mathematical formula and constraints, and then find the maximum or minimum. So many advanced optimization algorithms in machine learning first appeared in the field of logistics.

Think so much for the time being. As for the functional, differential manifold and algebraic topology mentioned by the subject, I don't need to know anything at all.

Edited on 20 15-04-28, with 26 comments, thank you.

I just transferred from math to ML. I knew that someone must talk about the "basic background" of pure mathematics. I talk about some real knowledge of differential geometry, manifold and algebraic topology. As long as you look up relevant research papers, you can always find the intersection with Ml. But that doesn't mean you have to master them. In most ML learning, the basic skills of calculus, linear algebra and probability statistics are the most important. Don't underestimate calculus and linear algebra. In many cases, the deduction for research still needs a lot of skilled skills to be competent. As for other knowledge, you can supplement it when you use it.

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What mathematical knowledge does machine learning need to learn [Question point: 20 points, hanyahui88 post bar]

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Hanyahui 88

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The landlord's telephone number is 2014-10-1611:07: 37.

Mathematical data analysis algorithm of machine learning

Recently, the company is doing data analysis, which I haven't contacted before. I have seen all the algorithms, many of which are related to mathematics, and I can't understand many mathematical symbols, so it seems necessary to ask me what mathematics I should study.

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OrthocenterCh ...

Kenny Qin

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# 1 score: 3 Reply: 2014-10-/613:18: 23.

As far as the machine learning algorithms I usually contact are concerned, the relevant mathematical knowledge includes: derivative, gradient, Lagrange multiplier method, Lagrange duality, Newton iteration method and so on. Mathematical knowledge is the foundation, and many machine learning algorithms are based on mathematics, but there are many numerical calculations that are not particularly related to discrete mathematics. Discrete mathematics is very important if you want to do graph algorithm.

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Hanyahui 88

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#2 Rating: 0 Reply: 2014-10-17 09:12: 48.

Quoting 1 floor orthocenterc chocolate reply: As far as the machine learning algorithms I usually come into contact with, the relevant mathematical knowledge includes: derivative, gradient, Lagrange multiplier method, Lagrange duality, Newton iteration method and so on. Mathematical knowledge is the foundation, and many machine learning algorithms are based on mathematics, but there are many numerical calculations that are not particularly related to discrete mathematics. If you want to do graph algorithm, it is discrete.

Recently, I am studying the mean shift algorithm. I can't understand many formulas in kernel function, and I don't know what math I have to learn to understand these formulas.

What do derivative, gradient, Lagrange multiplier method, Lagrange duality, Newton iteration method and so on mean?

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Lombrulin

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#3 Rating: 2 Reply: 2014-10-17 09: 51:41.

Reply from hanyahui88 on the 2nd floor: Quote: Quote 1 Floor orthocenterc Chocolate Reply: As far as the machine learning algorithms I usually come into contact with, the relevant mathematical knowledge includes: derivative, gradient, Lagrange multiplier method, Lagrange duality, Newton iteration method, etc. Mathematical knowledge is the foundation, and many machine learning algorithms are based on mathematics, and more are numerical calculation and discretization. Recently, I am studying the mean shift algorithm. I can't understand many formulas in kernel function, and I don't know what math I have to learn to understand these formulas.

What do derivative, gradient, Lagrange multiplier method, Lagrange duality, Newton iteration method and so on mean?

There seems to be nothing in numerical analysis except Lagrangian duality.

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OrthocenterCh ...

Kenny Qin

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#4 Rating: 0 Reply: 2014-10-1921:38:16.

What do derivative, gradient, Lagrange multiplier method, Lagrange duality, Newton iteration method and so on mean?

Derivation, gradient, Lagrange multiplier method in advanced mathematics, Lagrange duality, Newton iteration method. You can look at convex optimization. In fact, convex optimization should contain a lot of mathematical knowledge you want to see in machine learning, but they are based on some more basic mathematical knowledge (such as derivative).

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Hanyahui 88

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#5 Rating: 0 Reply: 2014-10-2114: 40: 54.

Quote the reply of OrthocenterChocolate on the 4th floor: Quote: Quote hanyahui88 on the 2nd floor: Quote: Quote 1 reply of OrthocenterChocolate on the 4th floor: As far as the machine learning algorithms I usually come into contact with are concerned, the relevant mathematical knowledge includes: derivative, gradient, Lagrange multiplier method, Lagrange duality, Newton iteration method, etc. Mathematical knowledge is the foundation. Many machine learning algorithms are based on mathematics, but there are many numerical calculations that are not particularly related to discrete mathematics. Discrete mathematics is very important if you want to do graph algorithm. Recently, I am studying the mean shift algorithm. I can't understand many formulas in kernel function, and I don't know what math I have to learn to understand these formulas.

What do derivative, gradient, Lagrange multiplier method, Lagrange duality, Newton iteration method and so on mean? ? Lagrange multiplier method in advanced mathematics, Lagrange duality, Newton iteration method, you can see convex optimization. In fact, convex optimization should contain a lot of mathematical knowledge in machine learning that you want to see, but they are based on some more basic mathematical knowledge (such as derivatives).

That is to say, only look at advanced mathematics and convex optimization?

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OrthocenterCh ...

Kenny Qin

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#6 Rating: 5 Reply: 2014-10-2314: 32: 40.

Quote the reply of hanyahui88 on the 5th floor: Quote: Quote: Quote the reply of hanyahui88 on the 2nd floor: Quote: Quote: Quote the reply of OrthocenterChocolate on the 6th floor: Take the machine learning algorithm that I usually contact. It is said that the relevant mathematical knowledge includes: derivative, gradient, Lagrange multiplier method, Lagrange duality, Newton iteration method and so on. Mathematical knowledge is the foundation, and many machine learning algorithms are based on mathematics, but there are many numerical calculations that are not particularly related to discrete mathematics. Discrete mathematics is very important if you want to do graph algorithm. Recently, I am studying the mean shift algorithm. I can't understand many formulas in kernel function, and I don't know what math I have to learn to understand these formulas.

That is to say, only look at advanced mathematics and convex optimization?

Yes, there are some matrix operations. If you are not familiar with them, look at linear algebra again. I suggest you check what you can't do, instead of reading it all in advance, otherwise there will be too many.

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q24302 1856

Wolf mark

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#7 Rating: 5 Reply: 2014-10-2314: 58:16.

Calculus, linear algebra, probability theory, discrete mathematics, statistics

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Shao Wei 2 13

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