[PYTHON] Summary of mathematical scope and learning resources required for machine learning and data science

In creating it, "Book for understanding mathematics for artificial intelligence programming", "Chainer Tutorial", "[Kikagaku style] Artificial intelligence / machine learning de-black box course-Beginner's edition" - ”was used as a reference.

Is Mathematics Essential for Practical Use and Introduction of Machine Learning?

From the perspective of "simply using machine learning," I don't think mathematics is essential. For example, in image posting SNS, consider harmful image detection by machine learning (a common use case). Now, if you use Google Cloud Vision API etc., you can easily incorporate the image filtering function (image detection function). You can use the trained model as it is, so you only need to incorporate the API to implement it.

Is Mathematics Essential for Machine Learning Engineers?

I think mathematics is indispensable if you call yourself a "machine learning engineer" rather than just using machine learning. The common AI programming school "No math!" Is just a catch phrase that feels good to the ear. It just gives the desired answer to the need to become an AI engineer if you are not good at math.

Machine learning and deep learning do not require so advanced programming skills, but I think that it is a world where mathematical backgrounds make a difference (React Native, Redux, TypeScript, etc. are much more difficult code. Then?).

The fact that mathematicians and physicists often turn into the field of machine learning and play an active role is proof of that.

List of mathematics for machine learning

Roughly speaking, ** "differentiation", "linear algebra", and "probability statistics" ** are required. And in order to understand them, we need ** "foundation of mathematics" ** such as sequences and trigonometric functions as prerequisite knowledge. In summary, about four items are required: "mathematical basics *", "differentiation", "linear algebra", and "probability statistics".

Although it has been collectively referred to as "foundation of mathematics", it is a bold theme such as "exponential function", "sequence", and "trigonometric function". If you are not confident, it will be difficult if you do not study properly using the Masema, etc. described later.

Foundations of mathematics

--Variables / constants --Order of expression --Function concept --Square root --Exponentiation and root --Exponential function / logarithmic function (log) --Natural logarithm (e/ln/exp) --Sigmoid function --Trigonometric function (sin/cos/tan) --Absolute value / Euclidean distance --Sequence --Elements and sets

differential

--Extreme (lim) --Differential foundation --Ordinary differential / partial differential --Graph description --Maximum and minimum values of the graph --Elementary function / composite function differential calculus / product differential calculus --Differentiation of special functions

linear algebra

--What is a vector? --Vector addition / subtraction / scalar times --Directed line segment --Inner product --Direct conditions --Normal vector --Vector norm --Cosine similarity --Matrix addition / subtraction --Matrix multiplication --Inverse matrix --Linear transformation --Eigenvalues and eigenvectors

Probability statistics

――What is probability? --Random variables and probability distributions --Join probability and conditional probability

Expected value --Average / variance / covariance --Correlation coefficient --Maximum likelihood estimation

Recommended books

"A book that understands mathematics for artificial intelligence programming" (Toshihiko Ishikawa)

"Written by President Ishikawa of Aidemy" "Recommended by Professor Yutaka Matsuo" Please do not refer to this area as it is just a catch phrase. Let's take a look at the contents. This book briefly summarizes the minimum mathematics required for artificial intelligence. ** The point to be evaluated is just enough coverage **, but ** on the other hand, the negative point is that the explanation of each item is thin **.

For those who have some background in mathematics, specifically those who are "not good at mathematics for university entrance exams" or "taken mathematics courses at university", efficiently use mathematics for artificial intelligence. It is a good book that you can review. However, on the contrary, it will be difficult to understand if it is only this book for those who are not, specifically those who "did not use mathematics in college entrance exams" and "have a weakness in high school mathematics".

Don't rush, let's review the basics of high school mathematics first. We recommend Massema's reference books and study supplements.

Massema "Mathematics from the beginning" series

It is a masterpiece of high school mathematics familiar with the catch phrase "The University of Tokyo students' most used mathematics reference book" (as an aside, the university mathematics reference book of Massema is often seen at the University of Tokyo Cooperative Bookstore, so it is credible. I think it's expensive).

The easy-to-speak style makes you understand the essence of mathematics carefully. To understand high school mathematics, junior high school mathematics is required as a prerequisite knowledge, but Massema looks back on the contents of junior high school mathematics and explains it.

I think that a proper review of high school mathematics as a whole seems to be a detour and is the shortest route after all.

As an aside, "Mathematics starting from the beginning" only explains the basic concept, so if you are going to take a university entrance exam, you can use "Math that gives you energy", "Mathematics that grows well", or "Chart formula". You need to do it. This time, all you have to do is acquire the mathematics necessary to understand machine learning, so it's okay if you understand the basic concepts properly. Doesn't it seem a lot easier when you think about it?

"Mathematics I Revised 8 Starting from the Beginning" (Takayuki Baba) "Mathematics A from the beginning A revision 8" (Takayuki Baba) "Mathematics II from the beginning revision 8" (Takayuki Baba) "Mathematics B Revised 8 Starting from the Beginning" (Takayuki Baba) "Mathematics III Part 1 Revised 7 from the beginning" (Takayuki Baba) "Mathematics from the beginning III Part2 Revised 7" (Takayuki Baba)

Massema University Mathematics "Campus Seminar" Series

Massema's College Mathematics Series. Ideally, if you can afford it, you should also study university mathematics. I feel that mathematical background is more important than programming skills in data science. For example, tuning parameters tends to waste time, but if you have a mathematical sense, it will go smoothly.

As an aside, Mr. Gochi, the founder of UTEC (Bunichi, University of Tokyo ⇨ enrolled in the Doctor of Engineering at the University of Tokyo after working at the Ministry of International Trade and Industry), also reviewed mathematics at Massema when he re-entered the research institute.

"I decided to take the exam in October of the year before last, and did my best in math after work and on holidays. I haven't done mathematics at university, so I couldn't do family services at all on Saturdays, Sundays, and summer vacations. I was lucky

Source: * Approaching Mr. Goji, the president of UTEC, who is investing in a venture from the University of Tokyo! !! *

"Linear Algebra Campus Seminar Revised 8" (Takayuki Baba) "Differential Integral Campus Seminar Revised 6" (Takayuki Baba) "Probability Statistics Campus Seminar Revised 6" (Takayuki Baba)

At the end

If you have the basic skills in mathematics, you don't need to do anything special. Especially if you can study properly at the level of university mathematics at Massema, you will be able to read mathematical formulas in machine learning and deep learning books and treatises.

Also, since providing a place for output is an effective learning technique, I think it is good to take a number test or a statistical test.

Reference material

"Book for understanding mathematics for artificial intelligence programming" Chainer Tutorial [Kikagaku style] Artificial intelligence / machine learning de-black box course --Beginner-

"Mathematics I Revised 8 Starting from the Beginning" (Takayuki Baba) "Mathematics A from the beginning A revision 8" (Takayuki Baba) "Mathematics II from the beginning revision 8" (Takayuki Baba) "Mathematics B Revised 8 Starting from the Beginning" (Takayuki Baba) "Mathematics III Part1 Revised 7 Starting from the Beginning" (Takayuki Baba) "Mathematics from the beginning III Part2 Revised 7" (Takayuki Baba)