Do you have this classic bestseller in the field of deep learning 《 Deep learning 》, Is there something you can't understand ? Are you worried about some math problems , Have you given up reading this classic book because of math problems . I'll give you a move .
You can prepare one 《 Mathematics of machine learning 》 Master the mathematical knowledge in machine learning . Let's look at deep learning .
Why do you say that? , Let's look at reading first 《 Deep learning 》 Mathematics knowledge needed . Take a look at the second one in the picture below 1 This part introduces the basic mathematical tools and the concept of machine learning .
Look again 《 Mathematics in machine learning 》 What mathematical knowledge is used in this course
probability theory
Probability theory is also very important for machine learning , It's an important tool . If the machine learning algorithm is input , The output is treated as a random variable / vector , Then we can use probability theory to model the problem . One advantage of using probability theory is that uncertainty can be modeled , This is very necessary for some problems . in addition , It can also mine the probability dependence between variables , Realizing causal reasoning . Probability theory for some stochastic algorithms - Such as Monte Carlo algorithm , genetic algorithm , And random number generation algorithm - Including basic random number generation , And the sampling algorithm provides a theoretical basis and guidance . last , Probability theory is also information theory , The pilot course of stochastic process .
Probability theory and mathematical statistics teaching materials for engineering , Most of the probabilistic knowledge required for machine learning has been described , Except for the following knowledge points ：
1. Conditional independence
2. Jensen Inequality
3. Some probability distributions , Such as multinomial distribution , Laplace distribution ,t Distribution, etc
4. Probability distribution transformation
5. Multidimensional normal distribution
6. Transformation of multidimensional probability distribution
7. Some parameter estimation methods , Including maximum a posteriori probability estimation , Bayesian estimation, etc
8. Random number generation algorithm , Including inverse transform sampling , Reject sampling and other algorithms
optimization method
Optimization methods play a central role in machine learning , Unfortunately, many readers have not systematically studied this course , Including linear programming , Convex optimization , nonlinear programming . In general numerical analysis course , Only a small part of the optimization method is described . Almost all machine learning algorithms come down to solving optimization problems , Then the model parameters are determined , Or get the prediction results directly . The typical representative of the former is supervised learning , The parameters of the model are determined by minimizing the loss function or optimizing other types of objective functions ; The typical representative of the latter is data dimension reduction algorithm , The result of dimension reduction is determined by optimizing some objective function , Such as principal component analysis .
information theory
Information theory is the extension of probability theory , It is usually used to construct objective function in machine learning and deep learning , As well as the theoretical analysis and proof of the algorithm . This is also a course that many readers have not learned .
In machine learning, especially in deep learning , The knowledge of information theory can be seen everywhere ：
1. In the training process of decision tree, entropy should be used as an index
2. Cross entropy is often used in deep learning ,KL divergence ,JS divergence , Mutual information and other concepts
3. The derivation of variational inference needs to be based on KL Based on divergence
4. Distance metric learning , Manifold dimension reduction algorithm also needs the knowledge of information theory
random process
Stochastic process is also an extension of probability theory , This is also a course that most readers haven't learned . In machine learning , Stochastic process is used in probability graph model , Reinforcement learning , And Bayesian optimization method . Don't understand Markov process , You will be right MCMC Sampling algorithm confused .
graph theory
Graph theory seems to have been studied only in computer related majors , And it's incomplete , For example, spectrum theory . In machine learning , Probabilistic graph model is a typical graph structure . Both manifold dimension reduction algorithm and spectral clustering algorithm use spectral graph theory . Computational graph is a typical representation of graph , Graph neural network as a new deep learning model , It is also closely related to graph theory . Therefore, it is necessary to supplement the knowledge of graph theory .
Are you happy to read this , This Bible level deep learning book can finally continue to learn .
Deep learning [deep learning]
《 Deep learning 》 By three world-renowned experts Ian Goodfellow,Yoshua Bengio and Aaron
Courville compose , It is a classic textbook in the field of deep learning . The contents of the book include 3 Three parts ： The third 1 This part introduces the basic mathematical tools and the concept of machine learning , They are the preparatory knowledge for deep learning ; The third 2 Part of the system in-depth explanation of today's mature deep learning methods and technologies ; The third 3 Some forward-looking directions and ideas are discussed , They are recognized as the future research focus of deep learning .
《 Deep learning 》 Suitable for all kinds of readers , Including related professional college students or graduate students , And no machine learning or statistical background , But want to quickly add deep learning knowledge , So as to be applied in the actual product or platform .
Mathematics of machine learning
The book consists of three parts 8 Chapter composition , It covers machine learning accurately and systematically in a very small space , Deep learning , Mathematics knowledge necessary for reinforcement learning , The content basically covers this 3 Most of the mathematical knowledge required for this course . For the undergraduate stage of science and Engineering “ Advanced mathematics / Calculus ”,“ linear algebra ”,“ Probability theory and mathematical statistics ” It was precisely supplemented . The main contents of each chapter are introduced below .
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